Supercurrent in the quantum Hall regime.
Amet, F; Ke, C T; Borzenets, I V; Wang, J; Watanabe, K; Taniguchi, T; Deacon, R S; Yamamoto, M; Bomze, Y; Tarucha, S; Finkelstein, G
2016-05-20
A promising route for creating topological states and excitations is to combine superconductivity and the quantum Hall (QH) effect. Despite this potential, signatures of superconductivity in the QH regime remain scarce, and a superconducting current through a QH weak link has been challenging to observe. We demonstrate the existence of a distinct supercurrent mechanism in encapsulated graphene samples contacted by superconducting electrodes, in magnetic fields as high as 2 tesla. The observation of a supercurrent in the QH regime marks an important step in the quest for exotic topological excitations, such as Majorana fermions and parafermions, which may find applications in fault-tolerant quantum computing.
Supercurrent in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Amet, F.; Ke, C. T.; Borzenets, I. V.; Wang, J.; Watanabe, K.; Taniguchi, T.; Deacon, R. S.; Yamamoto, M.; Bomze, Y.; Tarucha, S.; Finkelstein, G.
2016-05-01
A promising route for creating topological states and excitations is to combine superconductivity and the quantum Hall (QH) effect. Despite this potential, signatures of superconductivity in the QH regime remain scarce, and a superconducting current through a QH weak link has been challenging to observe. We demonstrate the existence of a distinct supercurrent mechanism in encapsulated graphene samples contacted by superconducting electrodes, in magnetic fields as high as 2 tesla. The observation of a supercurrent in the QH regime marks an important step in the quest for exotic topological excitations, such as Majorana fermions and parafermions, which may find applications in fault-tolerant quantum computing.
Supercurrent in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Wei, Ming-Tso; Amet, François; Ke, Chung-Ting; Borzenets, Ivan; Wang, Jiyingmei; Watanabe, Keji; Taniguchi, Takashi; Deacon, Russell; Yamamoto, Michihisa; Bomze, Yuriy; Tarucha, Seigo; Finkelstein, Gleb
Combining superconductivity and the quantum Hall (QH) effect is a promising route for creating new types of topological excitations. Despite this potential, signatures of superconductivity in the quantum Hall regime remain scarce, and a superconducting current through a QH weak link has so far eluded experimental observation. Here we demonstrate the existence of a novel type of Josephson coupling through a QH region at magnetic fields as high as 2 Tesla. The supercurrent is mediated by states encompassing QH edge channels, which are flowing on opposite sides of the sample. The edges are coupled together by the hybrid electron-hole modes at the interfaces between the QH region and the superconducting contacts. These chiral modes, which share some features with Majorana modes, are formed when electron and hole edge states are mixed by the superconductor.
Supercurrent in the quantum Hall regime, part II
NASA Astrophysics Data System (ADS)
Amet, Francois; Ke, Chung Ting; Borzenets, Ivan; Wang, Jiyingmei; Watanabe, Kenji; Taniguchi, Takashi; Deacon, Russel; Yamamoto, Michihisa; Bomze, Yuriy; Tarucha, Seigo; Finkelstein, Gleb
A novel promising route for creating topological states and excitations is to combine superconductivity and the quantum Hall effect. Despite this potential, signatures of superconductivity in the quantum Hall regime remain scarce, and a superconducting current through a Landau-quantized two-dimensional electron gas has so far eluded experimental observation. High-mobility graphene/BN heterostructures exhibit the quantum Hall effect at relatively low field and are therefore particularly suitable to study the fate of the Josephson effect in that regime. Here, we report the observation of a superconducting current through graphene at fields as high as 2 Tesla. In that regime, the normal-state resistance is quantized but pockets of superconductivity still persist at small current bias. We will describe their bias and temperature dependence. Magnetic field interference patterns in the supercurrent inform on possible mechanisms mediating this supercurrent.
Topologically induced fractional Hall steps in the integer quantum Hall regime of MoS 2.
Islam, S K Firoz; Benjamin, Colin
2016-09-23
The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. In particular, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivitity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms.
Topologically induced fractional Hall steps in the integer quantum Hall regime of MoS 2
NASA Astrophysics Data System (ADS)
Firoz Islam, SK; Benjamin, Colin
2016-09-01
The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. In particular, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivitity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms.
Optically Pumped NMR in the Fractional Quantum Hall Regime
NASA Astrophysics Data System (ADS)
Barrett, S. E.; Kuzma, N. N.; Khandelwal, P.; Pfeiffer, L. N.; West, K. W.
1998-03-01
Optically Pumped Nuclear Magnetic Resonance measurements are a local probe of the electron spin degree of freedom in n-type GaAs quantum wells.(S.E.Barrett et al.,Phys.Rev.Lett.72),1368(1994).^, footnote S. E. Barrett et al., Phys. Rev. Lett. 74, 5112 (1995)^, footnote R. Tycko et al., Science 268, 1460 (1995). We have recently shown that this OPNMR technique can be carried out in fields up to B=12 Tesla and temperatures down to T=0.3 K, making this technique a viable new probe of the Fractional Quantum Hall regime. We will discuss our latest measurements in these conditions, and compare our new results with previous measurements and the existing theoretical models for this regime.
Anisotropic electronic states in the fractional quantum Hall regime
NASA Astrophysics Data System (ADS)
Ciftja, Orion
2017-05-01
Recent experiments indicate the presence of new anisotropic fractional quantum Hall states at regimes not anticipated before. These experiments raise many fundamental questions regarding the inner nature of the electronic system that leads to such anisotropic states. Interplay between electron mass anisotropy and electron-electron correlation effects in a magnetic field can create a rich variety of possibilities. Several anisotropic electronic states ranging from anisotropic quantum Hall liquids to anisotropic Wigner solids may stabilize due to such effects. The electron mass anisotropy in a two-dimensional electron gas effectively leads to an anisotropic Coulomb interaction potential between electrons. An anisotropic interaction potential may strongly influence the stability of various quantum phases that are close in energy since the overall stability of an electronic system is very sensitive to local order. As a result there is a possibility that various anisotropic electronic phases may emerge even in the lowest Landau level in regimes where one would not expect them. In this work we study the state with filling factor 1/6 in the lowest Landau level, a state which is very close to the critical filling factor where the liquid-solid transition takes place. We investigate whether an anisotropic Coulomb interaction potential is able to stabilize an anisotropic electronic liquid state at this filling factor. We describe such an anisotropic state by means of a liquid crystalline wave function with broken rotational symmetry which can be adiabatically connected to the actual wave function for the corresponding isotropic phase. We perform quantum Monte Carlo simulations in a disk geometry to study the properties of the anisotropic electronic liquid state under consideration. The findings indicate stability of liquid crystalline order in presence of an anisotropic Coulomb interaction potential. The results are consistent with the existence of an anisotropic electronic
Optically Pumped Nuclear Magnetic Resonance in the Quantum Hall Regimes
NASA Astrophysics Data System (ADS)
Barrett, S. E.; Khandelwal, P.; Kuzma, N. N.; Pfeiffer, L. N.; West, K. W.
1997-03-01
Optical pumping enables the direct detection of the nuclear magnetic resonance signal of ^71Ga nuclei located in an electron doped GaAs quantum well.footnote S. E. Barrett et al., Phys. Rev. Lett. 72, 1368 (1994) Using this technique, measurements of the Knight shift (K_S)footnote S. E. Barrett et al., Phys. Rev. Lett. 74, 5112 (1995) and spin-lattice relaxation time (T_1)footnote R. Tycko et al., Science 268, 1460 (1995) have been carried out in the Quantum Hall regimes. This talk will focus on our latest measurements of KS and T1 near Landau level filling ν=1, which extend our earlier results to higher magnetic fields (B=12 Tesla) and lower temperatures (T < 1 Kelvin). We will compare these results to the theoretical predictionsfootnote S. L. Sondhi et al., Phys. Rev. B 47, 16419 (1993); H. A. Fertig et al., Phys. Rev. B 50, 11018 (1994) that the charged excitations of the ν = 1 ground state are novel spin textures called skyrmions. The current status of this picture will be discussed.
Optically Pumped Nuclear Magnetic Resonance in the Quantum Hall Regimes
NASA Astrophysics Data System (ADS)
Barrett, Sean E.
1998-03-01
Optical pumping enables the direct detection of the nuclear magnetic resonance signal of ^71Ga nuclei located in an electron doped GaAs quantum well.footnote S. E. Barrett et al., Phys. Rev. Lett. 72, 1368 (1994) This OPNMR technique was previously used to measure the Knight shift (K_S)footnote S. E. Barrett et al., Phys. Rev. Lett. 74, 5112 (1995) and spin-lattice relaxation time (T_1)footnote R. Tycko et al., Science 268, 1460 (1995) near Landau level filling ν=1, which provided the first experimental support for the theoretical predictionsfootnote S. L. Sondhi et al., Phys. Rev. B 47, 16419 (1993); H. A. Fertig et al., Phys. Rev. B 50, 11018 (1994) that the charged excitations of the ν = 1 ground state are novel spin textures called skyrmions. We have recently demonstrated that OPNMR is possible in fields up to B=12 Tesla, and temperatures down to T= 0.3 K, making it a viable new probe of the Fractional Quantum Hall Regime. In this talk we will present our latest OPNMR measurements near Landau level filling ν=1/3, which include the first direct measurement of the electron spin polarization at ν=1/3. The spin polarization drops as the filling factor is varied away from ν=1/3, indicating that the quasiparticles and quasiholes are not fully spin-polarized. We will also show how the NMR lineshape away from ν=1/3 changes dramatically at low temperatures, which is due to slowing of the electron dynamics, and a reduction in the motional narrowing of the NMR line. The current understanding of these results will be discussed.
Nonlinear transport of graphene in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Tian, Shibing; Wang, Pengjie; Liu, Xin; Zhu, Junbo; Fu, Hailong; Taniguchi, Takashi; Watanabe, Kenji; Chen, Jian-Hao; Lin, Xi
2017-03-01
We have studied the breakdown of the integer quantum Hall (QH) effect with fully broken symmetry, in an ultra-high mobility graphene device sandwiched between two single crystal hexagonal boron nitride substrates. The evolution and stabilities of the QH states are studied quantitatively through the nonlinear transport with dc Hall voltage bias. The mechanism of the QH breakdown in graphene and the movement of the Fermi energy with the electrical Hall field are discussed. This is the first study in which the stabilities of fully symmetry broken QH states are probed all together. Our results raise the possibility that the ν = ±6 states might be a better target for the quantum resistance standard.
Magneto-transport of graphene and quantum phase transitions in the quantum Hall regime.
Amado, Mario; Diez, Enrique; Rossella, Francesco; Bellani, Vittorio; López-Romero, David; Maude, Duncan K
2012-08-01
In this paper we show the electronic transport and the quantum phase transitions that characterize the quantum Hall regime in graphene placed on SiO(2) substrates at magnetic fields up to 28 T and temperatures down to 4 K. The analysis of the temperature dependence of the Hall and longitudinal resistivity reveals intriguing non-universalities of the critical exponents of the plateau-insulator transition. These exponents depend on the type of disorder that governs the electrical transport and its characterization is important for the design and fabrication of novel graphene nano-devices.
Edge mixing dynamics in graphene p-n junctions in the quantum Hall regime.
Matsuo, Sadashige; Takeshita, Shunpei; Tanaka, Takahiro; Nakaharai, Shu; Tsukagoshi, Kazuhito; Moriyama, Takahiro; Ono, Teruo; Kobayashi, Kensuke
2015-09-04
Massless Dirac electron systems such as graphene exhibit a distinct half-integer quantum Hall effect, and in the bipolar transport regime co-propagating edge states along the p-n junction are realized. Additionally, these edge states are uniformly mixed at the junction, which makes it a unique structure to partition electrons in these edge states. Although many experimental works have addressed this issue, the microscopic dynamics of electron partition in this peculiar structure remains unclear. Here we performed shot-noise measurements on the junction in the quantum Hall regime as well as at zero magnetic field. We found that, in sharp contrast with the zero-field case, the shot noise in the quantum Hall regime is finite in the bipolar regime, but is strongly suppressed in the unipolar regime. Our observation is consistent with the theoretical prediction and gives microscopic evidence that the edge states are uniquely mixed along the p-n junction.
Edge mixing dynamics in graphene p–n junctions in the quantum Hall regime
Matsuo, Sadashige; Takeshita, Shunpei; Tanaka, Takahiro; Nakaharai, Shu; Tsukagoshi, Kazuhito; Moriyama, Takahiro; Ono, Teruo; Kobayashi, Kensuke
2015-01-01
Massless Dirac electron systems such as graphene exhibit a distinct half-integer quantum Hall effect, and in the bipolar transport regime co-propagating edge states along the p–n junction are realized. Additionally, these edge states are uniformly mixed at the junction, which makes it a unique structure to partition electrons in these edge states. Although many experimental works have addressed this issue, the microscopic dynamics of electron partition in this peculiar structure remains unclear. Here we performed shot-noise measurements on the junction in the quantum Hall regime as well as at zero magnetic field. We found that, in sharp contrast with the zero-field case, the shot noise in the quantum Hall regime is finite in the bipolar regime, but is strongly suppressed in the unipolar regime. Our observation is consistent with the theoretical prediction and gives microscopic evidence that the edge states are uniquely mixed along the p–n junction. PMID:26337445
Edge mixing dynamics in graphene p-n junctions in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Matsuo, Sadashige; Takeshita, Shunpei; Tanaka, Takahiro; Nakaharai, Shu; Tsukagoshi, Kazuhito; Moriyama, Takahiro; Ono, Teruo; Kobayashi, Kensuke
2015-09-01
Massless Dirac electron systems such as graphene exhibit a distinct half-integer quantum Hall effect, and in the bipolar transport regime co-propagating edge states along the p-n junction are realized. Additionally, these edge states are uniformly mixed at the junction, which makes it a unique structure to partition electrons in these edge states. Although many experimental works have addressed this issue, the microscopic dynamics of electron partition in this peculiar structure remains unclear. Here we performed shot-noise measurements on the junction in the quantum Hall regime as well as at zero magnetic field. We found that, in sharp contrast with the zero-field case, the shot noise in the quantum Hall regime is finite in the bipolar regime, but is strongly suppressed in the unipolar regime. Our observation is consistent with the theoretical prediction and gives microscopic evidence that the edge states are uniquely mixed along the p-n junction.
Imaging currents in HgTe quantum wells in the quantum spin Hall regime
Nowack, Katja C.; Spanton, Eric M.; Baenninger, Matthias; König, Markus; Kirtley, John R.; Kalisky, Beena; Ames, C.; Leubner, Philipp; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W.; Goldhaber-Gordon, David; Moler, Kathryn A.
2013-06-16
The quantum spin Hall (QSH) state is a state of matter characterized by a non-trivial topology of its band structure, and associated conducting edge channels. The QSH state was predicted and experimentally demonstrated to be realized in HgTe quantum wells. The existence of the edge channels has been inferred from local and non-local transport measurements in sufficiently small devices. Here we directly confirm the existence of the edge channels by imaging the magnetic fields produced by current flowing in large Hall bars made from HgTe quantum wells. These images distinguish between current that passes through each edge and the bulk. On tuning the bulk conductivity by gating or raising the temperature, we observe a regime in which the edge channels clearly coexist with the conducting bulk, providing input to the question of how ballistic transport may be limited in the edge channels. Our results represent a versatile method for characterization of new QSH materials systems.
Minimal Excitations in the Fractional Quantum Hall Regime
NASA Astrophysics Data System (ADS)
Rech, J.; Ferraro, D.; Jonckheere, T.; Vannucci, L.; Sassetti, M.; Martin, T.
2017-02-01
We study the minimal excitations of fractional quantum Hall edges, extending the notion of levitons to interacting systems. Using both perturbative and exact calculations, we show that they arise in response to a Lorentzian potential with quantized flux. They carry an integer charge, thus involving several Laughlin quasiparticles, and leave a Poissonian signature in a Hanbury Brown-Twiss partition noise measurement at low transparency. This makes them readily accessible experimentally, ultimately offering the opportunity to study real-time transport of Abelian and non-Abelian excitations.
NASA Astrophysics Data System (ADS)
Leconte, Nicolas; Ortmann, Frank; Cresti, Alessandro; Roche, Stephan
2016-03-01
We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy band gap and Landau-level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large-size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size, and magnetic length, we elucidate the origin of anomalous quantum Hall features as magnetic-field-dependent impurity states, which percolate at some critical energies. These findings shed light on unidentified states and quantum-transport anomalies reported experimentally.
Crossover to the anomalous quantum regime in the extrinsic spin Hall effect of graphene
NASA Astrophysics Data System (ADS)
Milletarı, Mirco; Ferreira, Aires
2016-11-01
Recent reports of spin-orbit coupling enhancement in chemically modified graphene have opened doors to studies of the spin Hall effect with massless chiral fermions. Here, we theoretically investigate the interaction and impurity density dependence of the extrinsic spin Hall effect in spin-orbit coupled graphene. We present a nonperturbative quantum diagrammatic calculation of the spin Hall response function in the strong-coupling regime that incorporates skew scattering and anomalous impurity density-independent contributions on equal footing. The spin Hall conductivity dependence on Fermi energy and electron-impurity interaction strength reveals the existence of experimentally accessible regions where anomalous quantum processes dominate. Our findings suggest that spin-orbit-coupled graphene is an ideal model system for probing the competition between semiclassical and bona fide quantum scattering mechanisms underlying the spin Hall effect.
Variable-Range Hopping Conductivity in Quantum Hall Regime for HgTe-Based Heterostructure
NASA Astrophysics Data System (ADS)
Arapov, Yu. G.; Gudina, S. V.; Neverov, V. N.; Podgornykh, S. M.; Popov, M. R.; Harus, G. I.; Shelushinina, N. G.; Yakunin, M. V.; Dvoretsky, S. A.; Mikhailov, N. N.
2016-12-01
We have measured the longitudinal and Hall resistivities in the quantum Hall regime at magnetic fields B up to 9 T and temperatures T =(2.9div 50) K for the HgCdTe/HgTe/HgCdTe heterostructure with a wide HgTe quantum well. The temperature-induced transport at the resistivity minima corresponding to the quantum Hall plateaus has been studied within the concept of hopping conduction in a strongly localized electron system. An analysis of the variable-range hopping conductivity in the regions of the first and second quantum Hall plateaus provided an opportunity to determine the value and the magnetic-field dependence of the localization length with the experimental estimation of the critical indices.
Lineshape of Resonant Tunneling Peaks in Fractional Quantum Hall Regime.
NASA Astrophysics Data System (ADS)
Maasilta, Ilari J.; Goldman, V. J.
1996-03-01
Recently an experiment that measures the tunneling conductance between two fractional quantum Hall edges in a quantum antidot geometry was performed(V.J. Goldman and B. Su, Science 267), 1010 (1995).. We present measurements of the lineshape of these resonant tunneling peaks at ν=1/3 at several temperatures for 13 mK <= T < 100 mK. This subject was considered within the theories of one dimensional Luttinger liquids(X.G. Wen, Int. J. Mod. Phys. B6), 1711 (1992).(C.L. Kane and M.P.A. Fisher, Phys. Rev. Lett. 68), 1220 (1992).. Our analysis shows that, in an experiment at a given T, it is extremely difficult to distinguish between the recently calculated(K. Moon et al.), Phys. Rev. Lett. 71, 4381 (1993); P. Fendley, A.W.W. Ludwig and H. Saleur, Phys. Rev. Lett. 74, 3005 (1995). universal Luttinger liquid resonance lineshape and a regular thermally broadened Fermi liquid peak. Instead, the temperature dependence of the widths of the resonances can be analyzed, since the widths are predicted to scale as T^2/3 for ν=1/3 in the Luttinger case as opposed to T in the Fermi liquid.
Supercurrent in the quantum Hall regime: part I
NASA Astrophysics Data System (ADS)
Ke, Chung-Ting; Amet, Francois; Borzenets, Ivan; Wang, Jiyingmei; Watanabe, Keji; Taniguchi, Takashi; Deacon, Russell; Yamamoto, Michihisa; Bomze, Yuriy; Tarucha, Seigo; Finkelstein, Gleb
The remarkable electronic quality of graphene/boron nitride heterostructures makes them an ideal medium to study induced superconductivity. Our Josephson junctions are made of encapsulated graphene demonstrate ballistic superconducting transport at the micron scale. In the hole-doped regime, a Fabry-Perot resonator is formed by PN junctions close to superconducting contacts, which causes quantum interference of the critical current. We study variations of the Fraunhofer pattern (I_C vs. B) thought the gate voltage range. At higher magnetic fields, superconducting transport across the junctions becomes profoundly non-periodic. Despite demonstrating strong fluctuations as a function of density and magnetic field, we find that supercurrent persists in a wide range of parameters.
Electron Interferometry in the Quantum Hall Regime: Aharonov-Bohm Effect of Interacting Electrons
Lin, P.V.; Camino, F.; Goldman, V.J.
2009-09-01
An apparent h/fe Aharonov-Bohm flux period, where f is an integer, has been reported in coherent quantum Hall devices. Such subperiod is not expected for noninteracting electrons and thus is thought to result from interelectron Coulomb interaction. Here we report experiments in a Fabry-Perot interferometer comprised of two wide constrictions enclosing an electron island. By carefully tuning the constriction front gates, we find a regime where interference oscillations with period h/2e persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling. In a large quantum Hall sample, a transition between integer plateaus occurs near half-filling, where the bulk of the sample becomes delocalized and thus dissipative bulk current flows between the counterpropagating edges ('backscattering'). In a quantum Hall constriction, where conductance is due to electron tunneling, a transition between forward and backscattering is expected near the half-filling. In our experiment, neither period nor amplitude of the oscillations show a discontinuity at half-filling, indicating that only one interference path exists throughout the transition. We also present experiments and an analysis of the front-gate dependence of the phase of the oscillations. The results point to a single physical mechanism of the observed conductance oscillations: Aharonov-Bohm interference of interacting electrons in quantum Hall regime.
Selective equilibration among the current-carrying states in the quantum Hall regime
NASA Technical Reports Server (NTRS)
Alphenaar, B. W.; Mceuen, P. L.; Wheeler, R. G.; Sacks, R. N.
1990-01-01
The Hall resistance of a two-dimensional electron gas is measured with gated probes to determine the extent of equilibration among the N current-carrying states in the quantum Hall regime. After traveling macroscopic distances, current injected into the first state is equilibrated among the N - 1 lowest states but equilibration into the highest state varies strongly across the Hall plateau. This is attributed to a change in the Nth state from being localized within a magnetic length of the edge to substantially extending into the sample.
Selective equilibration among the current-carrying states in the quantum Hall regime
NASA Technical Reports Server (NTRS)
Alphenaar, B. W.; Mceuen, P. L.; Wheeler, R. G.; Sacks, R. N.
1990-01-01
The Hall resistance of a two-dimensional electron gas is measured with gated probes to determine the extent of equilibration among the N current-carrying states in the quantum Hall regime. After traveling macroscopic distances, current injected into the first state is equilibrated among the N - 1 lowest states but equilibration into the highest state varies strongly across the Hall plateau. This is attributed to a change in the Nth state from being localized within a magnetic length of the edge to substantially extending into the sample.
Scanned potential microscopy of edge and bulk currents in the quantum Hall regime
McCormick, K.L.; Woodside, M.T.; Huang, M.; Wu, M.; McEuen, P.L. |; Duruoz, C.; Harris, J.S. , Jr.
1999-02-01
Using an atomic force microscope as a local voltmeter, we measure the Hall voltage profile in a two-dimensional electron gas in the quantum Hall (QH) regime. We observe a linear profile in the bulk of the sample in the transition regions between QH plateaus and a distinctly nonlinear profile on the plateaus. In addition, localized voltage drops are observed at the sample edges in the transition regions. We interpret these results in terms of theories of edge and bulk current in the QH regime. {copyright} {ital 1999} {ital The American Physical Society}
Accessing the quantum Hall regime in cold atom traps using circularly polarized light
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Yan, Bin; Greene, Chris H.
2016-05-01
There has been considerable interest in designing cold atom experiments to explore the quantum Hall effect with the extreme control allowed in such trapped atom systems. Many theoretical proposals and experimental attempts have been made in the effort to construct a cold atom fractional quantum Hall experiment, but so far, the fractional quantum Hall regime has proven difficult to achieve in experimental setups. One method for reaching the quantum Hall effect consists of rapidly rotating a cold atom system in a harmonic trap to near the centrifugal limit, where the system's Hamiltonian matches the two-dimensional magnetic field Hamiltonian. This condition could be reached in a few-body system through a scheme which increases the angular momentum of the particles in the trap through precision photon excitations. According to the hyperspherical framework from few-body theory, when particle interactions break the harmonic energy spectrum degeneracy, it becomes possible for circularly polarized light to excite the system selectively into the high angular momentum states required for the quantum Hall effect. We will discuss possible experimental systems where this technique could be applicable and challenges that these systems may face.
Coherent nonlinear optical response of graphene in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Avetissian, H. K.; Mkrtchian, G. F.
2016-07-01
We study the nonlinear optical response of graphene in the quantum Hall regime to an intense laser pulse. In particular, we consider the harmonic generation process. We demonstrate that the generalized magneto-optical conductivity of graphene on the harmonics of a strong pump laser radiation has a characteristic Hall plateau feature. The plateau heights depend on the laser intensity and broadening of the Landau levels so that they are not quantized exactly. This nonlinear effect remains robust against the significant broadening of the Landau levels. We predict realization of an experiment through the observation of the third-harmonic signal and nonlinear Faraday effect, which are within the experimental feasibility.
Charge metastability and hysteresis in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Pollanen, J.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2016-12-01
We report simultaneous quasi-dc magnetotransport and high-frequency surface acoustic wave measurements on bilayer two-dimensional electron systems in GaAs. Near strong integer quantized Hall states, a strong magnetic-field-sweep hysteresis in the velocity of the acoustic waves is observed at low temperatures. This hysteresis indicates the presence of a metastable state with anomalously high conductivity in the interior of the sample. This nonequilibrium state is not revealed by conventional low-frequency transport measurements which are dominated by dissipationless transport at the edge of the two-dimensional system. We find that a field-cooling technique allows the equilibrium charge configuration within the interior of the sample to be established. A simple model for this behavior is discussed.
NASA Astrophysics Data System (ADS)
Lonchakov, A. T.; Okulov, V. I.; Pamyatnykh, E. A.; Bobin, S. B.; Deryushkin, V. V.; Govorkova, T. E.; Neverov, V. N.; Paranchich, L. D.
2017-10-01
The given report is devoted to the study of anomalous Hall resistance of donor electron system of hybridized states of transition element impurities of low concentration in quantum oscillation regime. There presented theoretical description of predicted specific behaviors on the base of the ideas about thermodynamic anomalous Hall effect. In experiments on mercury selenide crystals with cobalt impurities of low concentration one revealed the quantum oscillations of anomalous contribution to the Hall resistance corresponding to the developed concepts.
Giant Fano factor and bistability in a Corbino disk in the quantum Hall effect breakdown regime.
Hata, Tokuro; Arakawa, Tomonori; Chida, Kensaku; Matsuo, Sadashige; Kobayashi, Kensuke
2016-02-10
We performed noise measurements for a Corbino disk in the quantum Hall effect breakdown regime. We investigated two Corbino-disk-type devices with different sizes and observed that the Fano factor increases when the length between the contacts doubles. This observation is consistent with the avalanche picture suggested by the bootstrap electron heating model. The temperature dependence of the Fano factor indicates that the avalanche effect becomes more prominent as temperature decreases. Moreover, in the highly nonlinear regime, negative differential resistance and temporal oscillation due to bistability are found. A possible interpretation of this result is that Zener tunneling of electrons between Landau levels occurs.
Giant Fano factor and bistability in a Corbino disk in the quantum Hall effect breakdown regime
NASA Astrophysics Data System (ADS)
Hata, Tokuro; Arakawa, Tomonori; Chida, Kensaku; Matsuo, Sadashige; Kobayashi, Kensuke
2016-02-01
We performed noise measurements for a Corbino disk in the quantum Hall effect breakdown regime. We investigated two Corbino-disk-type devices with different sizes and observed that the Fano factor increases when the length between the contacts doubles. This observation is consistent with the avalanche picture suggested by the bootstrap electron heating model. The temperature dependence of the Fano factor indicates that the avalanche effect becomes more prominent as temperature decreases. Moreover, in the highly nonlinear regime, negative differential resistance and temporal oscillation due to bistability are found. A possible interpretation of this result is that Zener tunneling of electrons between Landau levels occurs.
Field effect in the quantum Hall regime of a high mobility graphene wire
Barraud, C. E-mail: clement.barraud@univ-paris-diderot.fr; Choi, T.; Ihn, T.; Ensslin, K.; Butti, P.; Shorubalko, I.; Taniguchi, T.; Watanabe, K.
2014-08-21
In graphene-based electronic devices like in transistors, the field effect applied thanks to a gate electrode allows tuning the charge density in the graphene layer and passing continuously from the electron to the hole doped regime across the Dirac point. Homogeneous doping is crucial to understand electrical measurements and for the operation of future graphene-based electronic devices. However, recently theoretical and experimental studies highlighted the role of the electrostatic edge due to fringing electrostatic field lines at the graphene edges [P. Silvestrov and K. Efetov, Phys. Rev. B 77, 155436 (2008); F. T. Vasko and I. V. Zozoulenko, Appl. Phys. Lett. 97, 092115 (2010)]. This effect originates from the particular geometric design of the samples. A direct consequence is a charge accumulation at the graphene edges giving a value for the density, which deviates from the simple picture of a plate capacitor and also varies along the width of the graphene sample. Entering the quantum Hall regime would, in principle, allow probing this accumulation thanks to the extreme sensitivity of this quantum effect to charge density and the charge distribution. Moreover, the presence of an additional and counter-propagating edge channel has been predicted [P. Silvestrov and K. Efetov, Phys. Rev. B 77, 155436 (2008)] giving a fundamental aspect to this technological issue. In this article, we investigate this effect by tuning a high mobility graphene wire into the quantum Hall regime in which charge carriers probe the electrostatic potential at high magnetic field close to the edges. We observe a slight deviation to the linear shift of the quantum Hall plateaus with magnetic field and we study its evolution for different filling factors, which correspond to different probed regions in real space. We discuss the possible origins of this effect including an increase of the charge density towards the edges.
AC-magnetotransport of a 2DEG in the quantum Hall regime
Hernández, C.; Chaubet, C.
2014-05-15
In this paper we present an ac-magneto-transport study of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime, for frequencies in the range [100Hz, 1MHz]. We present a new approach to understand admittance measurements based in the Landauer-Buttiker formalism for QHE edge channels and taking into account the capacitance and the topology of the cables connected to the contacts used in the measurements. Our model predicts an universal behavior with the a-dimensional parameter RCω where R is the 2 wires resistance of the 2DEG, C the capacitance cables and the angular frequency, in agreement with experiments.
A quantitative examination of the collapse of spin splitting in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Pan, W.; Baldwin, K. W.; West, K. W.; Pfeiffer, L. N.; Tsui, D. C.
2012-02-01
There is a great deal of current interest in understanding electron spin physics in semiconductors for potential quantum computation applications. The quantum Hall effect in the two-dimensional electron system (2DES) has proved to be a unique system in this avenue due to a tunability in the difference of spin population and thus the strength of exchange interaction provided by the formation of Landau levels. In this talk, we want to present our experimental results to quantitatively examine the theoretical model of spin splitting collapse in the quantum Hall regime [by Fogler and Shklovskii, Phys. Rev. B 52, 17366 (1995)] at fixed magnetic fields as a function of electron density in a high quality heterojunction insulated-gate field effect transistor. In the density range between n = 2x10^10 and 2x10^11 cm-2, the Landau level number N follows a power-law dependence on the critical electron density nc, where the spin splitting collapses, and N=11.47xnc^0.64±0.01. This power law dependence is in good agreement with the theoretical prediction in the low density regime.
Cooling of chiral heat transport in the quantum Hall effect regime of graphene
NASA Astrophysics Data System (ADS)
Slizovskiy, Sergey; Fal'ko, Vladimir
2017-08-01
In the quantum Hall effect (QHE) regime, heat is carried by electrons in the edge states of Landau levels. Here, we study cooling of hot electrons propagating along the edge of graphene at the filling factor ν =±2 , mediated by acoustic phonons. We determine the temperature profile extended from a hot spot, where the Hall current is injected into graphene from a metallic contact, taking into account specifics of boundary conditions for lattice displacements in graphene in a van der Waals heterostructure with an insulating substrate. Our calculations, performed using generic boundary conditions for Dirac electrons, show that emission of phonons can explain a short cooling length observed in graphene-based QHE devices by Nahm, Hwang, and Lee [Phys. Rev. Lett. 110, 226801 (2013), 10.1103/PhysRevLett.110.226801].
Arapov, Yu. G.; Gudina, S. V.; Neverov, V. N.; Podgornykh, S. M.; Popov, M. R. Harus, G. I.; Shelushinina, N. G.; Yakunin, M. V.; Mikhailov, N. N.; Dvoretsky, S. A.
2015-12-15
The longitudinal and Hall magnetoresistances of HgTe/HgCdTe heterostructures with an inverted energy spectrum (the HgTe quantum well width is d = 20.3 nm) are measured in the quantum-Hall-effect regime at T = 2–50 K in magnetic fields up to B = 9 T. Analysis of the temperature dependences of conductivity in the transition region between the first and second plateaus of the quantum Hall effect shows the feasibility of the scaling regime for a plateau–plateau quantum phase transition in 2D-structures on the basis of mercury telluride.
Quantitative examination of the collapse of spin splitting in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Pan, W.; Baldwin, K. W.; West, K. W.; Pfeiffer, L. N.; Tsui, D. C.
2011-10-01
We have quantitatively tested the theoretical model on the collapse of spin slitting in the quantum Hall effect regime proposed by Fogler and Shklovskii [Phys. Rev. BPLRBAQ0556-280510.1103/PhysRevB.52.17366 52, 17366 (1995)] in a high-mobility two-dimensional electron system (2DES) realized in a heterojunction insulated-gate field-effect transistor. In the 2DES density range between n = 2 × 1010 and 2 × 1011 cm-2, the Landau level number N displays a power-law dependence on the critical electron density nc where the spin splitting collapses and N = 11.47 × nc0.64±0.01 (nc is in units of 1011 cm-2). This power-law dependence is in good agreement with the theoretical prediction in the low-density regime.
Ultracold Bose gases: From the Gross-Pitaevskii to the fractional quantum Hall regime
NASA Astrophysics Data System (ADS)
Bhongale, Satyan Gopal
Ultra-cold Bose gases present an ideal environment for the study of many-body physics. These systems can be prepared under various experimental conditions with precise control. Techniques like Feshbach resonances allow us to dynamically tune the inter atomic interaction, from strongly attractive to a strongly repulsive one. In the first part of the thesis, we study the weakly interacting Bose gas in connection with the dynamics of an atom laser. Here we propose a possible optical pumping model for loading the reservoir of a continuous wave atom laser. The finite temperature effects like phase diffusion require a thorough understanding of the kinetic regime of the dilute Bose gas. In this respect, we develop a non-Markovian quantum kinetic theory and thereby show the emergence of different time scales for correlation and subsequent relaxation to an equilibrium states. Using numerical simulations, we also predict the damping rates and frequencies of collective modes. In the second part, we study the strongly correlated regime where the interaction energy is greater than any other (single particle) energy scale of the problem. Here, in the presence of a Feshbach interaction we predict the generation of novel strongly correlated paired states. Such states while similar to the one observed in a 5/2 fractional quantum hall effect, are unique in symmetry to the Bose gas system.
Nuclear magnetic resonance in the quantum Hall regime: Skyrmion diffusion model
NASA Astrophysics Data System (ADS)
Sinova, Jairo
As the Trojans strengthened their defenses, they believed their fortress invulnerable. Taking into the city the Trojan horse, with the easiness and self-praising of an assumed victor, proved to be fatal. Although not with such a tragic tone to the story, similar events are occurring in the exciting field of quantum Hall ferromagnets (QHF). Once the basis for the theory was settled, a surprisingly excellent agreement with a few experimental results was obtained during the first few years of research. Building on these initial successes, the theory has remained somewhat stationary in the past few years, while the experimentalists have gotten busy building their Trojan horse once again. The model that we present in this thesis has its origins in the non-disorder theory of the charged excitations in the quantum Hall regime. However, at the time of writing, new experiments are beginning to suggest that our understanding of the QHF needs some rethinking, or at the very least, aspects of the experiments need to be understood better. We present in this thesis a model for the nuclear magnetic resonance (NMR) line shapes in the absence of these experimental complications. We show that within this model the spectra have a very high sensitivity to nuclear polarization spatial profiles and a weak dependence on the dynamics of the charged excitations. It is plausible that some of the observed experimental features may be due to the specific experimental procedure used. Further work will be needed to settle the matter. Although this thesis does not attempt to be an exhaustive work on the understanding of NMR in the QHE, considerable effort has been made to lay down the basic experimental and theoretical details in order to understand both the trivial and subtle effects extractable from the experiments.
Superconductor-graphene-superconductor Josephson junction in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Liu, Jie; Liu, Haiwen; Song, Juntao; Sun, Qing-Feng; Xie, X. C.
2017-07-01
Using a nonequilibrium-Green-function method, we numerically studied the transport properties of a superconductor-graphene-superconductor Josephson junction hybrid system in the quantum Hall regime. Our numerical calculations show that there are two interference patterns of the critical current due to the unique band structure of graphene. One is caused by the usual intraband Andreev retroreflection process, and the other one is caused by the interband specular Andreev reflection process. In the Andreev retroreflection regime, chiral Andreev edge states are formed and a distinct supercurrent can be observed. The critical current displays an AB oscillation behavior and the period is approximately 2 Φ0=h /e . As for the specular Andreev refection process, the reflected holes are bent back to the reverse direction of the incident electrons and the supercurrent flows along both edges. It is similar to a superconductor ring Josephson junction and the period is Φ0=h /2 e . However, the critical current for the specular Andreev reflection process is very small and is unlikely to be observable in an experiment. Thus, we conclude that our numerical calculations are inconsistent to the experimental findings by Amet et al. [Science 352, 966 (2016), 10.1126/science.aad6203].
Exchange-mediated dynamic screening in the integer quantum Hall effect regime
NASA Astrophysics Data System (ADS)
Oswald, Josef; Römer, Rudolf A.
2017-03-01
We study many-body interaction effects in the spatially resolved filling factor (ν) distribution for higher Landau levels (LLs) via self-consistent Hartree-Fock simulations in the integer quantum Hall (IQH) regime. Our results indicate a strong, interaction-induced tendency to avoid the simultaneous existence of partially filled spin-up and spin-down LLs. Rather, we find that such partially filled LLs consist of coexisting regions of full and empty LLs. At the boundaries between the regions of full and empty LLs, we observe edge stripes of nearly constant ν close to half-filling. This suggests that the exchange interaction induces a behavior similar to a Hund's rule for the occupation of the spin split LLs. The screening of the disorder and edge potential appears significantly reduced as compared to static Thomas-Fermi screening (Chklovskii D. B. et al., Phys. Rev. B, 46 (1992) 4026). Our results are consistent with a local, lateral ν-dependence of the exchange-enhanced spin splitting. Hence, on quantum-coherent length scales as probed here, the electron system of the IQH effect behaves similarly to a non-interacting single particle system —not because of the absence, but rather due to the dominance of many-body effects.
Chida, K.; Yamauchi, Y.; Arakawa, T.; Kobayashi, K.; Ono, T.; Hashisaka, M.; Nakamura, S.; Machida, T.
2013-12-04
We performed the resistively-detected nuclear magnetic resonance (RDNMR) to study the electron spin polarization in the non-equilibrium quantum Hall regime. By measuring the Knight shift, we derive source-drain bias voltage dependence of the electron spin polarization in quantum wires. The electron spin polarization shows minimum value around the threshold voltage of the dynamic nuclear polarization.
NASA Astrophysics Data System (ADS)
Avdonin, A.; Skupiński, P.; Grasza, K.
2016-02-01
A simple description of the Hall effect in the hopping regime of conductivity in semiconductors is presented. Expressions for the Hall coefficient and Hall mobility are derived by considering averaged equilibrium electron transport in a single triangle of localization sites in a magnetic field. Dependence of the Hall coefficient is analyzed in a wide range of temperature and magnetic field values. Our theoretical result is applied to our experimental data on temperature dependence of Hall effect and Hall mobility in ZnO.
NASA Astrophysics Data System (ADS)
Wurstbauer, U.; Knott, S.; Westarp, C. G. v.; Mecking, N.; Rachor, K.; Heitmann, D.; Wegscheider, W.; Hansen, W.
2010-02-01
Low-temperature magnetotransport measurements and far-infrared transmission spectroscopy are reported in molecular beam epitaxial grown two-dimensional hole systems confined in strained InAs quantum wells with magnetic impurities in the channel. The interactions of the free holes spin with the magnetic moment of 5/2 provided by manganese features intriguing localization phenomena and anomalies in the Hall and the quantum Hall resistance. In magnetic field-dependent far-infrared spectroscopy measurements well-pronounced cyclotron resonance and an additional resonance are found that indicates an anti-crossing with the cyclotron resonance.
Manifestation of many-body interactions in the integer quantum Hall effect regime
NASA Astrophysics Data System (ADS)
Oswald, Josef; Römer, Rudolf A.
2017-09-01
We use the self-consistent Hartree-Fock approximation for numerically addressing the integer quantum Hall (IQH) regime in terms of many-body physics at higher Landau levels (LL). The results exhibit a strong tendency to avoid the simultaneous existence of partly filled spin-up and spin-down LLs. Partly filled LLs appear as a mixture of coexisting regions of full and empty LLs. We obtain edge stripes with approximately constant filling factor ν close to half-odd filling at the boundaries between the regions of full and empty LLs, which we explain in terms of the g -factor enhancement as a function of a locally varying ν across the compressible stripes. The many-particle interactions follow a behavior as it would result from applying Hund's rule for the occupation of the spin split LLs. The screening of the disorder and edge potential appears significantly reduced as compared to screening based on a Thomas-Fermi approximation. For addressing carrier transport, we use a nonequilibrium network model (NNM) that handles the lateral distribution of the experimentally injected nonequilibrium chemical potentials μ .
NASA Astrophysics Data System (ADS)
Rokhinson, Leonid; Kazakov, Aleksandr; Simion, George; Lyanda-Geller, Yuli; Kolkovsky, Valery; Karczewski, Grzegorz; Adamus, Zbigniew; Wojtowicz, Tomasz
2016-10-01
Several experiments in nanowires detected signatures of Majorana fermions, building block for topologicaly protected quantum computer. Now the focus of research is shifting toward systems where non-Abelian statistics of excitations can be demonstrated. To achieve this goal we are developing a new dilute magnetic semiconductor-based platform where non-Abelian excitations can be created and manipulated in a two-dimensional plane, with support for Majorana and higher order non-Abelian excitations. Here we report development of heterostructures where spin polarization of a two-dimensional electron gas in a quantum Hall regime can be controlled locally by electrostatic gating. This is demonstrated via voltage induced shift of quantum Hall ferromagnetic transition in the CdTe quantum wells with engineered placement of paramagnetic Mn impurities. The structures can be used to form helical domain walls in integer quantum Hall regime which, coupled to an s-wave superconductor, are expected to support Majorana zero modes. These heterostructures can be used as a testbed to study gate-reconfigurable domain walls networks.
Electronic transport in two-dimensional systems in the quantum hall regime
NASA Astrophysics Data System (ADS)
Tarquini, Vinicio
The integer and the fractional quantum Hall effects are essential to the exploration of quantum matters characterized by topological phases. A quantum Hall system hosts one-dimensional (1D) chiral edge channels that manifest zero magnetoresistance, dissipationless due to the broken time reversal symmetry, and quantized Hall resistance vhe2 with v being the topological invariant (or Chern number). The 1-1 correspondence between the conducting gapless edge channels to the gapped incompressible bulk states is a defining character of a topological insulator (TI). Understanding this correspondence in real systems, especially the origin of its robustness (in terms of the limit of breakdown), is important both fundamentally and practically (i.e. in relation to spintronics). However, the breakdown mechanism, especially in light of the edge-bulk correlation, is still an open question. We adopt GaAs two-dimensional (2D) high-mobility hole systems confined in a 20 nm wide (100)-GaAs quantum wells and have perform transport measurement for a range of charge densities between 4 and 5 x 1010 cm -2 with a carrier mobility of 2 - 4 x 106 cm 2/V·s down to millikelvin temperatures. Systematic characterization of the 2D systems through Shubnikov-de Haas (SdH) oscillations yields an effective mass between 0.30 and 0.50me, in good agreement with the cyclotron resonance results. We then modify a regular Hall bar system into a unique anti-Hall bar geometry that provides an extra set of independent chiral edge channels without altering the topological invariant. We perform systematic measurement of quantum oscillations via chiral edges while simultaneously probing the bulk dynamics, through measuring across independent edges, in respond to the edge excitations. The edge-bulk correspondence reveals a non-equilibrium dynamical development of the incompressible bulk states that leads to a novel asymmetrical 1-0 Hall potential distribution. Moreover, probing the breakdown via inner and outer
Non-equilibrium edge-channel spectroscopy in the integer quantum Hall regime
NASA Astrophysics Data System (ADS)
Altimiras, C.; Le Sueur, H.; Gennser, U.; Cavanna, A.; Mailly, D.; Pierre, F.
2010-01-01
The study of heat transport has the potential to reveal new insights into the physics of mesoscopic systems. This is especially true of those that show the integer quantum Hall effect, in which the robust quantization of Hall currents limits the amount of information that can be obtained from charge transport alone. As a consequence, our understanding of gapless edge excitations in these systems is incomplete. Effective edge-state theory describes them as prototypical one-dimensional chiral fermions-a simple picture that explains a large body of observations and suggests the use of quantum point contacts as electronic beam splitters to explore a variety of quantum mechanical phenomena. However, this picture is in apparent disagreement with the prevailing theoretical framework, which predicts in most situations extra gapless edge modes. Here, we present a spectroscopic technique that addresses the question of whether some of the injected energy is captured by the predicted extra states, by probing the distribution function and energy flow in an edge channel operated out-of-equilibrium. Our results show it is not the case and therefore that regarding energy transport, quantum point contacts do indeed behave as optical beam splitters. This demonstrates a useful new tool for heat transport and out-of-equilibrium experiments.
NASA Astrophysics Data System (ADS)
Singha, Aniket; Fauzi, M. H.; Hirayama, Y.; Muralidharan, Bhaskaran
2017-03-01
The interplay of spin-polarized electronic edge states with the dynamics of the host nuclei in quantum Hall systems presents rich and nontrivial transport physics. Here, we develop a Landauer-Büttiker approach to understand various experimental features observed in the integer quantum Hall setups featuring quantum point contacts. The approach developed here entails a phenomenological description of spin-resolved interedge scattering induced via hyperfine assisted electron-nuclear spin flip-flop processes. A self-consistent simulation framework between the nuclear spin dynamics and edge state electronic transport is presented in order to gain crucial insights into the dynamic nuclear polarization effects on electronic transport and in turn the electron-spin polarization effects on the nuclear spin dynamics. In particular, we show that the hysteresis noted experimentally in the conductance-voltage trace as well as in the resistively detected NMR line-shape results from a lack of quasiequilibrium between electronic transport and nuclear polarization evolution. In addition, we present circuit models to emulate such hyperfine mediated transport effects to further facilitate a clear understanding of the electronic transport processes occurring around the quantum point contact. Finally, we extend our model to account for the effects of quadrupolar splitting of nuclear levels and also depict the electronic transport signatures that arise from single and multiphoton processes.
Shot noise generated by graphene p-n junctions in the quantum Hall effect regime
NASA Astrophysics Data System (ADS)
Kumada, N.; Parmentier, F. D.; Hibino, H.; Glattli, D. C.; Roulleau, P.
2015-09-01
Graphene offers a unique system to investigate transport of Dirac Fermions at p-n junctions. In a magnetic field, combination of quantum Hall physics and the characteristic transport across p-n junctions leads to a fractionally quantized conductance associated with the mixing of electron-like and hole-like modes and their subsequent partitioning. The mixing and partitioning suggest that a p-n junction could be used as an electronic beam splitter. Here we report the shot noise study of the mode-mixing process and demonstrate the crucial role of the p-n junction length. For short p-n junctions, the amplitude of the noise is consistent with an electronic beam-splitter behaviour, whereas, for longer p-n junctions, it is reduced by the energy relaxation. Remarkably, the relaxation length is much larger than typical size of mesoscopic devices, encouraging using graphene for electron quantum optics and quantum information processing.
Shot noise generated by graphene p-n junctions in the quantum Hall effect regime.
Kumada, N; Parmentier, F D; Hibino, H; Glattli, D C; Roulleau, P
2015-09-04
Graphene offers a unique system to investigate transport of Dirac Fermions at p-n junctions. In a magnetic field, combination of quantum Hall physics and the characteristic transport across p-n junctions leads to a fractionally quantized conductance associated with the mixing of electron-like and hole-like modes and their subsequent partitioning. The mixing and partitioning suggest that a p-n junction could be used as an electronic beam splitter. Here we report the shot noise study of the mode-mixing process and demonstrate the crucial role of the p-n junction length. For short p-n junctions, the amplitude of the noise is consistent with an electronic beam-splitter behaviour, whereas, for longer p-n junctions, it is reduced by the energy relaxation. Remarkably, the relaxation length is much larger than typical size of mesoscopic devices, encouraging using graphene for electron quantum optics and quantum information processing.
NASA Astrophysics Data System (ADS)
Battista, F.; Samuelsson, P.
2012-02-01
We investigate theoretically a scheme for spectroscopy of electrons emitted by an on-demand single-particle source. The total system, with an electron turnstile source and a single-level quantum dot spectrometer, is implemented with edge states in a conductor in the quantum Hall regime. Employing a Floquet scattering approach, the source and the spectrometer are analyzed within a single theoretical framework. The nonequilibrium distribution of the emitted electrons is analyzed via the direct current at the dot spectrometer. In the adiabatic and intermediate source frequency regimes, the distribution is found to be strongly peaked around the active resonant level of the turnstile. At high frequencies the distribution is split up into a set of fringes, resulting from the interplay of resonant transport through the turnstile and absorption or emission of individual Floquet quanta. For ideal source operation, with exactly one electron emitted per cycle, an expression for the single-electron wave function is derived.
Magnetoconductance of interacting electrons in quantum wires in the integer quantum Hall regime.
NASA Astrophysics Data System (ADS)
Zozoulenko, Igor; Ihnatsenka, Siarhei
2008-03-01
We present systematic quantitative description of the magnetoconductance of the split-gate quantum wires. Accounting for the exchange and correlation interactions within the spin density function theory (DFT) leads to the lifting of the spin degeneracy and formation of the spin-resolved plateaus at odd values of e^2/h. We show that the width of the odd conductance steps in the spin DFT calculations is equal to the width of the transition intervals between the conductance steps for the spinless Hartree electrons. A detailed analysis of the structure of compressible/incompressible strips and the evolution of the Hartree and the spin-DFT subband structure provides an explanation of this finding. Our spin-DFT calculations reproduce not only qualitatively, but rather quantitatively all the features in the magnetoconductance observed in the experiment [1] including the unexpected effect of the collapse of the odd conductance plateaus at lower fields. [1] I. P. Radu, J. B. Miller, S. Amasha, E. Levenson-Falk, D. M. Zumbuhl, M. A. Kastner, C. M. Marcus, L. N. Pfeiffer, and K. W. West, unpublished.
Domain walls, fusion rules, and conformal field theory in the quantum Hall regime.
Ardonne, Eddy
2009-05-08
We provide a simple way to obtain the fusion rules associated with elementary quasiholes over quantum Hall wave functions, in terms of domain walls. The knowledge of the fusion rules is helpful in the identification of the underlying conformal field theory describing the wave functions. We show that, for a certain two-parameter family (k,r) of wave functions, the fusion rules are those of su(r)k. In addition, we give an explicit conformal field theory construction of these states, based on the Mk(k+1,k+r) "minimal" theories. For r=2, these states reduce to the Read-Rezayi states. The "Gaffnian" wave function is the prototypical example for r>2, in which case the conformal field theory is nonunitary.
Zero-bias anomalies in narrow tunnel junctions in the quantum Hall regime.
Jiang, P; Chien, C-C; Yang, I; Kang, W; Baldwin, K W; Pfeiffer, L N; West, K W
2010-12-10
We report on the study of cleaved-edge-overgrown line junctions with a serendipitously created narrow opening in an otherwise thin, precise line barrier. Two sets of zero-bias anomalies are observed with an enhanced conductance for filling factors ν>1 and a strongly suppressed conductance for ν<1. A transition between the two behaviors is found near ν≈1. The zero-bias anomaly (ZBA) line shapes find explanation in Luttinger liquid models of tunneling between quantum Hall edge states. The ZBA for ν<1 occurs from strong backscattering induced by suppression of quasiparticle tunneling between the edge channels for the n=0 Landau levels. The ZBA for ν>1 arises from weak tunneling of quasiparticles between the n=1 edge channels.
Resonant Raman Scattering from Bound Magnetorotons in the Fractional Quantum Hall Regime
NASA Astrophysics Data System (ADS)
He, Song
1996-03-01
We investigate excitation spectra of a fractional quantum Hall system at ν=1/3 using both theoretical and experimental techniques. Using finite-size numerical diagonalizations, we have studied systematically the excitation spectra, the nature of the low-lying excited states, and the density response function of a ν=1/3 system. Our numerical results indicate that two rotons at the roton minimum can form a weakly bound composite object, giving rise to excited states below the collective mode at long wavelengths. We argue that only these two roton composite objects contribute to the resonant Raman scattering at low momentum transfers. Using the experimental technique of resonant Raman scattering, we have identified the contributions to the Raman intensity from the internal excitations of the fractional quantum Hall system by studying their dependence on the incoming light energy, the filling factor, and the temperature. As a function of the energy shift, the Raman intensity shows a sharp peak at an energy shift of about twice of the energy gap at the roton minimum. We propose that this sharp peak is related to a two roton bound state. The sharp peak is followed by a broader peak, which we think is related to the two-roton continuum. When a grating pattern is put on the sample so that small but finite momentum transfer can be achieved, we observed another peak at about twice of the energy gap Δ_q=∞. We suspect this peak is related to the collective mode at long wavelength. Finally, we propose an excitation spectra consistent with our numerical and experimental results. * This work is a collaboration with P. M. Platzman, A. Pinczuk, B. S. Dennis, L. L. Sohn, L. N. Pfeiffer, and K. W. West.
Proliferation of upstream neutral modes in the fractional quantum Hall regime
NASA Astrophysics Data System (ADS)
Inoue, Hiroyuki; Grivnin, Anna; Ronen, Yuval; Heiblum, Moty; Umansky, Vladimir; Mahalu, Diana
2014-03-01
The fractional quantum Hall effects (FQHE) are canonical examples of topological phases, resulting from correlations among planar electrons under strong perpendicular magnetic field. Chargeless energy transport, in the form of upstream (anti-chiral) neutral edge modes, were recently observed in the hole-conjugate FQHEs (filling ν of the nth Landau level in the range n + 1/2> ν>n +1, with n = 0, 1, 2) as well as ν = 5/2. These modes had been predicted to appear due to edge reconstructions by Coulomb interaction and random tunneling among multiple channels. Here we report highly sensitive shot noise measurements that reveal, unexpected theoretically, the presence of such upstream neutral modes in electron-like FQHEs such as ν = 1/3, 2/5, etc . Furthermore, we also found neutral bulk modes that propagate through the incompressible bulk; though weaker than the edge modes. The proliferation of such neutral modes detected only in FQHEs drastically changes the accepted picture of the transport therein. Moreover, our observation may shed new light on a source of decoherence, which prevented thus far a definite observation of quantum interference of fractional quasiparticles.
NASA Astrophysics Data System (ADS)
Yun, Yoojoo; Kang, Haeyong; Kim, Joong-Gyu; Park, Jeongmin; Truong, Thuy Kieu; Park, Nahee; Kim, Jeong-Gyun; Lee, Yourack; Yun, Hoyeol; Lee, Sang Wook; Lee, Young Hee; Suh, Dongseok; Cinap, Ibs, Does, Sungkyunkwan Univ. Team; School Of Physics, Konkuk Univ. Collaboration
2015-03-01
We present the feature of conductance oscillation in the quantum Hall regime graphene FET on top of large gate-voltage hysteresis (up to 100 V). A mono-layer graphene was put on the hBN flake on the wet silicon oxide/silicon substrate. At 300 K, the normal conductance versus gate-voltage curve was observed showing the charge neutrality point without hysteresis. At 2 K, however, there was a huge conductance hysteresis during the sweep of gate-voltage, which could be attributed to the characteristics of charge-trap memory behavior because of defects located inside the dielectric playing a role of charge-trap sites. Even though the hysteresis during gate-voltage sweeping was enormous, in our device having hBN for graphene device preventing the deteriorating impacts from the defective SiO2, the conductance oscillation during the gate-voltage sweep was observed from the magnetic field 4 T. In summary, the results proved that the combination of quantum Hall related transport phenomena and the charge-trap memory operation was achieved successfully without affecting each other in our graphene-on-hBN FET device.
Bernevig, B.Andrei; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-01-15
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. Existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external magnetic field. In this work, we predict a quantized spin Hall effect in the absence of any magnetic field, where the intrinsic spin Hall conductance is quantized in units of 2 e/4{pi}. The degenerate quantum Landau levels are created by the spin-orbit coupling in conventional semiconductors in the presence of a strain gradient. This new state of matter has many profound correlated properties described by a topological field theory.
Temperature Dependent Transport of Two-Dimensional Electrons in the Integral Quantum Hall Regime.
NASA Astrophysics Data System (ADS)
Wei, Hsuang-Ping
This thesis is concerned with the temperature (T) dependent electronic transport properties of a two dimensional electron gas subject to background potential fluctuations and a perpendicular magnetic field. We have carried out an extensive temperature dependent study of the transport coefficients, in the region of an integral quantum plateau, in an In(,x)Ga(,1-x)As/InP heterostructure for 4.2K < T < 50K. By assuming a simple thermal activation picture, we demonstrate a quantitative deduction of the electron density of states. Our results indicate that there exists a significant number of states (1 x 10('10)cm(' -2)meV('-1)) even at the middle between two Landau levels, which is unexpected from model calculations based on short ranged randomness. In addition, the different T dependent behavior of (rho)(,xx) between the states in the tails and those near the center of a Landau level, indicates the existence of different electron states in a Landau level. Moreover, we have performed T dependent trans- port measurements in the transition region between two quantum plateaus, in several different materials. In the In(,x)Ga(,1-x)As/InP sample, when T(, )> 4K, the transport behavior can be attributed to the T dependent distribution function. When T(, )< 4K, our experi- mental T-driven (sigma)(,xx) vs. (sigma)(,xy) flow diagram is consistent with the pre- dicted theoretical renormalization group flow diagram, and suggests the existence of a critical point related to the localization to delocali- zation transition. However, in the GaAs/Al(,x)Ga(,1-x)As samples there is a difference in the T dependent behavior of (sigma)(,xx), between N = 1(UPARR) and 1(DARR) electrons. First, (sigma)(,xx)(1(UPARR)) decreases with decreasing T; whereas (sigma)(,xx)(1(DARR)) increases with decreasing T for 0.3K(, )< T < 4.2K. Second, (sigma)(,xx)('max) (1(DARR)) ('(TURN)) 3(sigma)(,xx)('max) (1(UPARR)) at T('(TURN))0.5K in all of our samples. These results indicate the existence of spin
Conductance noise of submicron wires in the regime of quantum Hall effect
NASA Astrophysics Data System (ADS)
Wróbel, J.; Jaroszyń Ski, J.; Dietl, T.; Regiń Ski, K.; Bugajski, M.
1998-12-01
A detailed study of low-temperature magnetoconductance in between quantized Hall plateaux is presented. The data are obtained for disordered two-terminal submicron wires defined in GaAs/AlGaAs heterostructures modulation-doped by Si. Slow time evolution of conductance G is observed on the high-field side of the quantized plateaux - for filling factors ν<3 and ν<2. This surprising noise is attributed to glassy dynamics of localized electrons in the wire centre, and to the corresponding time dependence of the impurity-assisted tunnelling probability between the current carrying regions.
Ofek, Nissim; Bid, Aveek; Heiblum, Moty; Stern, Ady; Umansky, Vladimir; Mahalu, Diana
2010-01-01
Interference of edge channels is expected to be a prominent tool for studying statistics of charged quasiparticles in the quantum Hall effect (QHE). We present here a detailed study of an electronic Fabry–Perot interferometer (FPI) operating in the QHE regime [C. Chamon, et al. (1997) Phys Rev B 55:2331–2334], with the phase of the interfering quasiparticles controlled by the Aharonov–Bohm effect. Our main finding is that Coulomb interactions among the electrons dominate the interference, even in a relatively large area FPI, leading to a strong dependence of the area enclosed by the interference loop on the magnetic field. In particular, for a composite edge structure, with a few independent edge channels propagating along the edge, interference of the outmost edge channel (belonging to the lowest Landau level) was insensitive to magnetic field—suggesting a constant enclosed flux. However, when any of the inner edge channels interfered, the enclosed flux decreased when the magnetic field increased. By intentionally varying the enclosed area with a biased metallic gate and observing the periodicity of the interference pattern, charges e (for integer filling factors) and e/3 (for a fractional filling factor) were found to be expelled from the FPI. Moreover, these observations provided also a novel way of detecting the charge of the interfering quasiparticles. PMID:20212147
Interaction-driven capacitance in graphene electron-hole bilayer in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Roostaei, Bahman; Joglekar, Yogesh
2014-03-01
Fabrication of devices made by isolated Graphene or Graphene-like single layers (such as h-BN) has opened up possibility of examining highly correlated states of electron systems in parts of their phase diagram that is impossible to access in their counterpart devices such as semiconductor heterostructures. An example of such states are Graphene (or Graphene like) double layer electron-hole systems under strong magnetic fields where the separation between layers can be of the order of one magnetic length with interlayer tunneling still suppressed. In those separations correlations between electrons and holes are of crucial importance and must be included in determination of observables. Here we report a thorough mean-field study of the coherent and crystalline ground states of the interacting balanced electron-hole Graphene systems in small and intermediate separations with each layer occupying up to four lowest lying Landau levels. We calculate the capacitance of such states as a function of layer separation and filling factor. Our calculations show significant enhancement of the capacitance compared to geometrical value due to quantum mechanical corrections. US nsf-dmr 1054020
NASA Astrophysics Data System (ADS)
Kumar, Akshay
We study several quantum phases that are related to the quantum Hall effect. Our initial focus is on a pair of quantum Hall ferromagnets where the quantum Hall ordering occurs simultaneously with a spontaneous breaking of an internal symmetry associated with a semiconductor valley index. In our first example ---AlAs heterostructures--- we study domain wall structure, role of random-field disorder and dipole moment physics. Then in the second example ---Si(111)--- we show that symmetry breaking near several integer filling fractions involves a combination of selection by thermal fluctuations known as "order by disorder" and a selection by the energetics of Skyrme lattices induced by moving away from the commensurate fillings, a mechanism we term "order by doping". We also study ground state of such systems near filling factor one in the absence of valley Zeeman energy. We show that even though the lowest energy charged excitations are charge one skyrmions, the lowest energy skyrmion lattice has charge > 1 per unit cell. We then broaden our discussion to include lattice systems having multiple Chern number bands. We find analogs of quantum Hall ferromagnets in the menagerie of fractional Chern insulator phases. Unlike in the AlAs system, here the domain walls come naturally with gapped electronic excitations. We close with a result involving only topology: we show that ABC stacked multilayer graphene placed on boron nitride substrate has flat bands with non-zero local Berry curvature but zero Chern number. This allows access to an interaction dominated system with a non-trivial quantum distance metric but without the extra complication of a non-zero Chern number.
Quantum Hall ferrimagnetism in lateral quantum dot molecules.
Abolfath, Ramin M; Hawrylak, Pawel
2006-11-03
We demonstrate the existence of ferrimagnetic and ferromagnetic phases in a spin phase diagram of coupled lateral quantum dot molecules in the quantum Hall regime. The spin phase diagram is determined from the Hartree-Fock configuration interaction method as a function of electron number N and magnetic field B. The quantum Hall ferrimagnetic phase corresponds to spatially imbalanced spin droplets resulting from strong interdot coupling of identical dots. The quantum Hall ferromagnetic phases correspond to ferromagnetic coupling of spin polarization at filling factors between nu=2 and nu=1.
Effect of disorder on longitudinal resistance of a graphene p-n junction in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Chen, Jiang-Chai; Yeung, T. C. Au; Sun, Qing-Feng
2010-06-01
The longitudinal resistances of a six-terminal graphene p-n junction under a perpendicular magnetic field are investigated. Because of the chirality of the Hall edge states, the longitudinal resistances on top and bottom edges of the graphene ribbon are not equal. In the presence of suitable disorder, the top-edge and bottom-edge resistances well show the plateau structures in the both unipolar and bipolar regimes, and the plateau values are determined by the Landau filling factors only. These plateau structures are in excellent agreement with the recent experiment. For the unipolar junction, the resistance plateaus emerge in the absence of impurity and they are destroyed by strong disorder. But for the bipolar junction, the resistances are very large without the plateau structures in the clean junction. The disorder can strongly reduce the resistances and leads the formation of the resistance plateaus due to the mixture of the Hall edge states in virtue of the disorder. In addition, the size effect of the junction on the resistances is studied and some extra resistance plateaus are found in the long graphene junction case. This is explained by the fact that only part of the edge states participate in the full mixing.
Effect of the Nuclear Hyperfine Field on the 2D Electron Conductivity in the Quantum Hall Regime
VITKALOV,S.A.; BOWERS,C.R.; SIMMONS,JERRY A.; RENO,JOHN L.
2000-07-13
The effect of the nuclear hyperfine interaction on the dc conductivity of 2D electrons under quantum Hall effect conditions at filling factor v= 1 is observed for the first time. The local hyperfine field enhanced by dynamic nuclear polarization is monitored via the Overhauser shift of the 2D conduction electron spin resonance in AlGaAs/GaAs multiquantum-well samples. The experimentally observed change in the dc conductivity resulting from dynamic nuclear polarization is in agreement with a thermal activation model incorporating the Zeeman energy change due to the hyperfine interaction. The relaxation decay time of the dc conductivity is, within experimental error, the same as the relaxation time of the nuclear spin polarization determined from the Overhauser shift. These findings unequivocally establish the nuclear spin origins of the observed conductivity change.
Quantum Hall effect in quantum electrodynamics
Penin, Alexander A.
2009-03-15
We consider the quantum Hall effect in quantum electrodynamics and find a deviation from the quantum-mechanical prediction for the Hall conductivity due to radiative antiscreening of electric charge in an external magnetic field. A weak dependence of the universal von Klitzing constant on the magnetic field strength, which can possibly be observed in a dedicated experiment, is predicted.
NASA Astrophysics Data System (ADS)
Nachtwei, G.; Salchow, O.; Breitlow, C.; Jaeger, A.; Krüger, H.
1991-07-01
The measurement of activation energies for various positions of the Fermi level between two Landau levels provides an opportunity to evaluate the density of states (DOS) in the quantum Hall regime. We present results of measurements of the temperature dependence of the magnetoresistivity ϱxx at filling factors ν = 2 and ν = 4 for several Si-MOS and MNOS samples with the same layout but different insulator layers of SiO 2 or SiO 2/Si 3N 4, respectively. The Hall mobility of the MNOS structures is noticeably higher than that of the MOS structures, whereas the DOS determined from activation energy measurements is lower. The measured DOS is higher than the simple overlap of two adjacent Gaussian-shaped Landau bands with broadening parameters taken from the Hall mobility data. This can be explained by a constant background contribution to the DOS. For the i = 2 plateau an estimate of the effective Landé-factor can be given.
Akiba, K; Kanasugi, S; Yuge, T; Nagase, K; Hirayama, Y
2015-07-10
We study nuclear spin polarization in the quantum Hall regime through the optically pumped electron spin polarization in the lowest Landau level. The nuclear spin polarization is measured as a nuclear magnetic field B(N) by means of the sensitive resistive detection. We find the dependence of B(N) on the filling factor nonmonotonic. The comprehensive measurements of B(N) with the help of the circularly polarized photoluminescence measurements indicate the participation of the photoexcited complexes, i.e., the exciton and trion (charged exciton), in nuclear spin polarization. On the basis of a novel estimation method of the equilibrium electron spin polarization, we analyze the experimental data and conclude that the filling factor dependence of B(N) is understood by the effect of electron spin polarization through excitons and trions.
Anomalous hydrodynamics of fractional quantum Hall states
Wiegmann, P.
2013-09-15
We propose a comprehensive framework for quantum hydrodynamics of the fractional quantum Hall (FQH) states. We suggest that the electronic fluid in the FQH regime can be phenomenologically described by the quantized hydrodynamics of vortices in an incompressible rotating liquid. We demonstrate that such hydrodynamics captures all major features of FQH states, including the subtle effect of the Lorentz shear stress. We present a consistent quantization of the hydrodynamics of an incompressible fluid, providing a powerful framework to study the FQH effect and superfluids. We obtain the quantum hydrodynamics of the vortex flow by quantizing the Kirchhoff equations for vortex dynamics.
Insulating to relativistic quantum Hall transition in disordered graphene
Pallecchi, E.; Ridene, M.; Kazazis, D.; Lafont, F.; Schopfer, F.; Poirier, W.; Goerbig, M. O.; Mailly, D.; Ouerghi, A.
2013-01-01
Quasi-particle excitations in graphene exhibit a unique behavior concerning two key phenomena of mesoscopic physics: electron localization and the quantum Hall effect. A direct transition between these two states has been found in disordered two-dimensional electron gases at low magnetic field. It has been suggested that it is a quantum phase transition, but the nature of the transition is still debated. Despite the large number of works studying either the localization or the quantum Hall regime in graphene, such a transition has not been investigated for Dirac fermions. Here we discuss measurements on low-mobility graphene where the localized state at low magnetic fields and a quantum Hall state at higher fields are observed. We find that the system undergoes a direct transition from the insulating to the Hall conductor regime. Remarkably, the transverse magneto-conductance shows a temperature independent crossing point, pointing to the existence of a genuine quantum phase transition.
Determination of the Hall Thruster Operating Regimes
L. Dorf; V. Semenov; Y. Raitses; N.J. Fisch
2002-04-09
A quasi one-dimensional (1-D) steady-state model of the Hall thruster is presented. For the same discharge voltage two operating regimes are possible -- with and without the anode sheath. For given mass flow rate, magnetic field profile and discharge voltage a unique solution can be constructed, assuming that the thruster operates in one of the regimes. However, we show that for a given temperature profile the applied discharge voltage uniquely determines the operating regime: for discharge voltages greater than a certain value, the sheath disappears. That result is obtained over a wide range of incoming neutral velocities, channel lengths and widths, and cathode plane locations. It is also shown that a good correlation between the quasi 1-D model and experimental results can be achieved by selecting an appropriate electron mobility and temperature profile.
NASA Astrophysics Data System (ADS)
Drichko, I. L.; Smirnov, I. Yu.; Suslov, A. V.; Galperin, Y. M.; Pfeiffer, L. N.; West, K. W.
2017-01-01
We review our work on high-frequency conductance in two-dimensional high-mobility electronic systems in wide n-AlGaAs/GaAs/AlGaAs quantum wells. Using simultaneous measurements of the attenuation and velocity of a surface acoustic wave we obtained both real and imaginary components of the complex high-frequency conductance. Based on the experimental results and their analysis we conclude that close to the filling factor ν = 1/5, as well as in the interval 0.18 > ν > 0.125, a Wigner crystal pinned by disorder is formed. Both the melting temperature and the correlation length of the pinning-induced domains in the Wigner crystal were found. In close vicinities of ν = 1 and 2, transitions from single-electron localization to a Wigner crystal were observed.
Tuning energy relaxation along quantum Hall channels.
Altimiras, C; le Sueur, H; Gennser, U; Cavanna, A; Mailly, D; Pierre, F
2010-11-26
The chiral edge channels in the quantum Hall regime are considered ideal ballistic quantum channels, and have quantum information processing potentialities. Here, we demonstrate experimentally, at a filling factor of ν(L)=2, the efficient tuning of the energy relaxation that limits quantum coherence and permits the return toward equilibrium. Energy relaxation along an edge channel is controllably enhanced by increasing its transmission toward a floating Ohmic contact, in quantitative agreement with predictions. Moreover, by forming a closed inner edge channel loop, we freeze energy exchanges in the outer channel. This result also elucidates the inelastic mechanisms at work at ν(L)=2, informing us, in particular, that those within the outer edge channel are negligible.
Fractional Quantum Hall States in a Ge Quantum Well.
Mironov, O A; d'Ambrumenil, N; Dobbie, A; Leadley, D R; Suslov, A V; Green, E
2016-04-29
Measurements of the Hall and dissipative conductivity of a strained Ge quantum well on a SiGe/(001)Si substrate in the quantum Hall regime are reported. We analyze the results in terms of thermally activated quantum tunneling of carriers from one internal edge state to another across saddle points in the long-range impurity potential. This shows that the gaps for different filling fractions closely follow the dependence predicted by theory. We also find that the estimates of the separation of the edge states at the saddle are in line with the expectations of an electrostatic model in the lowest spin-polarized Landau level (LL), but not in the spin-reversed LL where the density of quasiparticle states is not high enough to accommodate the carriers required.
Kleinbaum, Ethan; Kumar, Ashwani; Pfeiffer, L N; West, K W; Csáthy, G A
2015-02-20
In the region of the second Landau level several theories predict fractional quantum Hall states with novel topological order. We report the opening of an energy gap at the filling factor ν=3+1/3, firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifically, we find that the relative magnitudes of the energy gaps of the ν=3+1/3 and 3+1/5 states from the upper spin branch are reversed when compared to the ν=2+1/3 and 2+1/5 counterpart states in the lower spin branch. Our findings raise the possibility that at least one of the former states is of an unusual topological order.
Hyperbolic supersymmetric quantum Hall effect
Hasebe, Kazuki
2008-12-15
Developing a noncompact version of the supersymmetric Hopf map, we formulate the quantum Hall effect on a superhyperboloid. Based on OSp(1|2) group theoretical methods, we first analyze the one-particle Landau problem, and successively explore the many-body problem where the Laughlin wave function, hard-core pseudopotential Hamiltonian, and topological excitations are derived. It is also shown that the fuzzy superhyperboloid emerges at the lowest Landau level.
New melting transition in Quantum Hall systems
NASA Astrophysics Data System (ADS)
Simion, George; Lin, Tsuging; Watson, John D.; Manfra, Michael J.; Csathy, Gabor; Rokhinson, Leonid; Lyanda-Geller, Yuli
2014-03-01
We discover a new melting transition caused by topological excitations of two dimensional electrons in the quantum Hall regime. Experimentally, strain dependence of resistivity changes sign upon crossing filling-factor-specified boundaries of reentrant integer quantum Hall effect (RIQHE) states. This observation violates the symmetry of electron bubble crystal, whose melting was thought to be responsible for insulator to metal transition in the range of RIQHE filling factors. We demonstrate theoretically that electron bubbles become elongated in the vicinity of charge defects and form textures of finite size. Textures lower the energy of excitations. In the two-electron bubble crystal these textures form hedgehogs (vortices) around defects having (lacking) one extra electron. At low density these textures form an insulating Abrikosov lattice. At densities sufficient to cause the textures to overlap, their interactions are described by the XY-model and the defect lattice melts. This explains the sharp metal-insulator transition observed in finite temperature conductivity measurements. In this regime, melting is a function of several variables and forms a continuous phase boundary in the field-temperature (B - T) plane. Research was partially supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Awards DE-SC0010544 (Y.L-G), DE-SC0008630 (L.P.R.), DE-SC0006671 (G.S. and M.M.).
Collective edge modes in fractional quantum Hall systems
NASA Astrophysics Data System (ADS)
Nguyen, Hoang K.; Joglekar, Yogesh N.; Murthy, Ganpathy
2004-07-01
Over the past few years one of us (Murthy) in collaboration with Shankar has developed an extended Hamiltonian formalism capable of describing the ground-state and low-energy excitations in the fractional quantum Hall regime. The Hamiltonian, expressed in terms of composite fermion operators, incorporates all the nonperturbative features of the fractional Hall regime, so that conventional many-body approximations such as Hartree-Fock and time-dependent Hartree-Fock are applicable. We apply this formalism to develop a microscopic theory of the collective edge modes in fractional quantum Hall regime. We present the results for edge mode dispersions at principal filling factors ν=1/3 , 1/5 , and 2/5 for systems with unreconstructed edges. The primary advantage of the method is that one works in the thermodynamic limit right from the beginning, thus avoiding the finite-size effects which ultimately limit exact diagonalization studies.
On-Chip Microwave Quantum Hall Circulator
NASA Astrophysics Data System (ADS)
Mahoney, A. C.; Colless, J. I.; Pauka, S. J.; Hornibrook, J. M.; Watson, J. D.; Gardner, G. C.; Manfra, M. J.; Doherty, A. C.; Reilly, D. J.
2017-01-01
Circulators are nonreciprocal circuit elements that are integral to technologies including radar systems, microwave communication transceivers, and the readout of quantum information devices. Their nonreciprocity arises from the interference of microwaves over the centimeter scale of the signal wavelength, in the presence of bulky magnetic media that breaks time-reversal symmetry. Here, we realize a completely passive on-chip microwave circulator with size 1 /1000 th the wavelength by exploiting the chiral, "slow-light" response of a two-dimensional electron gas in the quantum Hall regime. For an integrated GaAs device with 330 μ m diameter and about 1-GHz center frequency, a nonreciprocity of 25 dB is observed over a 50-MHz bandwidth. Furthermore, the nonreciprocity can be dynamically tuned by varying the voltage at the port, an aspect that may enable reconfigurable passive routing of microwave signals on chip.
Fractional quantum Hall effect revisited
NASA Astrophysics Data System (ADS)
Jacak, J.; Łydżba, P.; Jacak, L.
2015-10-01
The topology-based explanation of the fractional quantum Hall effect (FQHE) is summarized. The cyclotron braid subgroups crucial for this approach are introduced in order to identify the origin of the Laughlin correlations in 2D (two-dimensional) Hall systems. Flux-tubes and vortices for composite fermions in their standard constructions are explained in terms of cyclotron braids. The derivation of the hierarchy of the FQHE is proposed by mapping onto the integer effect within the topology-based approach. The experimental observations of the FQHE supporting the cyclotron braid picture are reviewed with a special attention paid to recent experiments with a suspended graphene. The triggering role of a carrier mobility for organization of the fractional state in Hall configuration is emphasized. The prerequisites for the FQHE are indicated including topological conditions substantially increasing the previously accepted set of physical necessities. The explanation of numerical studies by exact diagonalizations of the fractional Chern insulator states is formulated in terms of the topology condition applied to the Berry field flux quantization. Some new ideas withz regard to the synthetic fractional states in the optical lattices are also formulated.
NASA Astrophysics Data System (ADS)
Hu, Binhui; Yazdanpanah, Mohamad Meqdad; Kane, Bruce E.
2015-03-01
The quality of hydrogen-terminated Si(111) (H-Si(111)) transistors has improved significantly. Peak electron mobility of 325,000 cm2/Vs was achieved at 90 mK, and the fractional quantum Hall effect (FQHE) at 1 < ν < 2 was studied extensively. We have further improved the device by solving gate leakage and contact problems with an updated design, in which a Si piece with thermal oxide acts as a gate through a vacuum cavity, and PN junctions are used to define a hexagonal two-dimensional (2D) region on a H-Si(111) piece. The device operates as an ambipolar transistor, in which a 2D electron system (2DES) and a 2D hole system can be induced at the same H-Si(111) surface. Peak electron mobility of more than 200,000 cm2/Vs is routinely achieved at 300 mK. The Si(111) surface has a six-fold valley degeneracy. The hexagonal device is designed to investigate the symmetry of the 2DES. Preliminary data show that the transport anisotropy at ν < 6 can be explained by the valley occupancy. The details of the valley occupancy can be caused by several mechanisms, such as miscut, magnetic field, pseudospin quantum Hall ferromagnetism (QHFM), and nematic valley polarization phases. The FQHE is investigated in magnetic fields up to 35T, and the properties of composite fermions will be discussed.
NASA Astrophysics Data System (ADS)
Komnik, A.; Saleur, H.
2011-09-01
We verify the validity of the Cohen-Gallavotti fluctuation theorem for the strongly correlated problem of charge transfer through an impurity in a chiral Luttinger liquid, which is realizable experimentally as a quantum point contact in a fractional quantum Hall edge state device. This is accomplished via the development of an analytical method to calculate the full counting statistics of the problem in all the parameter regimes involving the temperature, the Hall voltage, and the gate voltage.
Komnik, A; Saleur, H
2011-09-02
We verify the validity of the Cohen-Gallavotti fluctuation theorem for the strongly correlated problem of charge transfer through an impurity in a chiral Luttinger liquid, which is realizable experimentally as a quantum point contact in a fractional quantum Hall edge state device. This is accomplished via the development of an analytical method to calculate the full counting statistics of the problem in all the parameter regimes involving the temperature, the Hall voltage, and the gate voltage.
Quantum anomalous Hall effect in magnetically doped InAs/GaSb quantum wells.
Wang, Qing-Ze; Liu, Xin; Zhang, Hai-Jun; Samarth, Nitin; Zhang, Shou-Cheng; Liu, Chao-Xing
2014-10-03
The quantum anomalous Hall effect has recently been observed experimentally in thin films of Cr-doped (Bi,Sb)(2)Te(3) at a low temperature (∼ 30 mK). In this work, we propose realizing the quantum anomalous Hall effect in more conventional diluted magnetic semiconductors with magnetically doped InAs/GaSb type-II quantum wells. Based on a four-band model, we find an enhancement of the Curie temperature of ferromagnetism due to band edge singularities in the inverted regime of InAs/GaSb quantum wells. Below the Curie temperature, the quantum anomalous Hall effect is confirmed by the direct calculation of Hall conductance. The parameter regime for the quantum anomalous Hall phase is identified based on the eight-band Kane model. The high sample quality and strong exchange coupling make magnetically doped InAs/GaSb quantum wells good candidates for realizing the quantum anomalous Hall insulator at a high temperature.
New topological excitations in quantum Hall systems
NASA Astrophysics Data System (ADS)
Lyanda-Geller, Yuli; Lin, Tsuging; Simion, George; Watson, John D.; Manfra, Michael J.; Csathy, Gabor; Rokhinson, Leonid
2014-03-01
We discover new topological excitations of two dimensional electrons in the quantum Hall regime. The strain dependence of resistivity observed experimentally is shown to change sign upon crossing filling-factor-specified boundaries of reentrant integer quantum Hall effect (RIQHE) states. This observation violates the known symmetry of electron bubbles thought to be responsible for the RIQHE. We demonstrate theoretically that electron bubbles become elongated in the vicinity of charge defects and form textures of finite size. Calculations confirm that textures lower the energy of excitations. In the two-electron bubble crystal these textures form two-dimensional hedgehogs around defects having one extra electron, and vortices around defects lacking one electron. Strain affects vortices and hedgehogs differently, explaining striking strain-dependent resistivity. The sharp transition from insulating RIQHE state to conducting state is caused by melting of Abrikosov crystal comprised of the defects. The proposed physical mechanism of conductivity due to topological defects is shown to lead to an unusually large magnitude of the strain effect on resistivity in the range of RIQHE filling factors, in agreement with experiment. Research was partially supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Awards DE-SC0010544 (Y.L-G), DE-SC0008630 (L.P.R.), DE-SC0006671 (G.S. and M.M.).
Tunneling current through fractional quantum Hall interferometers
NASA Astrophysics Data System (ADS)
Smits, O.; Slingerland, J. K.; Simon, S. H.
2014-01-01
We calculate the tunneling current through a Fabry-Pérot interferometer in the fractional quantum Hall regime. Within linear response theory (weak tunneling but arbitrary source-drain voltage), we find a general expression for the current due to tunneling of quasiparticles in terms of Carlson's R function. Our result is valid for fractional quantum Hall states with an edge theory consisting of a charged channel and any number of neutral channels, with possibly different edge velocities and different chiralities. We analyze the case with a single neutral channel in detail, which applies for instance to the edge of the Moore-Read state. In addition, we consider an asymmetric interferometer with different edge lengths between the point contacts on opposite edges, and we study the behavior of the current as a function of varying edge length. Recent experiments attempted to measure the Aharanov-Bohm effect by changing the area inside the interferometer using a plunger gate. Theoretical analyses of these experiments have so far not taken into account the accompanying change in the edge lengths. We show that the tunneling current exhibits multiple oscillations as a function of this edge length, with frequencies proportional to the injected edge current and inversely proportional to the edge velocities. In particular, the edge velocities can be measured by looking at the Fourier spectrum of the edge current. We provide a numerical scheme to calculate and plot the R function, and include sample plots for a variety of edge states with parameter values, which are experimentally relevant.
The width of the plateaus of the quantum Hall effect
NASA Astrophysics Data System (ADS)
Groshev, Atanas; Scho¨n, Gerd
1994-02-01
We suggest that in high quality samples in the quantum Hall regime the interaction between localized states dominates over disorder effects. It leads to the formation of a Wigner crystal, which melts at a critical value ν c≈0.2 of the filling factor of the localized states. This leads to a finite width of the plateaus of the integer quantum Hall effect Δν=2ν c. This result describes well recent experimental data on single AlGaAs/GaAs heterojunctions (electron and hole gases) and double 2DEG systems.
Moiré assisted fractional quantum Hall state spectroscopy
NASA Astrophysics Data System (ADS)
Wu, Fengcheng; MacDonald, A. H.
2016-12-01
Intra-Landau level excitations in the fractional quantum Hall regime are not accessible via optical absorption measurements. We point out that optical probes are enabled by the periodic potentials produced by a moiré pattern. Our observation is motivated by the recent observations of fractional quantum Hall incompressible states in moiré-patterned graphene on a hexagonal boron nitride substrate, and is theoretically based on f -sum rule considerations supplemented by a perturbative analysis of the influence of the moiré potential on many-body states.
Moiré assisted fractional quantum Hall state spectroscopy
Wu, Fengcheng; MacDonald, A. H.
2016-12-14
Intra-Landau level excitations in the fractional quantum Hall regime are not accessible via optical absorption measurements. Here we point out that optical probes are enabled by the periodic potentials produced by a moire pattern. Our observation is motivated by the recent observations of fractional quantum Hall incompressible states in moire-patterned graphene on a hexagonal boron nitride substrate, and is theoretically based on f-sum rule considerations supplemented by a perturbative analysis of the influence of the moire potential on many-body states.
The quantum Hall effect helicity
Shrivastava, Keshav N.
2015-04-16
The quantum Hall effect in semiconductor heterostructures is explained by two signs in the angular momentum j=l±s and g=(2j+1)/(2l+1) along with the Landau factor (n+1/2). These modifications in the existing theories explain all of the fractional charges. The helicity which is the sign of the product of the linear momentum with the spin p.s plays an important role for the understanding of the data at high magnetic fields. In particular it is found that particles with positive sign in the spin move in one direction and those with negative sign move in another direction which explains the up and down stream motion of the particles.
The quantum Hall effects: Philosophical approach
NASA Astrophysics Data System (ADS)
Lederer, P.
2015-05-01
The Quantum Hall Effects offer a rich variety of theoretical and experimental advances. They provide interesting insights on such topics as gauge invariance, strong interactions in Condensed Matter physics, emergence of new paradigms. This paper focuses on some related philosophical questions. Various brands of positivism or agnosticism are confronted with the physics of the Quantum Hall Effects. Hacking's views on Scientific Realism, Chalmers' on Non-Figurative Realism are discussed. It is argued that the difficulties with those versions of realism may be resolved within a dialectical materialist approach. The latter is argued to provide a rational approach to the phenomena, theory and ontology of the Quantum Hall Effects.
Chiral Thermoelectrics with Quantum Hall Edge States
NASA Astrophysics Data System (ADS)
Sánchez, Rafael; Sothmann, Björn; Jordan, Andrew N.
2015-04-01
The thermoelectric properties of a three-terminal quantum Hall conductor are investigated. We identify a contribution to the thermoelectric response that relies on the chirality of the carrier motion rather than on spatial asymmetries. The Onsager matrix becomes maximally asymmetric with configurations where either the Seebeck or the Peltier coefficients are zero while the other one remains finite. Reversing the magnetic field direction exchanges these effects, which originate from the chiral nature of the quantum Hall edge states. The possibility to generate spin-polarized currents in quantum spin Hall samples is discussed.
Chiral thermoelectrics with quantum Hall edge states.
Sánchez, Rafael; Sothmann, Björn; Jordan, Andrew N
2015-04-10
The thermoelectric properties of a three-terminal quantum Hall conductor are investigated. We identify a contribution to the thermoelectric response that relies on the chirality of the carrier motion rather than on spatial asymmetries. The Onsager matrix becomes maximally asymmetric with configurations where either the Seebeck or the Peltier coefficients are zero while the other one remains finite. Reversing the magnetic field direction exchanges these effects, which originate from the chiral nature of the quantum Hall edge states. The possibility to generate spin-polarized currents in quantum spin Hall samples is discussed.
Metal-to-insulator switching in quantum anomalous Hall states
NASA Astrophysics Data System (ADS)
Pan, Lei; Kou, Xufeng; Wang, Jing; Fan, Yabin; Choi, Eun Sang; Shao, Qiming; Zhang, Shou Cheng; Wang, Kang Lung
Quantum anomalous Hall effect (QAHE) was recently achieved in magnetic topological insulator films as a form of dissipationless transport without external magnetic field. However, the universal phase diagram of QAHE and its relation with quantum Hall effect (QHE) remain to be investigated. Here, we report the experimental observation of the giant longitudinal resistance peak and zero Hall conductance plateau at the coercive field in the six quintuple-layer (Cr0.12Bi0.26Sb0.62)2 Te3 film, and demonstrate the metal-to-insulator switching between two opposite QAHE plateau states up to 0.3 K. The universal QAHE phase diagram is further confirmed through the angle-dependent measurements. Our results address that the quantum phase transitions in both QAHE and QHE regimes are in the same universality class, yet the microscopic details are different.
Integer quantum magnon Hall plateau-plateau transition in a spin-ice model
NASA Astrophysics Data System (ADS)
Xu, Baolong; Ohtsuki, Tomi; Shindou, Ryuichi
2016-12-01
Low-energy magnon bands in a two-dimensional spin-ice model become integer quantum magnon Hall bands under an out-of-plane field. By calculating the localization length and the two-terminal conductance of magnon transport, we show that the magnon bands with disorders undergo a quantum phase transition from an integer quantum magnon Hall regime to a conventional magnon localized regime. Finite size scaling analysis as well as a critical conductance distribution shows that the quantum critical point belongs to the same universality class as that in the quantum Hall transition. We characterize thermal magnon Hall conductivity in a disordered quantum magnon Hall system in terms of robust chiral edge magnon transport.
Competition between Kondo Screening and Quantum Hall Edge Reconstruction
NASA Astrophysics Data System (ADS)
Heine, A. W.; Tutuc, D.; Zwicknagl, G.; Haug, R. J.
2016-03-01
We report on a Kondo correlated quantum dot connected to two-dimensional leads where we demonstrate the renormalization of the g factor in the pure Zeeman case. i.e., for magnetic fields parallel to the plane of the quantum dot. For the same system, we study the influence of orbital effects by investigating the quantum Hall regime; i.e., a perpendicular magnetic field is applied. In this case an unusual behavior of the suppression of the Kondo effect and of the split zero-bias anomaly is observed. The splitting decreases with magnetic field and shows discontinuous changes that are attributed to the intricate interplay between Kondo screening and the quantum Hall edge structure originating from electrostatic screening. This edge structure, made up of compressible and incompressible stripes, strongly affects the Kondo temperature of the quantum dot and thereby influences the renormalized g factor.
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2013-12-01
Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low energy dynamics is described by Dirac electrons, but they are massive due to relatively large spin-orbit interactions. I will explain the following properties of silicene: 1) The band structure is controllable by applying an electric field. 2) Silicene undergoes a phase transition from a topological insulator to a band insulator by applying external electric field. 3) The topological phase transition can be detected experimentally by way of diamagnetism. 4) There is a novel valley-spin selection rules revealed by way of photon absorption. 5) Silicene yields a remarkably many phases such as quantum anomalous Hall phase and valley polarized metal when the exchange field is additionally introduced. 6) A silicon nanotubes can be used to convey spin currents under an electric field.
Quantum Hall effect in momentum space
NASA Astrophysics Data System (ADS)
Ozawa, Tomoki; Price, Hannah M.; Carusotto, Iacopo
2016-05-01
We theoretically discuss a momentum-space analog of the quantum Hall effect, which could be observed in topologically nontrivial lattice models subject to an external harmonic trapping potential. In our proposal, the Niu-Thouless-Wu formulation of the quantum Hall effect on a torus is realized in the toroidally shaped Brillouin zone. In this analogy, the position of the trap center in real space controls the magnetic fluxes that are inserted through the holes of the torus in momentum space. We illustrate the momentum-space quantum Hall effect with the noninteracting trapped Harper-Hofstadter model, for which we numerically demonstrate how this effect manifests itself in experimental observables. Extension to the interacting trapped Harper-Hofstadter model is also briefly considered. We finally discuss possible experimental platforms where our proposal for the momentum-space quantum Hall effect could be realized.
The Quantum Hall Liquid to Insulator Transitions.
NASA Astrophysics Data System (ADS)
Shahar, Dan
Among the stable phases known to exist in a two dimensional electronic system (2DES), the metallic phase is conspicuously missing. Nonetheless, metallic behavior characterized by finite conductivity as the temperature Tto 0, can be observed at local, isolated points. These are the critical points of quantum phase transitions separating the various stable phases. Although these phase transitions occur at T = 0 and are completely governed by quantum mechanical rules, the theoretical understanding of them is mainly in a critical phenomena framework, that is largely analogous to that used to describe traditional, thermodynamic, phase transitions. The purpose of this dissertation is to report on the identification and characterization of a new family of quantum transitions, between the quantum Hall effect and an insulating phase. In these transitions, the system is driven between a quantum Hall liquid and an insulating phase by changing the externally applied magnetic field (B), or the electronic density, n. We conducted a comprehensive, systematic experiment that virtually encompasses the full range of sample quality available to date. In all, 70 samples were prepared and studied, many at very low T ( >20 mK) and high B (<15.5 T). We studied systematically the transport near the transitions both, in the Ohmic, and non-Ohmic, high current, regimes. For each transition studied a clear, temperature independent, transition B field that separates the QHE liquid state and the insulating phase can be unambiguously determined. We find that despite the large disparity in the properties of our samples, the transport behavior near the transition points is virtually indistinguishable from sample to sample. In particular, the resistivity value at the transition point is found to be universal, and close to the quantum unit of resistance, h/e^2. Also, the behavior of the systems upon approaching the transitions obeys scaling rules with the same critical exponents for all the
Ideal Tearing in the Hall Regime
NASA Astrophysics Data System (ADS)
Pucci, F.; Velli, M.; Tenerani, A.
2015-12-01
Magnetic reconnection is generally believed to be the mechanism thatexplains explosive events in astrophysical plasmas, such as flares inthe solar corona, substorms. One of the main questions which remainsconcerns how magnetic reconnection may account for the fast magneticenergy conversion to kinetic and thermal energies. Recently it hasbeen shown by Pucci and Velli (2014) that, assuming that currentsheets scales as different powers of the magnetic Reynolds number S,the growth rate of the tearing mode instability in current sheetsincreases as the sheets thin and, once the thickness reaches a scalinga/L ˜ S-1/3, the time scale for the instability to develop becomesof the order of the Alfvén time. In Hall reconnection, dispersivewaves introduced by the Hall effect make the energy release ratesfaster. This effect becomes important to the collisional tearing modeinstability when the thickness of magnetic reversal layer iscomparable to the ion inertia length, where Hall currents produce athree-dimensional quadrupole structure of magnetic field. Here wepresent a linear study aiming to show how an "ideal tearing mode" isachieved when Hall effects are included, including scaling laws forsheet aspect ratios and growth rates.
Spectral Properties of Fractional Quantum Hall Hamiltonians
NASA Astrophysics Data System (ADS)
Weerasinghe, Amila
The fractional quantum Hall (FQH) effect plays a prominent role in the study of topological phases of matter and of strongly correlated electron systems in general. FQH systems have been demonstrated to show many interesting novel properties such as fractional charges, and are believed to harbor even more intriguing phenomena such as fractional statistics. However, there remain many interesting questions to be addressed in this regime. The work reported in this thesis aims to push the envelope of our understanding of the low-energy properties of FQH states using microscopic principles. In the first part of the thesis, we present a systematic perturbative approach to study excitations in the thin cylinder/torus limit of the quantum Hall states. The approach is applied to the Haldane-Rezayi and Gaffnian quantum Hall states, which are both expected to have gapless excitations in the usual two-dimensional thermodynamic limit. For the Haldane-Rezayi state, we confirm that gapless excitations are present also in the "one-dimensional" thermodynamic limit of an infinite thin cylinder, in agreement with earlier considerations based on the wave functions alone. In contrast, we identify the lowest excitations of the Gaffnian state in the thin cylinder limit, and conclude that they are gapped, using a combination of perturbative and numerical means. We discuss possible scenarios for the cross-over between the two-dimensional and the one-dimensional thermodynamic limit in this case. In the second part of the thesis, we study the low energy spectral properties of positive center-of-mass conserving two-body Hamiltonians as they arise in models of FQH states. Starting from the observation that positive many-body Hamiltonians must have ground state energies that increase monotonously in particle number, we explore what general additional constraints can be obtained for two-body interactions with "center-of-mass conservation" symmetry, both in the presence and absence of particle
NASA Astrophysics Data System (ADS)
Gerhardts, Rolf R.
2017-01-01
Recent low-temperature scanning-force-microscopy experiments on narrow Hall bars, under the conditions of the integer quantum Hall effect (IQHE) and its breakdown, have revealed an interesting position dependence of the Hall potential, which changes drastically with the applied magnetic field and the strength of the imposed current through the sample. The present paper shows, that inclusion of Joule heating into an existing self-consistent theory of screening and magneto-transport, which assumes translation invariant Hall bars with a homogeneous background charge due to doping, can explain the experimental results on the breakdown of the IQHE in the so called edge-dominated regime.
Modulated phases of graphene quantum Hall polariton fluids
Pellegrino, Francesco M. D.; Giovannetti, Vittorio; MacDonald, Allan H.; Polini, Marco
2016-01-01
There is a growing experimental interest in coupling cavity photons to the cyclotron resonance excitations of electron liquids in high-mobility semiconductor quantum wells or graphene sheets. These media offer unique platforms to carry out fundamental studies of exciton-polariton condensation and cavity quantum electrodynamics in a regime, in which electron–electron interactions are expected to play a pivotal role. Here, focusing on graphene, we present a theoretical study of the impact of electron–electron interactions on a quantum Hall polariton fluid, that is a fluid of magneto-excitons resonantly coupled to cavity photons. We show that electron–electron interactions are responsible for an instability of graphene integer quantum Hall polariton fluids towards a modulated phase. We demonstrate that this phase can be detected by measuring the collective excitation spectra, which is often at a characteristic wave vector of the order of the inverse magnetic length. PMID:27841346
Modulated phases of graphene quantum Hall polariton fluids
NASA Astrophysics Data System (ADS)
Pellegrino, Francesco M. D.; Giovannetti, Vittorio; MacDonald, Allan H.; Polini, Marco
2016-11-01
There is a growing experimental interest in coupling cavity photons to the cyclotron resonance excitations of electron liquids in high-mobility semiconductor quantum wells or graphene sheets. These media offer unique platforms to carry out fundamental studies of exciton-polariton condensation and cavity quantum electrodynamics in a regime, in which electron-electron interactions are expected to play a pivotal role. Here, focusing on graphene, we present a theoretical study of the impact of electron-electron interactions on a quantum Hall polariton fluid, that is a fluid of magneto-excitons resonantly coupled to cavity photons. We show that electron-electron interactions are responsible for an instability of graphene integer quantum Hall polariton fluids towards a modulated phase. We demonstrate that this phase can be detected by measuring the collective excitation spectra, which is often at a characteristic wave vector of the order of the inverse magnetic length.
Logarithmic correlations in quantum Hall plateau transitions
NASA Astrophysics Data System (ADS)
Vasseur, Romain
2015-07-01
The critical behavior of quantum Hall transitions in two-dimensional disordered electronic systems can be described by a class of complicated, nonunitary conformal field theories with logarithmic correlations. The nature and the physical origin of these logarithmic correlation functions remain, however, mysterious. Using the replica trick and the underlying symmetries of these quantum critical points, we show here how to construct nonperturbatively disorder-averaged observables in terms of Green's functions that scale logarithmically at criticality. In the case of the spin quantum Hall transition, which may occur in disordered superconductors with spin-rotation symmetry and broken time reversal invariance, we argue that our results are compatible with an alternative approach based on supersymmetry. The generalization to the integer quantum Hall plateau transition is also discussed.
Josephson effect without superconductivity: realization in quantum Hall bilayers.
Fogler, M M; Wilczek, F
2001-02-26
We show that a quantum Hall bilayer with the total filling nu = 1 should exhibit a dynamical regime similar to the flux flow in large Josephson junctions. This analogy may explain a conspicuous peak in the interlayer tunneling conductance [Phys. Rev. Lett. 84, 5808 (2000)]. The flux flow is likely to be spatiotemporally chaotic at low-bias voltage, which will manifest itself through broadband noise. The peak position can be controlled by an in-plane magnetic field.
Integer Quantum Hall Effect in Trilayer Graphene
NASA Astrophysics Data System (ADS)
Kumar, A.; Escoffier, W.; Poumirol, J. M.; Faugeras, C.; Arovas, D. P.; Fogler, M. M.; Guinea, F.; Roche, S.; Goiran, M.; Raquet, B.
2011-09-01
By using high-magnetic fields (up to 60 T), we observe compelling evidence of the integer quantum Hall effect in trilayer graphene. The magnetotransport fingerprints are similar to those of the graphene monolayer, except for the absence of a plateau at a filling factor of ν=2. At a very low filling factor, the Hall resistance vanishes due to the presence of mixed electron and hole carriers induced by disorder. The measured Hall resistivity plateaus are well reproduced theoretically, using a self-consistent Hartree calculations of the Landau levels and assuming an ABC stacking order of the three layers.
Quantum Hall Physics Equals Noncommutive Field Theory
Rammsdonk , Mark van
2001-08-09
In this note, we study a matrix-regularized version of non-commutative U(1) Chern-Simons theory proposed recently by Polychronakos. We determine a complete minimal basis of exact wavefunctions for the theory at arbitrary level k and rank N and show that these are in one-to-one correspondence with Laughlin-type wavefunctions describing excitations of a quantum Hall droplet composed of N electrons at filling fraction 1/k. The finite matrix Chern-Simons theory is shown to be precisely equivalent to the theory of composite fermions in the lowest Landau level, believed to provide an accurate description of the filling fraction 1/k fractional quantum Hall state. In the large N limit, this implies that level k noncommutative U(1) Chern-Simons theory is equivalent to the Laughlin theory of the filling fraction 1k quantum Hall fluid, as conjectured recently by Susskind.
Edge reconstructions in fractional quantum Hall systems.
NASA Astrophysics Data System (ADS)
Joglekar, Yogesh; Nguyen, Hoang; Murthy, Ganpathy
2003-03-01
Two dimensional electron systems exhibiting fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations are possible [1]. We present a microscopic calculation of these egde-states at filling factors ν=1/3 and ν=2/5 using the Hamiltonian theory of the fractional quantum Hall effect [2]. We find that the quantum Hall egde undergoes a reconstruction as the confining potential, produced by the background charge density, softens [3,4]. Our results have implications to the tunneling experiments into the edge of a fractional quantum Hall system [5]. 1: X. G.Wen, Phys. Rev. Lett. 64, 2206 (1990). 2: R. Shankar and G. Murthy, Phys. Rev. Lett. 79, 4437 (1997). 3: C. de C. Chamon and X. G. Wen, Phys. Rev. B 49, 8227 (1994). 4: X. Wan, K. Yang, and E. H. Razayi, Phys. Rev. Lett. 88, 056802 (2002). 5: A.M.Chang et al., Phys. Rev. Lett. 86, 143 (2000).
Quantum energy teleportation in a quantum Hall system
Yusa, Go; Izumida, Wataru; Hotta, Masahiro
2011-09-15
We propose an experimental method for a quantum protocol termed quantum energy teleportation (QET), which allows energy transportation to a remote location without physical carriers. Using a quantum Hall system as a realistic model, we discuss the physical significance of QET and estimate the order of energy gain using reasonable experimental parameters.
NASA Astrophysics Data System (ADS)
Guterding, Daniel; Jeschke, Harald O.; Valentí, Roser
2016-05-01
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach to the natural mineral herbertsmithite. We prove the feasibility of the proposed modifications by performing ab-initio density functional theory calculations and demonstrate the occurrence of the predicted effects using realistic models. Our results herald a new family of quantum anomalous Hall and quantum spin Hall insulators at affordable energy/temperature scales based on kagome lattices of transition metal ions.
Guterding, Daniel; Jeschke, Harald O.; Valentí, Roser
2016-01-01
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach to the natural mineral herbertsmithite. We prove the feasibility of the proposed modifications by performing ab-initio density functional theory calculations and demonstrate the occurrence of the predicted effects using realistic models. Our results herald a new family of quantum anomalous Hall and quantum spin Hall insulators at affordable energy/temperature scales based on kagome lattices of transition metal ions. PMID:27185665
Guterding, Daniel; Jeschke, Harald O; Valentí, Roser
2016-05-17
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach to the natural mineral herbertsmithite. We prove the feasibility of the proposed modifications by performing ab-initio density functional theory calculations and demonstrate the occurrence of the predicted effects using realistic models. Our results herald a new family of quantum anomalous Hall and quantum spin Hall insulators at affordable energy/temperature scales based on kagome lattices of transition metal ions.
Contactless measurement of alternating current conductance in quantum Hall structures
Drichko, I. L.; Diakonov, A. M.; Malysh, V. A.; Smirnov, I. Yu.; Ilyinskaya, N. D.; Usikova, A. A.; Galperin, Y. M.; Kummer, M.; Känel, H. von
2014-10-21
We report a procedure to determine the frequency-dependent conductance of quantum Hall structures in a broad frequency domain. The procedure is based on the combination of two known probeless methods—acoustic spectroscopy and microwave spectroscopy. By using the acoustic spectroscopy, we study the low-frequency attenuation and phase shift of a surface acoustic wave in a piezoelectric crystal in the vicinity of the electron (hole) layer. The electronic contribution is resolved using its dependence on a transverse magnetic field. At high frequencies, we study the attenuation of an electromagnetic wave in a coplanar waveguide. To quantitatively calibrate these data, we use the fact that in the quantum-Hall-effect regime the conductance at the maxima of its magnetic field dependence is determined by extended states. Therefore, it should be frequency independent in a broad frequency domain. The procedure is verified by studies of a well-characterized p-SiGe/Ge/SiGe heterostructure.
Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator.
Feng, Yang; Feng, Xiao; Ou, Yunbo; Wang, Jing; Liu, Chang; Zhang, Liguo; Zhao, Dongyang; Jiang, Gaoyuan; Zhang, Shou-Cheng; He, Ke; Ma, Xucun; Xue, Qi-Kun; Wang, Yayu
2015-09-18
We report experimental investigations on the quantum phase transition between the two opposite Hall plateaus of a quantum anomalous Hall insulator. We observe a well-defined plateau with zero Hall conductivity over a range of magnetic field around coercivity when the magnetization reverses. The features of the zero Hall plateau are shown to be closely related to that of the quantum anomalous Hall effect, but its temperature evolution exhibits a significant difference from the network model for a conventional quantum Hall plateau transition. We propose that the chiral edge states residing at the magnetic domain boundaries, which are unique to a quantum anomalous Hall insulator, are responsible for the novel features of the zero Hall plateau.
Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator
Feng, Yang; Feng, Xiao; Ou, Yunbo; Wang, Jing; Liu, Chang; Zhang, Liguo; Zhao, Dongyang; Jiang, Gaoyuan; Zhang, Shou-Cheng; He, Ke; Ma, Xucun; Xue, Qi-Kun; Wang, Yayu
2015-09-16
We report experimental investigations on the quantum phase transition between the two opposite Hall plateaus of a quantum anomalous Hall insulator. We observe a well-defined plateau with zero Hall conductivity over a range of magnetic field around coercivity when the magnetization reverses. The features of the zero Hall plateau are shown to be closely related to that of the quantum anomalous Hall effect, but its temperature evolution exhibits a significant difference from the network model for a conventional quantum Hall plateau transition. We propose that the chiral edge states residing at the magnetic domain boundaries, which are unique to a quantum anomalous Hall insulator, are responsible for the novel features of the zero Hall plateau.
Metal-to-insulator switching in quantum anomalous Hall states
NASA Astrophysics Data System (ADS)
Kou, Xufeng; Pan, Lei; Wang, Jing; Fan, Yabin; Choi, Eun Sang; Lee, Wei-Li; Nie, Tianxiao; Murata, Koichi; Shao, Qiming; Zhang, Shou-Cheng; Wang, Kang L.
2015-10-01
After decades of searching for the dissipationless transport in the absence of any external magnetic field, quantum anomalous Hall effect (QAHE) was recently achieved in magnetic topological insulator films. However, the universal phase diagram of QAHE and its relation with quantum Hall effect (QHE) remain to be investigated. Here, we report the experimental observation of the giant longitudinal resistance peak and zero Hall conductance plateau at the coercive field in the six quintuple-layer (Cr0.12Bi0.26Sb0.62)2Te3 film, and demonstrate the metal-to-insulator switching between two opposite QAHE plateau states up to 0.3 K. Moreover, the universal QAHE phase diagram is confirmed through the angle-dependent measurements. Our results address that the quantum phase transitions in both QAHE and QHE regimes are in the same universality class, yet the microscopic details are different. In addition, the realization of the QAHE insulating state unveils new ways to explore quantum phase-related physics and applications.
Metal-to-insulator switching in quantum anomalous Hall states
Kou, Xufeng; Pan, Lei; Wang, Jing; ...
2015-10-07
After decades of searching for the dissipationless transport in the absence of any external magnetic field, quantum anomalous Hall effect (QAHE) was recently achieved in magnetic topological insulator films. However, the universal phase diagram of QAHE and its relation with quantum Hall effect (QHE) remain to be investigated. Here, we report the experimental observation of the giant longitudinal resistance peak and zero Hall conductance plateau at the coercive field in the six quintuple-layer (Cr0.12Bi0.26Sb0.62)2Te3 film, and demonstrate the metal-to-insulator switching between two opposite QAHE plateau states up to 0.3 K. Moreover, the universal QAHE phase diagram is confirmed through themore » angle-dependent measurements. Our results address that the quantum phase transitions in both QAHE and QHE regimes are in the same universality class, yet the microscopic details are different. Additionally, the realization of the QAHE insulating state unveils new ways to explore quantum phase-related physics and applications.« less
Metal-to-insulator switching in quantum anomalous Hall states
Kou, Xufeng; Pan, Lei; Wang, Jing; Fan, Yabin; Choi, Eun Sang; Lee, Wei -Li; Nie, Tianxiao; Murata, Koichi; Shao, Qiming; Zhang, Shou -Cheng; Wang, Kang L.
2015-10-07
After decades of searching for the dissipationless transport in the absence of any external magnetic field, quantum anomalous Hall effect (QAHE) was recently achieved in magnetic topological insulator films. However, the universal phase diagram of QAHE and its relation with quantum Hall effect (QHE) remain to be investigated. Here, we report the experimental observation of the giant longitudinal resistance peak and zero Hall conductance plateau at the coercive field in the six quintuple-layer (Cr_{0.12}Bi_{0.26}Sb_{0.62})_{2}Te_{3} film, and demonstrate the metal-to-insulator switching between two opposite QAHE plateau states up to 0.3 K. Moreover, the universal QAHE phase diagram is confirmed through the angle-dependent measurements. Our results address that the quantum phase transitions in both QAHE and QHE regimes are in the same universality class, yet the microscopic details are different. Additionally, the realization of the QAHE insulating state unveils new ways to explore quantum phase-related physics and applications.
The Quantum Anomalous Hall Effect: Theory and Experiment
NASA Astrophysics Data System (ADS)
Liu, Chao-Xing; Zhang, Shou-Cheng; Qi, Xiao-Liang
2016-03-01
The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without an external magnetic field. The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have potential applications in future electronic devices. In recent years, the quantum anomalous Hall effect was proposed theoretically and realized experimentally. In this review article, we provide a systematic overview of the theoretical and experimental developments in this field.
Quantum anomalous Hall effect in real materials
NASA Astrophysics Data System (ADS)
Zhang, Jiayong; Zhao, Bao; Zhou, Tong; Yang, Zhongqin
2016-11-01
Under a strong magnetic field, the quantum Hall (QH) effect can be observed in two-dimensional electronic gas systems. If the quantized Hall conductivity is acquired in a system without the need of an external magnetic field, then it will give rise to a new quantum state, the quantum anomalous Hall (QAH) state. The QAH state is a novel quantum state that is insulating in the bulk but exhibits unique conducting edge states topologically protected from backscattering and holds great potential for applications in low-power-consumption electronics. The realization of the QAH effect in real materials is of great significance. In this paper, we systematically review the theoretical proposals that have been brought forward to realize the QAH effect in various real material systems or structures, including magnetically doped topological insulators, graphene-based systems, silicene-based systems, two-dimensional organometallic frameworks, quantum wells, and functionalized Sb(111) monolayers, etc. Our paper can help our readers to quickly grasp the recent developments in this field. Project supported by the National Basic Research Program of China (Grant No. 2011CB921803), the National Natural Science Foundation of China (Grant No. 11574051), the Natural Science Foundation of Shanghai, China (Grant No. 14ZR1403400), and Fudan High-end Computing Center, China.
Developments in the quantum Hall effect.
von Klitzing, Klaus
2005-09-15
The most important applications of the quantum Hall effect (QHE) are in the field of metrology. The observed quantization of the resistance is primarily used for the reproduction of the SI unit ohm, but is also important for high precision measurements of both the fine structure constant and the Planck constant. Some current QHE research areas include the analysis of new electron-electron correlation phenomena and the development of a more complete microscopic picture of this quantum effect. Recently, scanning force microscopy (SFM) of the potential distribution in QHE devices has been used to enhance the microscopic understanding of current flow in quantum Hall systems. This confirms the importance of the theoretically predicted stripes of compressible and incompressible electronic states close to the boundary of the QHE devices.
Integer quantum Hall effect in graphene
NASA Astrophysics Data System (ADS)
Jellal, Ahmed
2016-04-01
We study the quantum Hall effect in a monolayer graphene by using an approach based on thermodynamical properties. This can be done by considering a system of Dirac particles in an electromagnetic field and taking into account of the edges effect as a pseudo-potential varying continuously along the x direction. At low temperature and in the weak electric field limit, we explicitly determine the thermodynamical potential. With this, we derive the particle numbers in terms of the quantized flux and therefore the Hall conductivity immediately follows.
Induced Superconductivity in the Quantum Spin Hall Edge
NASA Astrophysics Data System (ADS)
Ren, Hechen; Hart, Sean; Wagner, Timo; Leubner, Philipp; Muehlbauer, Mathias; Bruene, Christoph; Buhmann, Hartmut; Molenkamp, Laurens; Yacoby, Amir
2014-03-01
Two-dimensional topological insulators have a gapped bulk and helical edge states, making it a quantum spin Hall insulator. Combining such edge states with superconductivity can be an excellent platform for observing and manipulating localized Majorana fermions. In the context of condensed matter, these are emergent electronic states that obey non-Abelian statistics and hence support fault-tolerant quantum computing. To realize such theoretical constructions, an essential step is to show these edge channels are capable of carrying coherent supercurrent. In our experiment, we fabricate Josephson junctions with HgTe/HgCdTe quantum wells, a two-dimensional material that becomes a quantum spin Hall insulator when the quantum well is thicker than 6.3 nm and the bulk density is depleted. In this regime, we observe supercurrents whose densities are confined to the edges of the junctions, with edge widths ranging from 180 nm to 408 nm. To verify the topological nature of these edges, we measure identical junctions with HgTe/HgCdTe quantum wells thinner than 6.3 nm and observe only uniform supercurrent density across the junctions. This research is supported by Microsoft Corporation Project Q, the NSF DMR-1206016, the DOE SCGF Program, the German Research Foundation, and EU ERC-AG program.
Tunnelling between the edges of two lateral quantum Hall systems
Kang; Stormer; Pfeiffer; Baldwin; West
2000-01-06
The edge of a two-dimensional electron system in a magnetic field consists of one-dimensional channels that arise from the confining electric field at the edge of the system. The crossed electric and magnetic fields cause electrons to drift parallel to the sample boundary, creating a chiral current that travels along the edge in only one direction. In an ideal two-dimensional electron system in the quantum Hall regime, all the current flows along the edge. Quantization of the Hall resistance arises from occupation of N one-dimensional edge channels, each contributing a conductance of e2/h. Here we report differential conductance measurements, in the integer quantum Hall regime, of tunnelling between the edges of a pair of two-dimensional electron systems that are separated by an atomically precise, high-quality, tunnel barrier. The resultant interaction between the edge states leads to the formation of new energy gaps and an intriguing dispersion relation for electrons travelling along the barrier: for example, we see a persistent conductance peak at zero bias voltage and an absence of tunnelling features due to electron spin. These features are unexpected and are not consistent with a model of weakly interacting edge states. Remnant disorder along the barrier and charge screening may each play a role, although detailed numerical studies will be required to elucidate these effects.
NASA Astrophysics Data System (ADS)
Nakagawa, Takahiro; Akera, Hiroshi; Suzuura, Hidekatsu
2005-06-01
Spatial variations of the electron temperature are calculated in the linear-response regime in a quantum Hall system with a potential discontinuity in the current direction. It is shown that the sign of the induced deviation of the electron temperature from the lattice temperature exhibits quantum oscillations.
Destruction of the Fractional Quantum Hall Effect by Disorder
DOE R&D Accomplishments Database
Laughlin, R. B.
1985-07-01
It is suggested that Hall steps in the fractional quantum Hall effect are physically similar to those in the ordinary quantum Hall effect. This proposition leads to a simple scaling diagram containing a new type of fixed point, which is identified with the destruction of the fractional states by disorder. 15 refs., 3 figs.
Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics.
Grauer, S; Fijalkowski, K M; Schreyeck, S; Winnerlein, M; Brunner, K; Thomale, R; Gould, C; Molenkamp, L W
2017-06-16
We report on the scaling behavior of V-doped (Bi,Sb)_{2}Te_{3} samples in the quantum anomalous Hall regime for samples of various thickness. While previous quantum anomalous Hall measurements showed the same scaling as expected from a two-dimensional integer quantum Hall state, we observe a dimensional crossover to three spatial dimensions as a function of layer thickness. In the limit of a sufficiently thick layer, we find scaling behavior matching the flow diagram of two parallel conducting topological surface states of a three-dimensional topological insulator each featuring a fractional shift of 1/2e^{2}/h in the flow diagram Hall conductivity, while we recover the expected integer quantum Hall behavior for thinner layers. This constitutes the observation of a distinct type of quantum anomalous Hall effect, resulting from 1/2e^{2}/h Hall conductance quantization of three-dimensional topological insulator surface states, in an experiment which does not require decomposition of the signal to separate the contribution of two surfaces. This provides a possible experimental link between quantum Hall physics and axion electrodynamics.
Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics
NASA Astrophysics Data System (ADS)
Grauer, S.; Fijalkowski, K. M.; Schreyeck, S.; Winnerlein, M.; Brunner, K.; Thomale, R.; Gould, C.; Molenkamp, L. W.
2017-06-01
We report on the scaling behavior of V-doped (Bi ,Sb )2Te3 samples in the quantum anomalous Hall regime for samples of various thickness. While previous quantum anomalous Hall measurements showed the same scaling as expected from a two-dimensional integer quantum Hall state, we observe a dimensional crossover to three spatial dimensions as a function of layer thickness. In the limit of a sufficiently thick layer, we find scaling behavior matching the flow diagram of two parallel conducting topological surface states of a three-dimensional topological insulator each featuring a fractional shift of 1/2 e2/h in the flow diagram Hall conductivity, while we recover the expected integer quantum Hall behavior for thinner layers. This constitutes the observation of a distinct type of quantum anomalous Hall effect, resulting from 1/2 e2/h Hall conductance quantization of three-dimensional topological insulator surface states, in an experiment which does not require decomposition of the signal to separate the contribution of two surfaces. This provides a possible experimental link between quantum Hall physics and axion electrodynamics.
Mani, Arjun; Benjamin, Colin
2016-04-13
On the surface of 2D topological insulators, 1D quantum spin Hall (QSH) edge modes occur with Dirac-like dispersion. Unlike quantum Hall (QH) edge modes, which occur at high magnetic fields in 2D electron gases, the occurrence of QSH edge modes is due to spin-orbit scattering in the bulk of the material. These QSH edge modes are spin-dependent, and chiral-opposite spins move in opposing directions. Electronic spin has a larger decoherence and relaxation time than charge. In view of this, it is expected that QSH edge modes will be more robust to disorder and inelastic scattering than QH edge modes, which are charge-dependent and spin-unpolarized. However, we notice no such advantage accrues in QSH edge modes when subjected to the same degree of contact disorder and/or inelastic scattering in similar setups as QH edge modes. In fact we observe that QSH edge modes are more susceptible to inelastic scattering and contact disorder than QH edge modes. Furthermore, while a single disordered contact has no effect on QH edge modes, it leads to a finite charge Hall current in the case of QSH edge modes, and thus a vanishing of the pure QSH effect. For more than a single disordered contact while QH states continue to remain immune to disorder, QSH edge modes become more susceptible--the Hall resistance for the QSH effect changes sign with increasing disorder. In the case of many disordered contacts with inelastic scattering included, while quantization of Hall edge modes holds, for QSH edge modes a finite charge Hall current still flows. For QSH edge modes in the inelastic scattering regime we distinguish between two cases: with spin-flip and without spin-flip scattering. Finally, while asymmetry in sample geometry can have a deleterious effect in the QSH case, it has no impact in the QH case.
NASA Astrophysics Data System (ADS)
Mani, Arjun; Benjamin, Colin
2016-04-01
On the surface of 2D topological insulators, 1D quantum spin Hall (QSH) edge modes occur with Dirac-like dispersion. Unlike quantum Hall (QH) edge modes, which occur at high magnetic fields in 2D electron gases, the occurrence of QSH edge modes is due to spin-orbit scattering in the bulk of the material. These QSH edge modes are spin-dependent, and chiral-opposite spins move in opposing directions. Electronic spin has a larger decoherence and relaxation time than charge. In view of this, it is expected that QSH edge modes will be more robust to disorder and inelastic scattering than QH edge modes, which are charge-dependent and spin-unpolarized. However, we notice no such advantage accrues in QSH edge modes when subjected to the same degree of contact disorder and/or inelastic scattering in similar setups as QH edge modes. In fact we observe that QSH edge modes are more susceptible to inelastic scattering and contact disorder than QH edge modes. Furthermore, while a single disordered contact has no effect on QH edge modes, it leads to a finite charge Hall current in the case of QSH edge modes, and thus a vanishing of the pure QSH effect. For more than a single disordered contact while QH states continue to remain immune to disorder, QSH edge modes become more susceptible—the Hall resistance for the QSH effect changes sign with increasing disorder. In the case of many disordered contacts with inelastic scattering included, while quantization of Hall edge modes holds, for QSH edge modes a finite charge Hall current still flows. For QSH edge modes in the inelastic scattering regime we distinguish between two cases: with spin-flip and without spin-flip scattering. Finally, while asymmetry in sample geometry can have a deleterious effect in the QSH case, it has no impact in the QH case.
Current Distributions in Quantum Hall Effect Devices
Cage, M. E.
1997-01-01
This paper addresses the question of how current is distributed within quantum Hall effect devices. Three types of flow patterns most often mentioned in the literature are considered. They are: (1) skipping orbits along the device periphery (which arise from elastic collisions off hard-walled potentials); (2) narrow conducting channels along the device sides (which are presumed to be generated from confining potentials); and (3) currents distributed throughout the device (which are assumed to arise from a combination of confining and charge-redistribution potentials). The major conclusions are that skipping orbits do not occur in quantum Hall effect devices, and that nearly all of the externally applied current is located within the device interior rather than along the device edges. PMID:27805115
Toward realistic effective models of quantum-Hall edges
NASA Astrophysics Data System (ADS)
Zülicke, U.; MacDonald, A. H.
1998-01-01
We have investigated the dynamical properties of edge excitations in the (fractional) quantum-Hall regime for a sharp confining potential, emphasizing the effects resulting from the presence of long-range interaction. Our study uses chiral-Luttinger-liquid models that are motivated by the close analogy between the physics of edge excitations and that of plasmons in quasi-one-dimensional electron systems. We find that incorporating realistic long-range interaction is especially important for multi-branch edges. Results are presented for the tunneling-IV-curve power-law exponent and the two-terminal conductance.
Energy relaxation at quantum Hall edge
NASA Astrophysics Data System (ADS)
Levkivskyi, Ivan P.; Sukhorukov, Eugene V.
2012-02-01
In this work, we address the recent experiments [C. Altimiras , Nat. Phys.1745-247310.1038/nphys1429 6, 34 (2010); H. le Sueur , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.105.056803 105, 056803 (2010);C. Altimiras , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.105.226804 105, 226804 (2010)], where an electron distribution function at the quantum Hall (QH) edge at filling factor ν=2 has been measured with high precision. It has been reported that the energy of electrons injected into one of the two chiral edge channels with the help of a quantum point contact (QPC) is equally distributed between them, in agreement with earlier predictions, one being based on the Fermi gas approach [A. M. Lunde , Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.81.041311 81, 041311(R) (2010)] and the other utilizing the Luttinger-liquid theory [P. Degiovanni , Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.81.121302 81, 121302(R) (2010)]. We argue that the physics of the energy relaxation process at the QH edge may in fact be more rich, providing the possibility for discriminating between two physical pictures in experiment. Namely, using the recently proposed nonequilibrium bosonization technique [I. P. Levkivskyi , Phys. Rev. Lett., PRLTAO0031-900710.1103/PhysRevLett.103.036801 103, 036801 (2009)], we evaluate the electron distribution function and find that the initial “double-step” distribution created at a QPC evolves through several intermediate asymptotics before reaching eventual equilibrium state. At short distances, the distribution function is found to be asymmetric due to non-Gaussian current noise effects. At larger distances, where noise becomes Gaussian, the distribution function acquires symmetric Lorentzian shape. Importantly, in the regime of low QPC transparencies T, the width of the Lorentzian scales linearly with T, in contrast to the case of equilibrium Fermi distribution, the width of which scales as T. Therefore, we propose to do measurements at
Vibrational modes in the quantum Hall system
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Yan, Bin; Daily, Kevin; Greene, Chris H.
The hyperspherical adiabatic technique is more familiar to atomic and nuclear few-body systems, but can also be applied with high accuracy to the many-body quantum Hall problem. This technique reformulates the Schrödinger equation for N electrons into hyperspherical coordinates, which, after extracting the trivial center of mass, describes the system in terms of a single global size coordinate known as the hyperradius R, and 2 N - 3 remaining internal angular coordinates. The solutions are approximately separable in the hyperradial coordinate, and solutions in the system are found by treating the hyperradius as an adiabatic coordinate. The approximate separability of the wave functions in this coordinate suggests the presence of hyperradial vibrational modes which are not described in conventional theories. The vibrationally excited states share the internal geometry of their quantum Hall ground states, and their excitation frequencies may vary with the number of participating particles or the strength of the confinement. We plan to discuss the features of these vibrational modes and their possible detection in quantum Hall systems. NSF.
Topological edge states and fractional quantum Hall effect from umklapp scattering.
Klinovaja, Jelena; Loss, Daniel
2013-11-08
We study anisotropic lattice strips in the presence of a magnetic field in the quantum Hall effect regime. At specific magnetic fields, causing resonant umklapp scattering, the system is gapped in the bulk and supports chiral edge states in close analogy to topological insulators. In electron gases with stripes, these gaps result in plateaus for the Hall conductivity exactly at the known fillings n/m (both positive integers and m odd) for the integer and fractional quantum Hall effect. For double strips, we find topological phase transitions with phases that support midgap edge states with flat dispersion. The topological effects predicted here could be tested directly in optical lattices.
Duality in the quantum Hall system
NASA Astrophysics Data System (ADS)
Lütken, C. A.; Ross, G. G.
1992-05-01
We suggest that a unified description of the integer and fractional phases of the quantum Hall system may be possible if the scaling diagram of transport coefficients is invariant under linear fractional (modular) transformations. In this model the hierarchy of states, as well as the observed universality of critical exponents, are consequences of a discrete SL(2,openZ) symmetry acting on the parameter space of an effective quantum-field theory. Available scaling data on the position of delocalization fixed points in the integer case and the position of mobility fixed points in the fractional case agree with the model within experimental accuracy.
Dissipation and tunneling in quantum Hall bilayers.
Jack, Robert L; Lee, Derek K K; Cooper, Nigel R
2004-09-17
We discuss the interplay between transport and intrinsic dissipation in quantum Hall bilayers, within the framework of a simple thought experiment. We compute, for the first time, quantum corrections to the semiclassical dynamics of this system. This allows us to reinterpret tunneling measurements on these systems. We find a strong peak in the zero-temperature tunneling current that arises from the decay of Josephson-like oscillations into incoherent charge fluctuations. In the presence of an in-plane field, resonances in the tunneling current develop an asymmetric line shape.
From quantum confinement to quantum Hall effect in graphene nanostructures
NASA Astrophysics Data System (ADS)
Guimarães, M. H. D.; Shevtsov, O.; Waintal, X.; van Wees, B. J.
2012-02-01
We study the evolution of the two-terminal conductance plateaus with a magnetic field for armchair graphene nanoribbons (GNRs) and graphene nanoconstrictions (GNCs). For GNRs, the conductance plateaus of (2e2)/(h) at zero magnetic field evolve smoothly to the quantum Hall regime, where the plateaus in conductance at even multiples of (2e2)/(h) disappear. It is shown that the relation between the energy and magnetic field does not follow the same behavior as in “bulk” graphene, reflecting the different electronic structure of a GNR. For the nanoconstrictions we show that the conductance plateaus do not have the same sharp behavior in zero magnetic field as in a GNR, which reflects the presence of backscattering in such structures. Our results show good agreement with recent experiments on high-quality graphene nanoconstrictions. The behavior with the magnetic field for a GNC shows some resemblance to the one for a GNR but now depends also on the length of the constriction. By analyzing the evolution of the conductance plateaus in the presence of the magnetic field we can obtain the width of the structures studied and show that this is a powerful experimental technique in the study of the electronic and structural properties of narrow structures.
Supersonic regime of the Hall-magnetohydrodynamics resistive tearing instability
Ahedo, Eduardo; Ramos, Jesus J.
2012-07-15
An earlier analysis of the Hall-magnetohydrodynamics (MHD) tearing instability [E. Ahedo and J. J. Ramos, Plasma Phys. Controlled Fusion 51, 055018 (2009)] is extended to cover the regime where the growth rate becomes comparable or exceeds the sound frequency. Like in the previous subsonic work, a resistive, two-fluid Hall-MHD model with massless electrons and zero-Larmor-radius ions is adopted and a linear stability analysis about a force-free equilibrium in slab geometry is carried out. A salient feature of this supersonic regime is that the mode eigenfunctions become intrinsically complex, but the growth rate remains purely real. Even more interestingly, the dispersion relation remains of the same form as in the subsonic regime for any value of the instability Mach number, provided only that the ion skin depth is sufficiently small for the mode ion inertial layer width to be smaller than the macroscopic lengths, a generous bound that scales like a positive power of the Lundquist number.
Theory of fractional quantum Hall interferometers
NASA Astrophysics Data System (ADS)
Levkivskyi, Ivan P.; Fröhlich, Jürg; Sukhorukov, Eugene V.
2012-12-01
Interference of fractionally charged quasiparticles is expected to lead to Aharonov-Bohm oscillations with periods larger than the flux quantum. However, according to the Byers-Yang theorem, observables of an electronic system are invariant under an adiabatic insertion of a quantum of singular flux. We resolve this seeming paradox by considering a microscopic model of electronic interferometers made from a quantum Hall liquid at filling factor 1/m with the shape of a Corbino disk. In such interferometers, the quantum Hall edge states are utilized in place of optical beams, the quantum point contacts play the role of beam splitters connecting different edge channels, and Ohmic contacts represent a source and drain of quasiparticle currents. Depending on the position of Ohmic contacts, one distinguishes interferometers of Fabry-Pérot (FP) and Mach-Zehnder (MZ) type. An approximate ground state of such interferometers is described by a Laughlin-type wave function, and low-energy excitations are incompressible deformations of this state. We construct a low-energy effective theory by restricting the microscopic Hamiltonian of electrons to the space of incompressible deformations and show that the theory of the quantum Hall edge so obtained is a generalization of a chiral conformal field theory. In our theory, a quasiparticle tunneling operator is found to be a single-valued function of tunneling point coordinates, and its phase depends on the topology determined by the positions of Ohmic contacts. We describe strong coupling of the edge states to Ohmic contacts and the resulting quasiparticle current through the interferometer with the help of a master equation. We find that the coherent contribution to the average quasiparticle current through MZ interferometers does not vanish after summation over quasiparticle degrees of freedom. However, it acquires oscillations with the electronic period, in agreement with the Byers-Yang theorem. Importantly, our theory does not
Intrinsic Capacitances and Inductances of Quantum Hall Effect Devices.
Cage, M E; Jeffery, A
1996-01-01
Analytic solutions are obtained for the internal capacitances, kinetic inductances, and magnetic inductances of quantum Hall effect devices to investigate whether or not the quantized Hall resistance is the only intrinsic impedance of importance in measurements of the ac quantum Hall effect. The internal capacitances and inductances are obtained by using the results of Cage and Lavine, who determined the current and potential distributions across the widths of quantum Hall effect devices. These intrinsic capacitances and inductances produce small out-of-phase impedance corrections to the in-phase quantized Hall resistance and to the in-phase longitudinal resistance.
Tunneling between the Edges of Laterally Separated Quantum Hall Systems
NASA Astrophysics Data System (ADS)
Kang, Woowon
2001-03-01
In the quantum Hall effect (QHE) effect regime of a two-dimensional electron system (2DES), quantization of the Hall resistance, σ_xy= Ne^2/h, arises from occupation of N one-dimensional edge channels. As a prototypical one-dimensional electronic system, the physics of edge states in the QHE regime is of considerable theoretical and experimental interest. In this talk, we present our study of tunneling between two counter-flowing edge states separated by a barrier with high integrity. By embedding a thin, precise barrier in the plane of 2DES via cleaved edge overgrowth, we have successfully fabricated an in-plane tunneling device in which two 2DES's are separated by an atomically precise barrier on the order of magnetic length[1]. The tunneling in the quantum Hall regime is characterized by a rich spectrum of tunnel gaps and conductance peaks. While the relevant energy scale in the tunneling is largely determined by the bulk 2DES, evolution of the tunneling spectra with magnetic field reveals the electronic structure arising from superposition of two edge states near the barrier. However, the observed features are not consistent with a model of weakly interacting edge states and indicates importance of electron-electron interaction. In particular, absence of features due to the electron spin and the persistence of conductance peaks at zero bias point to existence of novel electronic correlation between the two edge states[2]. [1] W. Kang, H.L. Stormer, K.B. Baldwin, L.N. Pfeiffer, and K.W. West, Nature 403, 59 (2000) [2] A. Mitra and S. Girvin, preprint.
Quantum Beats of Resonant Tunneling between Fractional Quantum Hall Edges
NASA Astrophysics Data System (ADS)
Maasilta, Ilari J.; Goldman, V. J.
1997-03-01
We report measurements of resonant tunneling between two fractional quantum Hall edges in a quantum antidot geometry (I. J. Maasilta and V. J. Goldman, to appear in Phys. Rev. B 55),(1997).. We observe beats in the conductance oscillations, whose evolution as a function of experimental parameters is discussed. Possible explanations in terms of different models (G. Kirczenow Phys. Rev. B 53), 15767 (1996), M. Geller et. al, preprint. are presented.
Giant anisotropic magnetoresistance in a quantum anomalous Hall insulator
NASA Astrophysics Data System (ADS)
Kandala, Abhinav; Richardella, Anthony; Kempinger, Susan; Liu, Chao-Xing; Samarth, Nitin
2015-07-01
When a three-dimensional ferromagnetic topological insulator thin film is magnetized out-of-plane, conduction ideally occurs through dissipationless, one-dimensional (1D) chiral states that are characterized by a quantized, zero-field Hall conductance. The recent realization of this phenomenon, the quantum anomalous Hall effect, provides a conceptually new platform for studies of 1D transport, distinct from the traditionally studied quantum Hall effects that arise from Landau level formation. An important question arises in this context: how do these 1D edge states evolve as the magnetization is changed from out-of-plane to in-plane? We examine this question by studying the field-tilt-driven crossover from predominantly edge-state transport to diffusive transport in Crx(Bi,Sb)2-xTe3 thin films. This crossover manifests itself in a giant, electrically tunable anisotropic magnetoresistance that we explain by employing a Landauer-Büttiker formalism. Our methodology provides a powerful means of quantifying dissipative effects in temperature and chemical potential regimes far from perfect quantization.
Giant anisotropic magnetoresistance in a quantum anomalous Hall insulator.
Kandala, Abhinav; Richardella, Anthony; Kempinger, Susan; Liu, Chao-Xing; Samarth, Nitin
2015-07-07
When a three-dimensional ferromagnetic topological insulator thin film is magnetized out-of-plane, conduction ideally occurs through dissipationless, one-dimensional (1D) chiral states that are characterized by a quantized, zero-field Hall conductance. The recent realization of this phenomenon, the quantum anomalous Hall effect, provides a conceptually new platform for studies of 1D transport, distinct from the traditionally studied quantum Hall effects that arise from Landau level formation. An important question arises in this context: how do these 1D edge states evolve as the magnetization is changed from out-of-plane to in-plane? We examine this question by studying the field-tilt-driven crossover from predominantly edge-state transport to diffusive transport in Crx(Bi,Sb)(2-x)Te3 thin films. This crossover manifests itself in a giant, electrically tunable anisotropic magnetoresistance that we explain by employing a Landauer-Büttiker formalism. Our methodology provides a powerful means of quantifying dissipative effects in temperature and chemical potential regimes far from perfect quantization.
Line defects and quantum Hall plateaus in graphene
NASA Astrophysics Data System (ADS)
Dal Lago, V.; Foa Torres, L. E. F.
2015-04-01
Line defects in graphene can be either tailored-growth or arise naturally and are at the center of many discussions. Here we study the multiterminal conductance of graphene with an extended line defect in the quantum Hall regime analyzing the effects of the geometry of the setup, disorder and strain on the quantum Hall plateaus. We show that the defect turns out to affect the local and non-local conductance in very different ways depending on the geometrical configuration. When the defect is parallel to the sample edges one gets an equivalent circuit formed by parallel resistors. In contrast, when the defect bridges opposite edges, the Hall conductance may remain unaltered depending on the geometry of the voltage/current probes. The role of disorder, strain and the microscopic details of the defect in our results is also discussed. We show that the defect provides a realization of the electrical analog of an optical beam splitter. Its peculiar energy dependent inter-edge transmission allows it to be turned on or off at will and it may be used for routing the chiral edge states.
Line defects and quantum Hall plateaus in graphene.
Dal Lago, V; Torres, L E F Foa
2015-04-15
Line defects in graphene can be either tailored-growth or arise naturally and are at the center of many discussions. Here we study the multiterminal conductance of graphene with an extended line defect in the quantum Hall regime analyzing the effects of the geometry of the setup, disorder and strain on the quantum Hall plateaus. We show that the defect turns out to affect the local and non-local conductance in very different ways depending on the geometrical configuration. When the defect is parallel to the sample edges one gets an equivalent circuit formed by parallel resistors. In contrast, when the defect bridges opposite edges, the Hall conductance may remain unaltered depending on the geometry of the voltage/current probes. The role of disorder, strain and the microscopic details of the defect in our results is also discussed. We show that the defect provides a realization of the electrical analog of an optical beam splitter. Its peculiar energy dependent inter-edge transmission allows it to be turned on or off at will and it may be used for routing the chiral edge states.
Spatially resolved breakdown in reentrant quantum Hall states
NASA Astrophysics Data System (ADS)
Rossokhaty, Oleksandr; Folk, Joshua; Baum, Yuval; Stern, Ady; Watson, John; Gardner, Geoffrey; Manfra, Michael
Electrons in a two dimensional electron gas in the fractional quantum Hall regime may rearrange into a quasi-crystalline structure that gives rise to a reentrant Integer Quantum Hall (RIQH) effect in transport. As bias current increases, longitudinal and Hall resistivities measured for these states show multiple sharp breakdown transitions, a signature that is unique to RIQH states and has previously been ascribed to pinning-depinning transitions or to the development of bias-induced anisotropy. We present an alternate interpretation of the characteristic features of RIQH breakdown at high bias, based on spatially-resolved measurements that indicate a phase boundary between broken-down and unbroken regions propagating chirally from source and drain contacts as a function of bias current. As the phase boundary passes various contacts, its spreading generates multi-stage breakdown signatures like those reported elsewhere. Confirming numerical simulations, the chiral sense of the spreading is set not by the chirality of the edge state itself, but instead depends on electron- or hole-like character of the RIQH state.
Spin and Isospin: Exotic Order in Quantum Hall Ferromagnets
NASA Astrophysics Data System (ADS)
Girvin, Steven M.
Quantum mechanics is a strange business, and the quantum physics of strongly correlated many-electron systems can be stranger still. Good examples are the various quantum Hall effects. They are among the most remarkable many-body quantum phenomena discovered in the second half of the 20th century, comparable in intellectual import to superconductivity and superfluidity. The quantum Hall effects are an extremely rich set of phenomena with deep and truly fundamental theoretical implications...
Universality and phase diagram in the quantum Hall effect
NASA Astrophysics Data System (ADS)
Wong, Lauren Wai-Wing
We have designed and conducted detailed experiments to explore the following critical, unsolved issues in regarding to the global behavior of the two-dimensional electron gas (2DEG) in the presence of disorder and many-body interaction in the quantum Hall effect (QHE) regime: (1) nature of the quantum Hall liquid-Hall insulator (QHL-HI) phase transition induced by disorder, (2) topological phase diagram and possible existence of a thermodynamically stable "metallic phase" around filling factor nu =1/2, and (3) whether the termination of spin-resolved Landau levels in general a phase transition. First, I present our studies of the disorder-tuned QHL-HI phase transition in both the integer and fractional QHE regimes. We found that the longitudinal resistivity near the critical points shows reflection symmetry and good scaling behavior over a wide range of densities and temperature with the same critical exponent. This supports the notion that quantum phase transitions in the QHE belong to same universality class. Furthermore, the critical conductivities are universal at the transitions. Our approach to investigate the second issue is to map out the phase boundaries corresponding to different QHLs around nu =1/2. We identified a line on which the value of the Hall conductivity equals to 1/2(esp2/h) in the phase diagram; and an another line on which the value of the Hall resistivity equals to 2(h/esp2). We interpreted the later is a result predicted by the composite-fermion theory. The phase boundaries between the HI and the principal QHLs at nu =1 and 1/3 show levitation of the delocalized states of the first Landau levels for electrons and Composite fermions. Our data suggest that there is no true metallic state around nu =1/2. Finally, I present our magnetotransport studies of the spin-resolved integer QHE by changing disorder. For a given Landau level, the difference in filling factors of a pair of spin-split resistivity peaks changes rapidly from one to zero near
Thermoelectric effects in quantum Hall systems beyond linear response
NASA Astrophysics Data System (ADS)
López, Rosa; Hwang, Sun-Yong; Sánchez, David
2014-12-01
We consider a quantum Hall system with an antidot acting as a energy dependent scatterer. In the purely charge case, we find deviations from the Wiedemann-Franz law that take place in the nonlinear regime of transport. We also discuss Peltier effects beyond linear response and describe both effects using magnetic-field asymmetric transport coefficients. For the spin case such as that arising along the helical edge states of a two-dimensional topological insulator, we investigate the generation of spin currents as a result of applied voltage and temperature differences in samples attached to ferromagnetic leads. We find that in the parallel configuration the spin current can be tuned with the leads' polarization even in the linear regime of transport. In contrast, for antiparallel magnetizations the spin currents has a strict nonlinear dependence on the the applied fields.
Quantum pump in quantum spin Hall edge states
NASA Astrophysics Data System (ADS)
Cheng, Fang
2016-09-01
We present a theory for quantum pump in a quantum spin Hall bar with two quantum point contacts (QPCs). The pump currents can be generated by applying harmonically modulating gate voltages at QPCs. The phase difference between the gate voltages introduces an effective gauge field, which breaks the time-reversal symmetry and generates pump currents. The pump currents display very different pump frequency dependence for weak and strong e-e interaction. These unique properties are induced by the helical feature of the edge states, and therefore can be used to detect and control edge state transport.
Quantum Hall superfluids in topological insulator thin films.
Tilahun, Dagim; Lee, Byounghak; Hankiewicz, E M; MacDonald, A H
2011-12-09
Three-dimensional topological insulators have protected Dirac-cone surface states. In this Letter we argue that gapped excitonic superfluids with spontaneous coherence between top and bottom surfaces can occur in the topological insulator (TI)-thin-film quantum Hall regime. We find that the large dielectric constants of TI materials increase the layer separation range over which coherence survives and decrease the superfluid sound velocity, but have little influence on the superfluid density or on the charge gap. The coherent state at total Landau-level filling factor νT=0 is predicted to be free of edge modes, qualitatively altering its transport phenomenology compared to the widely studied case of νT=1 in GaAs double-quantum wells.
Excitons in the Fractional Quantum Hall Effect
DOE R&D Accomplishments Database
Laughlin, R. B.
1984-09-01
Quasiparticles of charge 1/m in the Fractional Quantum Hall Effect form excitons, which are collective excitations physically similar to the transverse magnetoplasma oscillations of a Wigner crystal. A variational exciton wavefunction which shows explicitly that the magnetic length is effectively longer for quasiparticles than for electrons is proposed. This wavefunction is used to estimate the dispersion relation of these excitons and the matrix elements to generate them optically out of the ground state. These quantities are then used to describe a type of nonlinear conductivity which may occur in these systems when they are relatively clean.
Quantum-Hall Activation Gaps in Graphene
NASA Astrophysics Data System (ADS)
Giesbers, A. J. M.; Zeitler, U.; Katsnelson, M. I.; Ponomarenko, L. A.; Mohiuddin, T. M.; Maan, J. C.
2007-11-01
We have measured the quantum-Hall activation gaps in graphene at filling factors ν=2 and ν=6 for magnetic fields up to 32 T and temperatures from 4 to 300 K. The ν=6 gap can be described by thermal excitation to broadened Landau levels with a width of 400 K. In contrast, the gap measured at ν=2 is strongly temperature and field dependent and approaches the expected value for sharp Landau levels for fields B>20T and temperatures T>100K. We explain this surprising behavior by a narrowing of the lowest Landau level.
Disordered Interactions and Fractional Quantum Hall States
NASA Astrophysics Data System (ADS)
Degottardi, Wade; Hafezi, Mohammad
The possibility that topological ordered states may be realized in photonic systems has recently attracted a great deal of attention. Given the rich phenomenology of the fractional quantum Hall effect, the bosonic Laughlin states have been of particular focus in this context. These states are known to arise in strongly nonlinear photonic lattices with artificial gauge fields, where nonlinearities associated with the resonators mimic on-site interactions. These effective interaction strengths are not universal and are subject to spatial disorder. We present a detailed study of the stability of these states and what implications they have for experiments.
Quantum inferring acausal structures and the Monty Hall problem
NASA Astrophysics Data System (ADS)
Kurzyk, Dariusz; Glos, Adam
2016-12-01
This paper presents a quantum version of the Monty Hall problem based upon the quantum inferring acausal structures, which can be identified with generalization of Bayesian networks. Considered structures are expressed in formalism of quantum information theory, where density operators are identified with quantum generalization of probability distributions. Conditional relations between quantum counterpart of random variables are described by quantum conditional operators. Presented quantum inferring structures are used to construct a model inspired by scenario of well-known Monty Hall game, where we show the differences between classical and quantum Bayesian reasoning.
In-plane magnetization-induced quantum anomalous Hall effect.
Liu, Xin; Hsu, Hsiu-Chuan; Liu, Chao-Xing
2013-08-23
The quantum Hall effect can only be induced by an out-of-plane magnetic field for two-dimensional electron gases, and similarly, the quantum anomalous Hall effect has also usually been considered for systems with only out-of-plane magnetization. In the present work, we predict that the quantum anomalous Hall effect can be induced by in-plane magnetization that is not accompanied by any out-of-plane magnetic field. Two realistic two-dimensional systems, Bi2Te3 thin film with magnetic doping and HgMnTe quantum wells with shear strains, are presented and the general condition for the in-plane magnetization-induced quantum anomalous Hall effect is discussed based on the symmetry analysis. Nonetheless, an experimental setup is proposed to confirm this effect, the observation of which will pave the way to search for the quantum anomalous Hall effect in a wider range of materials.
The Quantum Spin Hall Effect: Theory and Experiment
Konig, Markus; Buhmann, Hartmut; Molenkamp, Laurens W.; Hughes, Taylor L.; Liu, Chao-Xing; Qi, Xiao-Liang; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. Here we review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the band structure changes from a normal to an 'inverted' type at a critical thickness d{sub c}. We present an analytical solution of the helical edge states and explicitly demonstrate their topological stability. We also review the recent experimental observation of the QSH state in HgTe/(Hg,Cd)Te quantum wells. We review both the fabrication of the sample and the experimental setup. For thin quantum wells with well width d{sub QW} < 6.3 nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d{sub QW} > 6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2e{sup 2}/h. The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d{sub c} = 6.3 nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.
Quantum anomalous Hall and quantum spin-Hall phases in flattened Bi and Sb bilayers
Jin, Kyung-Hwan; Jhi, Seung-Hoon
2015-01-01
Discovery of two-dimensional topological insulator such as Bi bilayer initiates challenges in exploring exotic quantum states in low dimensions. We demonstrate a promising way to realize the Kane-Mele-type quantum spin Hall (QSH) phase and the quantum anomalous Hall (QAH) phase in chemically-modified Bi and Sb bilayers using first-principles calculations. We show that single Bi and Sb bilayers exhibit topological phase transitions from the band-inverted QSH phase or the normal insulator phase to Kane-Mele-type QSH phase upon chemical functionalization. We also predict that the QAH effect can be induced in Bi or Sb bilayers upon nitrogen deposition as checked from calculated Berry curvature and the Chern number. We explicitly demonstrate the spin-chiral edge states to appear in nitrogenated Bi-bilayer nanoribbons. PMID:25672932
Supersymmetric Quantum-Hall Effect on a Fuzzy Supersphere
Hasebe, Kazuki
2005-05-27
Supersymmetric quantum-Hall liquids are constructed on a supersphere in a supermonopole background. We derive a supersymmetric generalization of the Laughlin wave function, which is a ground state of a hard-core OSp(1 vertical bar 2) invariant Hamiltonian. We also present excited topological objects, which are fractionally charged deficits made by super Hall currents. Several relations between quantum-Hall systems and their supersymmetric extensions are discussed.
Quantum Hall Effect and Quillen Metric
NASA Astrophysics Data System (ADS)
Klevtsov, Semyon; Ma, Xiaonan; Marinescu, George; Wiegmann, Paul
2017-02-01
We study the generating functional, the adiabatic curvature and the adiabatic phase for the integer quantum Hall effect (QHE) on a compact Riemann surface. For the generating functional we derive its asymptotic expansion for the large flux of the magnetic field, i.e., for the large degree k of the positive Hermitian line bundle L k . The expansion consists of the anomalous and exact terms. The anomalous terms are the leading terms of the expansion. This part is responsible for the quantization of the adiabatic transport coefficients in QHE. We then identify the non-local (anomalous) part of the expansion with the Quillen metric on the determinant line bundle, and the subleading exact part with the asymptotics of the regularized spectral determinant of the Laplacian for the line bundle L k , at large k. Finally, we show how the generating functional of the integer QHE is related to the gauge and gravitational (2+1)d Chern-Simons functionals. We observe the relation between the Bismut-Gillet-Soulé curvature formula for the Quillen metric and the adiabatic curvature for the electromagnetic and geometric adiabatic transport of the integer Quantum Hall state. We then obtain the geometric part of the adiabatic phase in QHE, given by the Chern-Simons functional.
Universality in the Fractional Quantum Hall
NASA Astrophysics Data System (ADS)
Fradkin, Eduardo; Lopez, Ana
In this set of lectures we review the fermion field theoretic approach to the Fractional Quantum Hall Effect and use it to discuss the origin of its remarkable universality. We discuss the semiclassical expansion around the average field approximation (AFA). We reexamine the AFA and the role of fluctuations. We argue that, order-by-order in the semiclassical expansion, the response functions obey the correct symmetry properties required by Galilean and Gauge Invariance and by the incompressibility of the fluid. In particular, we find that the low-momentum limit of the semiclassical approximation to the response functions is exact and that it saturates the f-sum rule. We discuss the nature of the spectrum of collective excitations of FQHE systems in the low-momentum limit. We applied these results to the problem of the screening of external charges and fluxes by the electron fluid, and obtained asymptotic expressions of the charge and current density profiles, for different types of interactions. The universality of the FQHE is demonstrated by deriving the form of the wave function of the ground state at long distances. We show that the wave functions of the fluid ground states of Fractional Quantum Hall systems, in the thermodynamic limit, are universal at long distances and that they have a generalized Laughlin form. This universality is a consequence of the analytic properties of the equaltime density correlation functions at long distances.
Universality in the Fractional Quantum Hall effect
NASA Astrophysics Data System (ADS)
Fradkin, Eduardo; Lopez, Ana
1993-11-01
In this lectures we review the fermion field theoretic approach to the Fractional Quantum Hall Effect and use it to discuss the origin of its remarkable universality. We discuss the semiclassical expansion around the average field approximation (AFA). We reexamine the AFA and the role of fluctuations. We argue that, order-by-order in the semiclassical expansion, the response functions obey the correct symmetry properties required by Galilean and Gauge Invariance and by the incompressibility of the fluid. In particular, we find that the low-momentum limit of the semiclassical approximation to the response functions is exact and that it saturates the f-sum rule. We discuss the nature of the spectrum of collective excitations of FQHE systems in the low-momentum limit. We applied these results to the problem of the screening of external charges and fluxes by the electron fluid, and obtained asymptotic expressions of the charge and current density profiles, for different types of interactions. The universality of the FQHE is demonstrated by deriving the form of the wave function of the ground state at long distances. We show that the wave functions of the fluid ground states of Fractional Quantum Hall systems, in the thermodynamic limit, are universal at long distances and that they have a generalized Laughlin form. This universality is a consequence of the analytic properties of the equal-time density correlation functions at long distances.
Multiparticle pseudopotentials for multicomponent quantum Hall systems
NASA Astrophysics Data System (ADS)
Davenport, Simon C.; Simon, Steven H.
2012-02-01
The Haldane pseudopotential construction has been an extremely powerful concept in quantum Hall physics—it not only gives a minimal description of the space of Hamiltonians but also suggests special model Hamiltonians (those where certain pseudopotential are set to zero) that may have exactly solvable ground states with interesting properties. The purpose of this paper is to generalize the pseudopotential construction to situations where interactions are N-body and where the particles may have internal degrees of freedom such as spin or valley index. Assuming a rotationally invariant Hamiltonian, the essence of the problem is to obtain a full basis of wave functions for N particles with fixed relative angular momentum L. This basis decomposes into representations of SU(n) with n the number of internal degrees of freedom. We give special attention to the case where the internal degree of freedom has n=2 states, which encompasses the important cases of spin-1/2 particles and quantum Hall bilayers. We also discuss in some detail the cases of spin-1 particles (n=3) and graphene (n=4, including two spin and two valley degrees of freedom).
Quantum anomalous Hall state in bilayer graphene
NASA Astrophysics Data System (ADS)
Nandkishore, Rahul; Levitov, Leonid
2010-09-01
We present a symmetry-based analysis of competition between different gapped states that have been proposed in bilayer graphene (BLG), which are all degenerate on a mean-field level. We classify the states in terms of a hidden SU(4) symmetry, and distinguish symmetry-protected degeneracies from accidental degeneracies. One of the states, which spontaneously breaks discrete time-reversal symmetry but no continuous symmetry, is identified as a quantum anomalous Hall (QAH) state, which exhibits quantum Hall effect at zero magnetic field. We investigate the lifting of the accidental degeneracies by thermal and zero-point fluctuations, taking account of the modes softened under renormalization group (RG). Working in a “saddle point plus quadratic fluctuations” approximation, we identify two types of RG-soft modes which have competing effects. Zero-point fluctuations, dominated by “transverse” modes which are unique to BLG, favor the QAH state. Thermal fluctuations, dominated by “longitudinal” modes, favor a SU(4) symmetry-breaking multiplet of states. We discuss the phenomenology and experimental signatures of the QAH state in BLG, and also propose a way to induce the QAH state using weak external magnetic fields.
Fractional quantum Hall states of bosons on cones
NASA Astrophysics Data System (ADS)
Wu, Ying-Hai; Tu, Hong-Hao; Sreejith, G. J.
2017-09-01
Motivated by a recent experiment, which synthesizes Landau levels for photons on cones [Schine et al., Nature (London) 534, 671 (2016), 10.1038/nature17943], and more generally the interest in understanding gravitational responses of quantum Hall states, we study fractional quantum Hall states of bosons on cones. A variety of trial wave functions for conical systems are constructed and compared with exact diagonalization results. The tip of a cone is a localized geometrical defect with singular curvature, which can modify the density profiles of quantum Hall states. The density profiles on cones can be used to extract some universal information about quantum Hall states. The values of certain quantities are computed numerically using the density profiles of some quantum Hall states and they agree with analytical predictions.
The Quantum Hall Effect in Finite Magnetic Fields
NASA Astrophysics Data System (ADS)
Sondhi, Shivaji Lal
In the theory of the Quantum Hall Effect it is often technically and conceptually convenient to ignore terms in the Hamiltonian that scatter electrons between different Landau levels. Physically, this is equivalent to assuming the presence of an infinite magnetic field. This dissertation consists of three studies which move beyond this approximation. The first study considers the effects of including Landau level mixing on the structure of the quasiparticles and on the ground state correlation functions. By means of perturbation theory in the interactions and by using the Landau-Ginzburg theory of the Hall Effect it is shown that for Coulomb (1/r) interactions the asymptotic long distance behavior of the charge and current profiles of the quasiparticles and of the correlation functions becomes algebraic when Landau level mixing is included and is therefore greatly altered from the exponential behavior in the infinite field limit. Among the consequences is that the quasiparticle charge in experimental geometries is not quantized as precisely as the Hall conductance. The long range of the quasiparticle current distribution makes the angular momentum of an isolated quasiparticle ill-defined and thus appears to rule out a spin-statistics connection in the Hall Effect. The second study is concerned with the Quantum Hall Effect at odd integer filling factors, and at nu = 1/3 and 1/5, in a parameter space characterized by an arbitrary ratio of the Zeeman gap to the typical interaction energy. It is shown that the system is incompressible, even when the Zeeman gap vanishes. However the quasiparticles are very different in different regimes. When the Zeeman gap is large they are microscopic but in the limit of a vanishing Zeeman gap they are Skyrmions--spatially unbounded distortions of the spin density. Exact asymptotic results for the size, spin and energy of these excitations at small Zeeman energies are presented. The last study examines the problem of rigorously
NASA Astrophysics Data System (ADS)
Bagrov, Andrey A.; Principi, Alessandro; Katsnelson, Mikhail I.
2017-03-01
We address the question of the stability of the fractional quantum Hall effect in the presence of pseudomagnetic disorder generated by mechanical deformations of a graphene sheet. Neglecting the potential disorder and taking into account only strain-induced random pseudomagnetic fields, it is possible to write down a Laughlin-like trial ground-state wave function explicitly. Exploiting the Laughlin plasma analogy, we demonstrate that in the case of fluctuating pseudomagnetic fluxes of a relatively small amplitude, the fractional quantum Hall effect is always stable upon the deformations. By contrast, in the case of bubble-induced pseudomagnetic fields in graphene on a substrate (a small number of large fluxes) the disorder can be strong enough to cause a glass transition in the corresponding classical Coulomb plasma, resulting in the destruction of the fractional quantum Hall regime and in a quantum phase transition to a nonergodic state of the lowest Landau level.
Locating an individual quantum hall island inside a quantum ring
Martins, F.; Hackens, B.; Sellier, H.; Huant, S.; Desplanque, L.; Wallart, X.; Bayot, V.
2013-12-04
Scanning gate microscopy is used to find the position of a quantum Hall island (QHI) which controls the electron transport through a mesoscopic quantum ring. Such QHIs emerging around potential inhomogeneities are tunnel-coupled with edge states. Approaching a polarized metallic tip over the QHIs gradually changes their surface and generates Coulomb blockade oscillations. This mechanism permits the identification of the center of the QHIs. Here, by sweeping the distance between the tip and the two dimensional electron gas, we clearly locate the center of an individual QHI.
Hall effect of triplons in a dimerized quantum magnet
NASA Astrophysics Data System (ADS)
Romhányi, Judit; Penc, Karlo; Ganesh, R.
2015-04-01
SrCu2(BO3)2 is the archetypal quantum magnet with a gapped dimer-singlet ground state and triplon excitations. It serves as an excellent realization of the Shastry-Sutherland model, up to small anisotropies arising from Dzyaloshinskii-Moriya interactions. Here we demonstrate that these anisotropies, in fact, give rise to topological character in the triplon band structure. The triplons form a new kind of Dirac cone with three bands touching at a single point, a spin-1 generalization of graphene. An applied magnetic field opens band gaps resulting in topological bands with Chern numbers +/-2. SrCu2(BO3)2 thus provides a magnetic analogue of the integer quantum Hall effect and supports topologically protected edge modes. At a threshold value of the magnetic field set by the Dzyaloshinskii-Moriya interactions, the three triplon bands touch once again in a spin-1 Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime.
Hall effect of triplons in a dimerized quantum magnet
NASA Astrophysics Data System (ADS)
Romhanyi, Judit; Penc, Karlo; Ganesh, Ramachandran
2015-03-01
SrCu2(BO3)2 is the archetypal quantum magnet with a gapped dimer-singlet ground state and triplon excitations. It serves as a realization of the Shastry Sutherland model, up to small anisotropies arising from Dzyaloshinskii-Moriya (DM) interactions. We demonstrate that the DM couplings give rise to topological character in the triplon band structure. The triplons form a new kind of a Dirac cone with three bands touching at a single point, a spin-1 generalization of graphene. An applied magnetic field opens band gaps and as a result topological bands with Chern numbers +/- 2 develop. Thus SrCu2(BO3)2 is a magnetic analogue of the integer quantum Hall effect and supports topologically protected edge modes. At a critical value of the magnetic field set by the strength of DM interactions, the three triplon bands touch again in a spin-1 Dirac cone, and lose their topological character. We predict thermal Hall signature in the topological regime.
Reprint of : Effect of incoherent scattering on three-terminal quantum Hall thermoelectrics
NASA Astrophysics Data System (ADS)
Sánchez, Rafael; Sothmann, Björn; Jordan, Andrew N.
2016-08-01
A three-terminal conductor presents peculiar thermoelectric and thermal properties in the quantum Hall regime: it can behave as a symmetric rectifier and as an ideal thermal diode. These properties rely on the coherent propagation along chiral edge channels. We investigate the effect of breaking the coherent propagation by the introduction of a probe terminal. It is shown that chiral effects not only survive the presence of incoherence but they can even improve the thermoelectric performance in the totally incoherent regime.
Unconventional quantum Hall effect in Floquet topological insulators.
Tahir, M; Vasilopoulos, P; Schwingenschlögl, U
2016-09-28
We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the light's polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity [Formula: see text] at zero Fermi energy, to a Hall insulator state with [Formula: see text]. These findings open new possibilities for experimentally realizing nontrivial quantum states and unusual quantum Hall plateaus at [Formula: see text].
Quantum Hall effect in (cadmium flouride)-based nanostructures
Bagraev, N. T. Gimbitskaya, O. N.; Klyachkin, L. E.; Malyarenko, A. M.; Shelykh, I. A.; Ryskin, A. I.; Shcheulin, A. S.
2009-01-15
Shubnikov-de Haas oscillations and a ladder of quantum steps in the Hall resistance were observed in a p-CdF{sub 2} quantum well confined by {delta}-like barriers for CdB{sub x}F{sub 2-x} on the surface of n-CdF{sub 2}. Due to the small effective mass of two-dimensional holes, observation of the quantum Hall effect became possible at room temperature.
NASA Astrophysics Data System (ADS)
Cui, Yong-Tao; Wen, Bo; Ma, Eric Y.; Diankov, Georgi; Han, Zheng; Amet, Francois; Taniguchi, Takashi; Watanabe, Kenji; Goldhaber-Gordon, David; Dean, Cory R.; Shen, Zhi-Xun
2016-10-01
We report simultaneous transport and scanning microwave impedance microscopy to examine the correlation between transport quantization and filling of the bulk Landau levels in the quantum Hall regime in gated graphene devices. Surprisingly, a comparison of these measurements reveals that quantized transport typically occurs below the complete filling of bulk Landau levels, when the bulk is still conductive. This result points to a revised understanding of transport quantization when carriers are accumulated by gating. We discuss the implications on transport study of the quantum Hall effect in graphene and related topological states in other two-dimensional electron systems.
Algebraic geometry realization of quantum Hall soliton
NASA Astrophysics Data System (ADS)
Abounasr, R.; Ait Ben Haddou, M.; El Rhalami, A.; Saidi, E. H.
2005-02-01
Using the Iqbal-Netzike-Vafa dictionary giving the correspondence between the H2 homology of del Pezzo surfaces and p-branes, we develop a way to approach the system of brane bounds in M-theory on S1. We first review the structure of 10-dimensional quantum Hall soliton (QHS) from the view of M-theory on S1. Then, we show how the D0 dissolution in D2-brane is realized in M-theory language and derive the p-brane constraint equations used to define appropriately the QHS. Finally, we build an algebraic geometry realization of the QHS in type IIA superstring and show how to get its type IIB dual. Other aspects are also discussed.
Noncommutative Skyrmions in Quantum Hall Systems
NASA Astrophysics Data System (ADS)
Ezawa, Z. F.; Tsitsishvili, G.
Charged excitations in quantum Hall (QH) systems are noncommutative skyrmions. QH systems represent an ideal system equipped with noncommutative geometry. When an electron is confined within the lowest Landau level, its position is described solely by the guiding center, whose X and Y coordinates do not commute with one another. Topological excitations in such a noncommutative plane are noncommutative skyrmions flipping several spins coherently. We construct a microscopic skyrmion state by applying a certain unitary transformation to an electron or hole state. A remarkable property is that a noncommutative skyrmion carries necessarily the electron number proportional to the topological charge. More remarkable is the bilayer QH system with the layer degree of freedom acting as the pseudospin, where the quasiparticle is a topological soliton to be identified with the pseudospin skyrmion. Such a skyrmion is deformed into a bimeron (a pair of merons) by the parallel magnetic field penetrated between the two layers. Each meron carries the electric charge ±e/2.
Layered quantum Hall insulators with ultracold atoms
Zamora, A.; Szirmai, G.; Lewenstein, M.
2011-11-15
We consider a generalization of the two-dimensional (2D) quantum Hall insulator to a noncompact, non-Abelian gauge group, the Heisenberg-Weyl group. We show that this kind of insulator is actually a layered three-dimensional (3D) insulator with nontrivial topology. We further show that nontrivial combinations of quantized transverse conductivities can be engineered with the help of a staggered potential. We investigate the robustness and topological nature of this conductivity and connect it to the surface modes of the system. We also propose a simple experimental realization with ultracold atoms in 3D confined to a 2D square lattice with the third dimension being mapped to a gauge coordinate.
Photonic versus electronic quantum anomalous Hall effect
NASA Astrophysics Data System (ADS)
Bleu, O.; Solnyshkov, D. D.; Malpuech, G.
2017-03-01
We derive the diagram of the topological phases accessible within a generic Hamiltonian describing quantum anomalous Hall effect for photons and electrons in honeycomb lattices in the presence of a Zeeman field and spin-orbit coupling (SOC). The two cases differ crucially by the winding number of their SOC, which is 1 for the Rashba SOC of electrons, and 2 for the photon SOC induced by the energy splitting between the TE and TM modes. As a consequence, the two models exhibit opposite Chern numbers ±2 at low field. Moreover, the photonic system shows a topological transition absent in the electronic case. If the photonic states are mixed with excitonic resonances to form interacting exciton-polaritons, the effective Zeeman field can be induced and controlled by a circularly polarized pump. This new feature allows an all-optical control of the topological phase transitions.
Reprint of : Flux sensitivity of quantum spin Hall rings
NASA Astrophysics Data System (ADS)
Crépin, F.; Trauzettel, B.
2016-08-01
We analyze the periodicity of persistent currents in quantum spin Hall loops, partly covered with an s-wave superconductor, in the presence of a flux tube. Much like in normal (non-helical) metals, the periodicity of the single-particle spectrum goes from Φ0 = h / e to Φ0 / 2 as the length of the superconductor is increased past the coherence length of the superconductor. We further analyze the periodicity of the persistent current, which is a many-body effect. Interestingly, time reversal symmetry and parity conservation can significantly change the period. We find a 2Φ0-periodic persistent current in two distinct regimes, where one corresponds to a Josephson junction and the other one to an Aharonov-Bohm setup.
Puddle-Induced Resistance Oscillations in the Breakdown of the Graphene Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Yang, M.; Couturaud, O.; Desrat, W.; Consejo, C.; Kazazis, D.; Yakimova, R.; Syväjärvi, M.; Goiran, M.; Béard, J.; Frings, P.; Pierre, M.; Cresti, A.; Escoffier, W.; Jouault, B.
2016-12-01
We report on the stability of the quantum Hall plateau in wide Hall bars made from a chemically gated graphene film grown on SiC. The ν =2 quantized plateau appears from fields B ≃5 T and persists up to B ≃80 T . At high current density, in the breakdown regime, the longitudinal resistance oscillates with a 1 /B periodicity and an anomalous phase, which we relate to the presence of additional electron reservoirs. The high field experimental data suggest that these reservoirs induce a continuous increase of the carrier density up to the highest available magnetic field, thus enlarging the quantum plateaus. These in-plane inhomogeneities, in the form of high carrier density graphene pockets, modulate the quantum Hall effect breakdown and decrease the breakdown current.
Puddle-Induced Resistance Oscillations in the Breakdown of the Graphene Quantum Hall Effect.
Yang, M; Couturaud, O; Desrat, W; Consejo, C; Kazazis, D; Yakimova, R; Syväjärvi, M; Goiran, M; Béard, J; Frings, P; Pierre, M; Cresti, A; Escoffier, W; Jouault, B
2016-12-02
We report on the stability of the quantum Hall plateau in wide Hall bars made from a chemically gated graphene film grown on SiC. The ν=2 quantized plateau appears from fields B≃5 T and persists up to B≃80 T. At high current density, in the breakdown regime, the longitudinal resistance oscillates with a 1/B periodicity and an anomalous phase, which we relate to the presence of additional electron reservoirs. The high field experimental data suggest that these reservoirs induce a continuous increase of the carrier density up to the highest available magnetic field, thus enlarging the quantum plateaus. These in-plane inhomogeneities, in the form of high carrier density graphene pockets, modulate the quantum Hall effect breakdown and decrease the breakdown current.
Quantum Hall effect in black phosphorus two-dimensional electron system.
Li, Likai; Yang, Fangyuan; Ye, Guo Jun; Zhang, Zuocheng; Zhu, Zengwei; Lou, Wenkai; Zhou, Xiaoying; Li, Liang; Watanabe, Kenji; Taniguchi, Takashi; Chang, Kai; Wang, Yayu; Chen, Xian Hui; Zhang, Yuanbo
2016-07-01
The development of new, high-quality functional materials has been at the forefront of condensed-matter research. The recent advent of two-dimensional black phosphorus has greatly enriched the materials base of two-dimensional electron systems (2DESs). Here, we report the observation of the integer quantum Hall effect in a high-quality black phosphorus 2DES. The high quality is achieved by embedding the black phosphorus 2DES in a van der Waals heterostructure close to a graphite back gate; the graphite gate screens the impurity potential in the 2DES and brings the carrier Hall mobility up to 6,000 cm(2) V(-1) s(-1). The exceptional mobility enabled us to observe the quantum Hall effect and to gain important information on the energetics of the spin-split Landau levels in black phosphorus. Our results set the stage for further study on quantum transport and device application in the ultrahigh mobility regime.
High-Field Fractional Quantum Hall Effect in Optical Lattices
Palmer, R.N.; Jaksch, D.
2006-05-12
We consider interacting bosonic atoms in an optical lattice subject to a large simulated magnetic field. We develop a model similar to a bilayer fractional quantum Hall system valid near simple rational numbers of magnetic flux quanta per lattice cell. Then we calculate its ground state, magnetic lengths, fractional fillings, and find unexpected sign changes in the Hall current. Finally we study methods for detecting these novel features via shot noise and Hall current measurements.
Geometric Construction of Quantum Hall Clustering Hamiltonians
NASA Astrophysics Data System (ADS)
Lee, Ching Hua; Papić, Zlatko; Thomale, Ronny
2015-10-01
Many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain "pseudopotential" Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU (n ) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.
Geometric construction of quantum hall clustering Hamiltonians
Lee, Ching Hua; Papić, Zlatko; Thomale, Ronny
2015-10-08
In this study, many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain “pseudopotential” Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-bodymore » interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.« less
Geometric defects in quantum Hall states
NASA Astrophysics Data System (ADS)
Gromov, Andrey
2016-08-01
We describe a geometric (or gravitational) analog of the Laughlin quasiholes in fractional quantum Hall states. Analogously to the quasiholes, these defects can be constructed by an insertion of an appropriate vertex operator into the conformal block representation of a trial wave function; however, unlike the quasiholes these defects are extrinsic and do not correspond to true excitations of the quantum fluid. We construct a wave function in the presence of such defects and explain how to assign an electric charge and a spin to each defect and calculate the adiabatic, non-Abelian statistics of the defects. The defects turn out to be equivalent to the genons in that their adiabatic exchange statistics can be described in terms of representations of the mapping class group of an appropriate higher genus Riemann surface. We present a general construction that, in principle, makes it possible to calculate the statistics of Zn genons for any "parent" topological phase. We illustrate the construction on the example of the Laughlin state and perform an explicit calculation of the braiding matrices. In addition to non-Abelian statistics, geometric defects possess a universal Abelian overall phase, determined by the gravitational anomaly.
Higher (odd) dimensional quantum Hall effect and extended dimensional hierarchy
NASA Astrophysics Data System (ADS)
Hasebe, Kazuki
2017-07-01
We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S 2 k - 1 in the SO (2 k - 1) monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S 2 k - 1 to the one-dimension higher SO (2 k) gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah-Patodi-Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.
Fractional quantum Hall effect in the absence of Landau levels.
Sheng, D N; Gu, Zheng-Cheng; Sun, Kai; Sheng, L
2011-07-12
It is well known that the topological phenomena with fractional excitations, the fractional quantum Hall effect, will emerge when electrons move in Landau levels. Here we show the theoretical discovery of the fractional quantum Hall effect in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically non-trivial flat-band model on a checkerboard lattice. In the presence of nearest-neighbouring repulsion, we find that at 1/3 filling, the Fermi-liquid state is unstable towards the fractional quantum Hall effect. At 1/5 filling, however, a next-nearest-neighbouring repulsion is needed for the occurrence of the 1/5 fractional quantum Hall effect when nearest-neighbouring repulsion is not too strong. We demonstrate the characteristic features of these novel states and determine the corresponding phase diagram.
Nambu Geometry in Quantum Hall Effect and Topological Insulator
NASA Astrophysics Data System (ADS)
Hasebe, Kazuki
2017-08-01
This short review is a contribution to the conference proceeding of IF-YITP Symposium VI, 2016. We discuss how Nambu geometry emerges in the context of higher dimensional quantum Hall effect or A-class topological insulators [1].
Model Fractional Quantum Hall States and Jack Polynomials
Bernevig, B. Andrei; Haldane, F. D. M.
2008-06-20
We describe an occupation-number-like picture of fractional quantum Hall states in terms of polynomial wave functions characterized by a dominant occupation-number configuration. The bosonic variants of single-component Abelian and non-Abelian fractional quantum Hall states are modeled by Jack symmetric polynomials (Jacks), characterized by dominant occupation-number configurations satisfying a generalized Pauli principle. In a series of well-known quantum Hall states, including the Laughlin, Read-Moore, and Read-Rezayi, the Jack polynomials naturally implement a ''squeezing rule'' that constrains allowed configurations to be restricted to those obtained by squeezing the dominant configuration. The Jacks presented in this Letter describe new trial uniform states, but it is yet to be determined to which actual experimental fractional quantum Hall effect states they apply.
Revealing topological superconductivity in extended quantum spin Hall Josephson junctions.
Lee, Shu-Ping; Michaeli, Karen; Alicea, Jason; Yacoby, Amir
2014-11-07
Quantum spin Hall-superconductor hybrids are promising sources of topological superconductivity and Majorana modes, particularly given recent progress on HgTe and InAs/GaSb. We propose a new method of revealing topological superconductivity in extended quantum spin Hall Josephson junctions supporting "fractional Josephson currents." Specifically, we show that as one threads magnetic flux between the superconductors, the critical current traces an interference pattern featuring sharp fingerprints of topological superconductivity-even when noise spoils parity conservation.
Josephson inplane and tunneling currents in bilayer quantum Hall system
Ezawa, Z. F.; Tsitsishvili, G.; Sawada, A.
2013-12-04
A Bose-Einstein condensation is formed by composite bosons in the quantum Hall state. A composite boson carries the fundamental charge (–e). We investigate Josephson tunneling of such charges in the bilayer quantum Hall system at the total filling ν = 1. We show the existence of the critical current for the tunneling current to be coherent and dissipationless in tunneling experiments with various geometries.
25 Years quantum Hall effect: how it all came about
NASA Astrophysics Data System (ADS)
Landwehr, G.
2003-12-01
The quantum Hall effect (QHE) was discovered by Klaus von Klitzing in the spring of 1980. However, the plateaus in the Hall resistance of silicon metal oxide semiconductor devices which can be observed in high magnetic fields at low temperatures showed up several years earlier. The world wide research, which eventually culminated in the discovery, is briefly reviewed. The QHE was not predicted by theory, there were only approximate indications of quantization of the Hall resistance in whole fractions of h/ e2. The exceptional precision of the resistance values of the Hall plateau led very soon to a new resistance standard.
Fractional quantum Hall effect in HgTe quantum wells
NASA Astrophysics Data System (ADS)
Wang, Jianhui
2016-02-01
We study the possibility of fractional quantum Hall effects in HgTe quantum wells using exact diagonalization. Our results show that Laughlin states, the Moore-Read state, and the Read-Rezayi Z3 state can all be supported. However, near the level crossing point (of the single-particle spectrum) the gap can be destroyed by Landau level mixing, and the Moore-Read state and the Read-Rezayi state dominate over their respective competing states only for wide wells. For smaller well widths the Moore-Read state crosses over to the composite fermion Fermi sea, while the Read-Rezayi state loses its dominance over the hierarchy state.
Few-body, hyperspherical treatment of the quantum Hall effect
NASA Astrophysics Data System (ADS)
Wooten, R. E.; Daily, K. M.; Greene, Chris H.
2016-03-01
The quantum Hall effect arises from the quantum behavior of two-dimensional, strongly-interacting electrons exposed to a strong, perpendicular magnetic field [1, 2]. Conventionally treated from a many-body perspective, we instead treat the system from the few-body perspective using collective coordinates and the hyperspherical adiabatic technique developed originally for atomic systems [3]. The grand angular momentum K from K-harmonic few-body theory, is shown to be an approximate good collective quantum number in this system, and is shown to correlate with known fractional quantum Hall (FQH) states at experimentally observed filling factors.
Quantum Hall effect in n-InGaAs/InAlAs metamorphic nanoheterostructures with high InAs content
NASA Astrophysics Data System (ADS)
Gudina, Svetlana V.; Arapov, Yurii G.; Savelyev, Alexander P.; Neverov, Vladimir N.; Podgornykh, Sergey M.; Shelushinina, Nina G.; Yakunin, Michail V.; Rogacki, Krzysztof; Vasil'evskii, Ivan S.; Vinichenko, Alexander N.
2017-10-01
For an investigation of the quantum Hall effect on n-In0.85Ga0.18As/In0.82Al0.82As metamorphic nanoheterostructures with high InAs content the longitudinal and Hall magnetoresistances were measured in magnetic fields up to 9 T at T = (1.8 ÷ 30) K . The results for a temperature dependence of conductivity on the delocalized states at the center of Landau level were analysed within the scaling concept for a plateau-plateau transition in quantum Hall regime.
Edge reconstruction in fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Sabo, Ron; Gurman, Itamar; Rosenblatt, Amir; Lafont, Fabien; Banitt, Daniel; Park, Jinhong; Heiblum, Moty; Gefen, Yuval; Umansky, Vladimir; Mahalu, Diana
2017-01-01
The nature of edge reconstruction in the quantum Hall effect (QHE) and the issue of where the current flows have been debated for years. Moreover, the recent observation of proliferation of `upstream’ neutral modes in the fractional QHE has raised doubts about the present models of edge channels. Here, we present a new picture of the edge reconstruction in two of the hole-conjugate states. For example, while the present model for ν = (2/3) consists of a single downstream chiral charge channel with conductance (2/3)(e2/h) and an upstream neutral mode, we show that the current is carried by two separate downstream chiral edge channels, each with conductance (1/3)(e2/h). We uncover a novel mechanism of fragmentation of upstream neutral modes into downstream propagating charge modes that induces current fluctuations with zero net current. Our unexpected results underline the need for better understanding of edge reconstruction and energy transport in all fractional QHE states.
Reprint of : Thermodynamic properties of a quantum Hall anti-dot interferometer
NASA Astrophysics Data System (ADS)
Levy Schreier, Sarah; Stern, Ady; Rosenow, Bernd; Halperin, Bertrand I.
2016-08-01
We study quantum Hall interferometers in which the interference loop encircles a quantum anti-dot. We base our study on thermodynamic considerations, which we believe reflect the essential aspects of interference transport phenomena. We find that similar to the more conventional Fabry-Perot quantum Hall interferometers, in which the interference loop forms a quantum dot, the anti-dot interferometer is affected by the electro-static Coulomb interaction between the edge modes defining the loop. We show that in the Aharonov-Bohm regime, in which effects of fractional statistics should be visible, is easier to access in interferometers based on anti-dots than in those based on dots. We discuss the relevance of our results to recent measurements on anti-dots interferometers.
Quenching of the quantum Hall effect in graphene with scrolled edges.
Cresti, Alessandro; Fogler, Michael M; Guinea, Francisco; Castro Neto, A H; Roche, Stephan
2012-04-20
Edge nanoscrolls are shown to strongly influence transport properties of suspended graphene in the quantum Hall regime. The relatively long arclength of the scrolls in combination with their compact transverse size results in formation of many nonchiral transport channels in the scrolls. They short circuit the bulk current paths and inhibit the observation of the quantized two-terminal resistance. Unlike competing theoretical proposals, this mechanism of disrupting the Hall quantization in suspended graphene is not caused by ill-chosen placement of the contacts, singular elastic strains, or a small sample size.
Quenching of the Quantum Hall Effect in Graphene with Scrolled Edges
NASA Astrophysics Data System (ADS)
Cresti, Alessandro; Fogler, Michael M.; Guinea, Francisco; Castro Neto, A. H.; Roche, Stephan
2012-04-01
Edge nanoscrolls are shown to strongly influence transport properties of suspended graphene in the quantum Hall regime. The relatively long arclength of the scrolls in combination with their compact transverse size results in formation of many nonchiral transport channels in the scrolls. They short circuit the bulk current paths and inhibit the observation of the quantized two-terminal resistance. Unlike competing theoretical proposals, this mechanism of disrupting the Hall quantization in suspended graphene is not caused by ill-chosen placement of the contacts, singular elastic strains, or a small sample size.
Engineering quantum spin Hall insulators by strained-layer heterostructures
NASA Astrophysics Data System (ADS)
Akiho, T.; Couëdo, F.; Irie, H.; Suzuki, K.; Onomitsu, K.; Muraki, K.
2016-11-01
Quantum spin Hall insulators (QSHIs), also known as two-dimensional topological insulators, have emerged as an unconventional class of quantum states with insulating bulk and conducting edges originating from nontrivial inverted band structures and have been proposed as a platform for exploring spintronics applications and exotic quasiparticles related to the spin-helical edge modes. Despite theoretical proposals for various materials, however, experimental demonstrations of QSHIs have so far been limited to two systems—HgTe/CdTe and InAs/GaSb—both of which are lattice-matched semiconductor heterostructures. Here, we report transport measurements in yet another realization of a band-inverted heterostructure as a QSHI candidate—InAs/InxGa1-xSb with lattice mismatch. We show that the compressive strain in the InxGa1-xSb layer enhances the band overlap and energy gap. Consequently, high bulk resistivity, two orders of magnitude higher than for InAs/GaSb, is obtained deep in the band-inverted regime. The strain also enhances bulk Rashba spin-orbit splitting, leading to an unusual situation where the Fermi level crosses only one spin branch for electronlike and holelike bands over a wide density range. These properties make this system a promising platform for robust QSHIs with unique spin properties and demonstrate the strain to be an important ingredient for tuning spin-orbit interaction.
A realistic quantum capacitance model for quantum Hall edge state based Fabry-Pérot interferometers
NASA Astrophysics Data System (ADS)
Kilicoglu, O.; Eksi, D.; Siddiki, A.
2017-01-01
In this work, the classical and the quantum capacitances are calculated for a Fabry-Pérot interferometer operating in the integer quantized Hall regime. We first consider a rotationally symmetric electrostatic confinement potential and obtain the widths and the spatial distribution of the insulating (incompressible) circular strips using a charge density profile stemming from self-consistent calculations. Modelling the electrical circuit of capacitors composed of metallic gates and incompressible/compressible strips, we investigate the conditions to observe Aharonov-Bohm (quantum mechanical phase dependent) and Coulomb blockade (capacitive coupling dependent) effects reflected in conductance oscillations. In a last step, we solve the Schrödinger and the Poisson equations self-consistently in a numerical manner taking into account realistic experimental geometries. We find that, describing the conductance oscillations either by Aharanov-Bohm or Coulomb blockade strongly depends on sample properties also other than size, therefore, determining the origin of these oscillations requires further experimental and theoretical investigation.
A realistic quantum capacitance model for quantum Hall edge state based Fabry-Pérot interferometers.
Kilicoglu, O; Eksi, D; Siddiki, A
2017-01-25
In this work, the classical and the quantum capacitances are calculated for a Fabry-Pérot interferometer operating in the integer quantized Hall regime. We first consider a rotationally symmetric electrostatic confinement potential and obtain the widths and the spatial distribution of the insulating (incompressible) circular strips using a charge density profile stemming from self-consistent calculations. Modelling the electrical circuit of capacitors composed of metallic gates and incompressible/compressible strips, we investigate the conditions to observe Aharonov-Bohm (quantum mechanical phase dependent) and Coulomb blockade (capacitive coupling dependent) effects reflected in conductance oscillations. In a last step, we solve the Schrödinger and the Poisson equations self-consistently in a numerical manner taking into account realistic experimental geometries. We find that, describing the conductance oscillations either by Aharanov-Bohm or Coulomb blockade strongly depends on sample properties also other than size, therefore, determining the origin of these oscillations requires further experimental and theoretical investigation.
Complex scattering dynamics and the quantum Hall effects
Trugman, S.A.
1994-12-16
We review both classical and quantum potential scattering in two dimensions in a magnetic field, with applications to the quantum Hall effect. Classical scattering is complex, due to the approach of scattering states to an infinite number of dynamically bound states. Quantum scattering follows the classical behavior rather closely, exhibiting sharp resonances in place of the classical bound states. Extended scatterers provide a quantitative explanation for the breakdown of the QHE at a comparatively small Hall voltage as seen by Kawaji et al., and possibly for noise effects.
Few-body treatment of the quantum Hall system
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Daily, Kevin; Greene, Chris H.
2015-05-01
When confined to a finite, two-dimensional area and exposed to a strong magnetic field, fermions exhibit complicated, highly-correlated quantum behavior known as the quantum Hall effect. At certain electron densities and magnetic fields, the system exhibits strong quantization due entirely to Coulomb interactions. Typical theoretical studies in the field consist of many-body numerical configuration interaction calculations performed in an energy-restricted single-particle Hilbert subspace. So far, quantum Hall behavior has been observed experimentally only in condensed matter systems, but there is significant interest in reproducing and studying the effect in highly-controlled cold atom systems. In light of such potential experimental developments, we approach the theoretical study of the quantum Hall system from a few-body perspective using the hyperspherical adiabatic technique developed originally for atomic systems. We gratefully acknowledge support from NSF.
Anisotropic intrinsic spin Hall effect in quantum wires.
Cummings, A W; Akis, R; Ferry, D K
2011-11-23
We use numerical simulations to investigate the spin Hall effect in quantum wires in the presence of both Rashba and Dresselhaus spin-orbit coupling. We find that the intrinsic spin Hall effect is highly anisotropic with respect to the orientation of the wire, and that the nature of this anisotropy depends strongly on the electron density and the relative strengths of the Rashba and Dresselhaus spin-orbit couplings. In particular, at low densities, when only one subband of the quantum wire is occupied, the spin Hall effect is strongest for electron momentum along the [N110] axis, which is the opposite of what is expected for the purely 2D case. In addition, when more than one subband is occupied, the strength and anisotropy of the spin Hall effect can vary greatly over relatively small changes in electron density, which makes it difficult to predict which wire orientation will maximize the strength of the spin Hall effect. These results help to illuminate the role of quantum confinement in spin-orbit-coupled systems, and can serve as a guide for future experimental work on the use of quantum wires for spin-Hall-based spintronic applications.
The spin Hall effect in a quantum gas.
Beeler, M C; Williams, R A; Jiménez-García, K; LeBlanc, L J; Perry, A R; Spielman, I B
2013-06-13
Electronic properties such as current flow are generally independent of the electron's spin angular momentum, an internal degree of freedom possessed by quantum particles. The spin Hall effect, first proposed 40 years ago, is an unusual class of phenomena in which flowing particles experience orthogonally directed, spin-dependent forces--analogous to the conventional Lorentz force that gives the Hall effect, but opposite in sign for two spin states. Spin Hall effects have been observed for electrons flowing in spin-orbit-coupled materials such as GaAs and InGaAs (refs 2, 3) and for laser light traversing dielectric junctions. Here we observe the spin Hall effect in a quantum-degenerate Bose gas, and use the resulting spin-dependent Lorentz forces to realize a cold-atom spin transistor. By engineering a spatially inhomogeneous spin-orbit coupling field for our quantum gas, we explicitly introduce and measure the requisite spin-dependent Lorentz forces, finding them to be in excellent agreement with our calculations. This 'atomtronic' transistor behaves as a type of velocity-insensitive adiabatic spin selector, with potential application in devices such as magnetic or inertial sensors. In addition, such techniques for creating and measuring the spin Hall effect are clear prerequisites for engineering topological insulators and detecting their associated quantized spin Hall effects in quantum gases. As implemented, our system realizes a laser-actuated analogue to the archetypal semiconductor spintronic device, the Datta-Das spin transistor.
Quantum Anomalous Hall Effect in Hg_1-yMn_yTe Quantum Wells
Liu, Chao-Xing; Qi, Xiao-Liang; Dai, Xi; Fang, Zhong; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
The quantum Hall effect is usually observed when the two-dimensional electron gas is subjected to an external magnetic field, so that their quantum states form Landau levels. In this work we predict that a new phenomenon, the quantum anomalous Hall effect, can be realized in Hg{sub 1-y}Mn{sub y}Te quantum wells, without the external magnetic field and the associated Landau levels. This effect arises purely from the spin polarization of the Mn atoms, and the quantized Hall conductance is predicted for a range of quantum well thickness and the concentration of the Mn atoms. This effect enables dissipationless charge current in spintronics devices.
Markovian quantum master equation beyond adiabatic regime.
Yamaguchi, Makoto; Yuge, Tatsuro; Ogawa, Tetsuo
2017-01-01
By introducing a temporal change time scale τ_{A}(t) for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate situations, the framework is well justified even if τ_{A}(t) is faster than the decay time scale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings are applicable to a wide range of fields, providing a basis for quantum control beyond the adiabatic regime.
Markovian quantum master equation beyond adiabatic regime
NASA Astrophysics Data System (ADS)
Yamaguchi, Makoto; Yuge, Tatsuro; Ogawa, Tetsuo
2017-01-01
By introducing a temporal change time scale τA(t ) for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate situations, the framework is well justified even if τA(t ) is faster than the decay time scale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings are applicable to a wide range of fields, providing a basis for quantum control beyond the adiabatic regime.
Topological insulator in junction with ferromagnets: Quantum Hall effects
NASA Astrophysics Data System (ADS)
Chudnovskiy, A. L.; Kagalovsky, V.
2015-06-01
The ferromagnet-topological insulator-ferromagnet (FM-TI-FM) junction exhibits thermal and electrical quantum Hall effects. The generated Hall voltage and transverse temperature gradient can be controlled by the directions of magnetizations in the FM leads, which inspires the use of FM-TI-FM junctions as electrical and as heat switches in spintronic devices. Thermal and electrical Hall coefficients are calculated as functions of the magnetization directions in ferromagnets and the spin-relaxation time in TI. Both the Hall voltage and the transverse temperature gradient decrease but are not completely suppressed even at very short spin-relaxation times. The Hall coefficients turn out to be independent of the spin-relaxation time for symmetric configuration of FM leads.
Gated THz magneto-optics of the Quantum spin Hall state in InAs/GaSb double quantum wells
NASA Astrophysics Data System (ADS)
Jenkins, Gregory S.; Sushkov, Andrei B.; Carey, Remington L.; Drew, H. Dennis; Sullivan, Gerard; Du, Lingjie; Du, Rui-Rui
2015-03-01
Gate-modulated THz cyclotron resonance and Kerr effect are used to characterize the electronic structure and the roles of hybridization and excitonic effects in band inverted InAs/GaSb quantum wells. In contrast to previous optical studies, a gate tunes the chemical potential through the hybridization gap. Measured magnetic state transitions are used to delineate the inverted gap which is thought to determine the observed large critical field transition Bc from the non-trivial Z2 state to the trivial Z state of the system as predicted by the Benevig-Hughes-Zhang (BHZ) model, as well as transitions from the quantum spin Hall to Quantum Hall Effect regimes, as a function of gate, frequency, and magnetic field. Evidence for excitonic condensation using zero field THz Kerr rotation to detect broken time reversal ground states will be discussed. UMD supported by DOE #ER-46741-SC0005436, Rice by DOE #DE-FG02-06ER46274.
Pairing in Luttinger Liquids and Quantum Hall States
NASA Astrophysics Data System (ADS)
Kane, Charles L.; Stern, Ady; Halperin, Bertrand I.
2017-07-01
We study spinless electrons in a single-channel quantum wire interacting through attractive interaction, and the quantum Hall states that may be constructed by an array of such wires. For a single wire, the electrons may form two phases, the Luttinger liquid and the strongly paired phase. The Luttinger liquid is gapless to one- and two-electron excitations, while the strongly paired state is gapped to the former and gapless to the latter. In contrast to the case in which the wire is proximity coupled to an external superconductor, for an isolated wire there is no separate phase of a topological, weakly paired superconductor. Rather, this phase is adiabatically connected to the Luttinger liquid phase. The properties of the one-dimensional topological superconductor emerge when the number of channels in the wire becomes large. The quantum Hall states that may be formed by an array of single-channel wires depend on the Landau-level filling factors. For odd-denominator fillings ν =1 /(2 n +1 ), wires at the Luttinger phase form Laughlin states, while wires in the strongly paired phase form a bosonic fractional quantum Hall state of strongly bound pairs at a filling of 1 /(8 n +4 ). The transition between the two is of the universality class of Ising transitions in three dimensions. For even-denominator fractions ν =1 /2 n , the two single-wire phases translate into four quantum Hall states. Two of those states are bosonic fractional quantum Hall states of weakly and strongly bound pairs of electrons. The other two are non-Abelian quantum Hall states, which originate from coupling wires close to their critical point. One of these non-Abelian states is the Moore-Read state. The transitions between all of these states are of the universality class of Majorana transitions. We point out some of the properties that characterize the different phases and the phase transitions.
Is the quantum Hall effect influenced by the gravitational field?
Hehl, Friedrich W; Obukhov, Yuri N; Rosenow, Bernd
2004-08-27
Most of the experiments on the quantum Hall effect (QHE) were made at approximately the same height above sea level. A future international comparison will determine whether the gravitational field g(x) influences the QHE. In the realm of (1+2)-dimensional phenomenological macroscopic electrodynamics, the Ohm-Hall law is metric independent ("topological"). This suggests that it does not couple to g(x). We corroborate this result by a microscopic calculation of the Hall conductance in the presence of a post-Newtonian gravitational field.
Zimmermann, Katrin; Jordan, Anna; Gay, Frédéric; Watanabe, Kenji; Taniguchi, Takashi; Han, Zheng; Bouchiat, Vincent; Sellier, Hermann; Sacépé, Benjamin
2017-04-13
Charge carriers in the quantum Hall regime propagate via one-dimensional conducting channels that form along the edges of a two-dimensional electron gas. Controlling their transmission through a gate-tunable constriction, also called quantum point contact, is fundamental for many coherent transport experiments. However, in graphene, tailoring a constriction with electrostatic gates remains challenging due to the formation of p-n junctions below gate electrodes along which electron and hole edge channels co-propagate and mix, short circuiting the constriction. Here we show that this electron-hole mixing is drastically reduced in high-mobility graphene van der Waals heterostructures thanks to the full degeneracy lifting of the Landau levels, enabling quantum point contact operation with full channel pinch-off. We demonstrate gate-tunable selective transmission of integer and fractional quantum Hall edge channels through the quantum point contact. This gate control of edge channels opens the door to quantum Hall interferometry and electron quantum optics experiments in the integer and fractional quantum Hall regimes of graphene.
Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
Barkeshli, Maissam; Wen Xiaogang
2011-09-15
We study continuous quantum phase transitions that can occur in bilayer fractional quantum Hall (FQH) systems as the interlayer tunneling and interlayer repulsion are tuned. We introduce a slave-particle gauge theory description of a series of continuous transitions from the (ppq) Abelian bilayer states to a set of non-Abelian FQH states, which we dub orbifold FQH states, of which the Z{sub 4} parafermion (Read-Rezayi) state is a special case. This provides an example in which Z{sub 2} electron fractionalization leads to non-Abelian topological phases. The naive ''ideal'' wave functions and ideal Hamiltonians associated with these orbifold states do not in general correspond to incompressible phases but, instead, lie at a nearby critical point. We discuss this unusual situation from the perspective of the pattern-of-zeros/vertex algebra frameworks and discuss implications for the conceptual foundations of these approaches. Due to the proximity in the phase diagram of these non-Abelian states to the (ppq) bilayer states, they may be experimentally relevant, both as candidates for describing the plateaus in single-layer systems at filling fractions 8/3 and 12/5 and as a way to tune to non-Abelian states in double-layer or wide quantum wells.
Quantum anomalous Hall effect in magnetic insulator heterostructure.
Xu, Gang; Wang, Jing; Felser, Claudia; Qi, Xiao-Liang; Zhang, Shou-Cheng
2015-03-11
On the basis of ab initio calculations, we predict that a monolayer of Cr-doped (Bi,Sb)2Te3 and GdI2 heterostructure is a quantum anomalous Hall insulator with a nontrivial band gap up to 38 meV. The principle behind our prediction is that the band inversion between two topologically trivial ferromagnetic insulators can result in a nonzero Chern number, which offers a better way to realize the quantum anomalous Hall state without random magnetic doping. In addition, a simple effective model is presented to describe the basic mechanism of spin polarized band inversion in this system. Moreover, we predict that 3D quantum anomalous Hall insulator could be realized in (Bi2/3Cr1/3)2Te3 /GdI2 superlattice.
Quantum Hall effect in semiconductor systems with quantum dots and antidots
Beltukov, Ya. M.; Greshnov, A. A.
2015-04-15
The integer quantum Hall effect in systems of semiconductor quantum dots and antidots is studied theoretically as a factor of temperature. It is established that the conditions for carrier localization in quantum-dot systems favor the observation of the quantum Hall effect at higher temperatures than in quantum-well systems. The obtained numerical results show that the fundamental plateau corresponding to the transition between the ground and first excited Landau levels can be retained up to a temperature of T ∼ 50 K, which is an order of magnitude higher than in the case of quantum wells. Implementation of the quantum Hall effect at such temperatures requires quantum-dot systems with controllable characteristics, including the optimal size and concentration and moderate geometrical and composition fluctuations. In addition, ordered arrangement is desirable, hence quantum antidots are preferable.
Revealing the quantum regime in tunnelling plasmonics.
Savage, Kevin J; Hawkeye, Matthew M; Esteban, Rubén; Borisov, Andrei G; Aizpurua, Javier; Baumberg, Jeremy J
2012-11-22
When two metal nanostructures are placed nanometres apart, their optically driven free electrons couple electrically across the gap. The resulting plasmons have enhanced optical fields of a specific colour tightly confined inside the gap. Many emerging nanophotonic technologies depend on the careful control of this plasmonic coupling, including optical nanoantennas for high-sensitivity chemical and biological sensors, nanoscale control of active devices, and improved photovoltaic devices. But for subnanometre gaps, coherent quantum tunnelling becomes possible and the system enters a regime of extreme non-locality in which previous classical treatments fail. Electron correlations across the gap that are driven by quantum tunnelling require a new description of non-local transport, which is crucial in nanoscale optoelectronics and single-molecule electronics. Here, by simultaneously measuring both the electrical and optical properties of two gold nanostructures with controllable subnanometre separation, we reveal the quantum regime of tunnelling plasmonics in unprecedented detail. All observed phenomena are in good agreement with recent quantum-based models of plasmonic systems, which eliminate the singularities predicted by classical theories. These findings imply that tunnelling establishes a quantum limit for plasmonic field confinement of about 10(-8)λ(3) for visible light (of wavelength λ). Our work thus prompts new theoretical and experimental investigations into quantum-domain plasmonic systems, and will affect the future of nanoplasmonic device engineering and nanoscale photochemistry.
NASA Astrophysics Data System (ADS)
Kawamura, Minoru; Yoshimi, Ryutaro; Tsukazaki, Atsushi; Takahashi, Kei S.; Kawasaki, Masashi; Tokura, Yoshinori
2017-07-01
The instability of the quantum anomalous Hall (QAH) effect has been studied as a function of the electric current and temperature in ferromagnetic topological insulator thin films. We find that a characteristic current for the breakdown of the QAH effect is roughly proportional to the Hall-bar width, indicating that the Hall electric field is relevant to the breakdown. We also find that electron transport is dominated by variable range hopping (VRH) at low temperatures. Combining the current and temperature dependences of the conductivity in the VRH regime, the localization length of the QAH state is evaluated to be about 5 μ m . The long localization length suggests a marginally insulating nature of the QAH state due to a large number of in-gap states.
A programmable quantum current standard from the Josephson and the quantum Hall effects
Poirier, W. Lafont, F.; Djordjevic, S.; Schopfer, F.; Devoille, L.
2014-01-28
We propose a way to realize a programmable quantum current standard (PQCS) from the Josephson voltage standard and the quantum Hall resistance standard (QHR) exploiting the multiple connection technique provided by the quantum Hall effect (QHE) and the exactness of the cryogenic current comparator. The PQCS could lead to breakthroughs in electrical metrology like the realization of a programmable quantum current source, a quantum ampere-meter, and a simplified closure of the quantum metrological triangle. Moreover, very accurate universality tests of the QHE could be performed by comparing PQCS based on different QHRs.
Quantum Hall Fabry-Pérot interferometer: Logic gate responses
NASA Astrophysics Data System (ADS)
Bellucci, S.; Onorato, P.
2010-08-01
We discuss the electron transport through a quantum Hall Fabry-Pérot interferometer (QHFPI) obtained with two quantum point contacts (QPCs) in series along a ballistic quantum wire by focusing on the effects due to quantum interference and to quantum Hall effect. We calculate the conductance-energy and conductance-magnetic field characteristics as functions of the geometrical parameters and gate voltages. QHFPI may be utilized in designing electronic logic gates: XOR and OR (NOR and XNOR) gates responses are investigated. The width of each QPC is modulated by metallic electrodes where two gate voltages, namely, Va and Vb, are applied. Those external voltages are treated as the two inputs of the gates. After fixing appropriately the working Fermi energy, the magnetic field strength, and the distance between the barriers, a low output Hall current (0) (in the logical sense) appears just if both inputs are low (0), while a high output Hall current (1) results otherwise. It clearly demonstrates the OR gate behavior. By changing the parameters, a XOR gate can be produced, where a high output current (1) appears, when just one of the two inputs is low (0), while a low output current (0) results if both inputs are low (0) or high (1).
Quantum Hall physics: Hierarchies and conformal field theory techniques
NASA Astrophysics Data System (ADS)
Hansson, T. H.; Hermanns, M.; Simon, S. H.; Viefers, S. F.
2017-04-01
The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past 30 years, has generated many ground-breaking new ideas and concepts. Very early on it was realized that the zoo of emerging states of matter would need to be understood in a systematic manner. The first attempts to do this, by Haldane and Halperin, set an agenda for further work which has continued to this day. Since that time the idea of hierarchies of quasiparticles condensing to form new states has been a pillar of our understanding of fractional quantum Hall physics. In the 30 years that have passed since then, a number of new directions of thought have advanced our understanding of fractional quantum Hall states and have extended it in new and unexpected ways. Among these directions is the extensive use of topological quantum field theories and conformal field theories, the application of the ideas of composite bosons and fermions, and the study of non-Abelian quantum Hall liquids. This article aims to present a comprehensive overview of this field, including the most recent developments.
Disorder effects in the quantum Hall effect of graphene p-n junctions
NASA Astrophysics Data System (ADS)
Li, Jian; Shen, Shun-Qing
2008-11-01
The quantum Hall effect in graphene p-n junctions is studied numerically with emphasis on the effect of disorder at the interface of two adjacent regions. Conductance plateaus are found to be attached to the intensity of the disorder and are accompanied by universal conductance fluctuations in the bipolar regime, which is in good agreement with theoretical predictions of the random matrix theory on quantum chaotic cavities. The calculated Fano factors can be used in an experimental identification of the underlying transport character.
Tuning the spin Hall effect of Pt from the moderately dirty to the superclean regime
NASA Astrophysics Data System (ADS)
Sagasta, Edurne; Omori, Yasutomo; Isasa, Miren; Gradhand, Martin; Hueso, Luis E.; Niimi, Yasuhiro; Otani, YoshiChika; Casanova, Fèlix
2016-08-01
We systematically measure and analyze the spin diffusion length and the spin Hall effect in Pt with a wide range of conductivities using the spin absorption method in lateral spin valve devices. We observe a linear relation between the spin diffusion length and the conductivity, evidencing that the spin relaxation in Pt is governed by the Elliott-Yafet mechanism. We find a single intrinsic spin Hall conductivity (σSHint=1600 ±150 Ω-1c m-1) for Pt in the full range studied which is in good agreement with theory. We have obtained the crossover between the moderately dirty and the superclean scaling regimes of the spin Hall effect by tuning the conductivity. This is equivalent to that obtained for the anomalous Hall effect. Our results explain the spread of the spin Hall angle values in the literature and find a route to maximize this important parameter.
Minimal excitation states for heat transport in driven quantum Hall systems
NASA Astrophysics Data System (ADS)
Vannucci, Luca; Ronetti, Flavio; Rech, Jérôme; Ferraro, Dario; Jonckheere, Thibaut; Martin, Thierry; Sassetti, Maura
2017-06-01
We investigate minimal excitation states for heat transport into a fractional quantum Hall system driven out of equilibrium by means of time-periodic voltage pulses. A quantum point contact allows for tunneling of fractional quasiparticles between opposite edge states, thus acting as a beam splitter in the framework of the electron quantum optics. Excitations are then studied through heat and mixed noise generated by the random partitioning at the barrier. It is shown that levitons, the single-particle excitations of a filled Fermi sea recently observed in experiments, represent the cleanest states for heat transport since excess heat and mixed shot noise both vanish only when Lorentzian voltage pulses carrying integer electric charge are applied to the conductor. This happens in the integer quantum Hall regime and for Laughlin fractional states as well, with no influence of fractional physics on the conditions for clean energy pulses. In addition, we demonstrate the robustness of such excitations to the overlap of Lorentzian wave packets. Even though mixed and heat noise have nonlinear dependence on the voltage bias, and despite the noninteger power-law behavior arising from the fractional quantum Hall physics, an arbitrary superposition of levitons always generates minimal excitation states.
Multimode optomechanical system in the quantum regime.
Nielsen, William Hvidtfelt Padkær; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S; Schliesser, Albert
2017-01-03
We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 10(7)) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.
Multimode optomechanical system in the quantum regime
NASA Astrophysics Data System (ADS)
Hvidtfelt Padkær Nielsen, William; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S.; Schliesser, Albert
2017-01-01
We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 107) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry–Perot resonator detects these modes’ motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to ‑2.4 dB (‑3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry–Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.
The local nature of incompressibility of quantum Hall effect.
Kendirlik, E M; Sirt, S; Kalkan, S B; Ofek, N; Umansky, V; Siddiki, A
2017-01-10
Since the experimental realization of the integer quantum Hall effect in a two-dimensional electron system, the interrelation between the conductance quantization and the topological properties of the system has been investigated. Assuming that the two-dimensional electron system is described by a Bloch Hamiltonian, system is insulating in the bulk of sample throughout the quantum Hall plateau due to a magnetic field induced energy gap. Meanwhile, the system is conducting at the edges resembling a 2+1 dimensional topological insulator without time-reversal symmetry. Here, by our magneto-transport measurements performed on GaAs/AlGaAs high purity Hall bars with two inner contacts we show that incompressible strips formed at the edges result in Hall quantization, even if the bulk is compressible. Consequently, the relationship between the quantum Hall effect and topological bulk insulator breaks for specific field intervals within the plateaus. The measurement of conducting bulk, strongly challenges all existing single-particle theories.
The local nature of incompressibility of quantum Hall effect
NASA Astrophysics Data System (ADS)
Kendirlik, E. M.; Sirt, S.; Kalkan, S. B.; Ofek, N.; Umansky, V.; Siddiki, A.
2017-01-01
Since the experimental realization of the integer quantum Hall effect in a two-dimensional electron system, the interrelation between the conductance quantization and the topological properties of the system has been investigated. Assuming that the two-dimensional electron system is described by a Bloch Hamiltonian, system is insulating in the bulk of sample throughout the quantum Hall plateau due to a magnetic field induced energy gap. Meanwhile, the system is conducting at the edges resembling a 2+1 dimensional topological insulator without time-reversal symmetry. Here, by our magneto-transport measurements performed on GaAs/AlGaAs high purity Hall bars with two inner contacts we show that incompressible strips formed at the edges result in Hall quantization, even if the bulk is compressible. Consequently, the relationship between the quantum Hall effect and topological bulk insulator breaks for specific field intervals within the plateaus. The measurement of conducting bulk, strongly challenges all existing single-particle theories.
The local nature of incompressibility of quantum Hall effect
Kendirlik, E. M.; Sirt, S.; Kalkan, S. B.; Ofek, N.; Umansky, V.; Siddiki, A.
2017-01-01
Since the experimental realization of the integer quantum Hall effect in a two-dimensional electron system, the interrelation between the conductance quantization and the topological properties of the system has been investigated. Assuming that the two-dimensional electron system is described by a Bloch Hamiltonian, system is insulating in the bulk of sample throughout the quantum Hall plateau due to a magnetic field induced energy gap. Meanwhile, the system is conducting at the edges resembling a 2+1 dimensional topological insulator without time-reversal symmetry. Here, by our magneto-transport measurements performed on GaAs/AlGaAs high purity Hall bars with two inner contacts we show that incompressible strips formed at the edges result in Hall quantization, even if the bulk is compressible. Consequently, the relationship between the quantum Hall effect and topological bulk insulator breaks for specific field intervals within the plateaus. The measurement of conducting bulk, strongly challenges all existing single-particle theories. PMID:28071652
Cavity Optomechanics in the Quantum Regime
NASA Astrophysics Data System (ADS)
Botter, Thierry Claude Marc
An exciting scientific goal, common to many fields of research, is the development of ever-larger physical systems operating in the quantum regime. Relevant to this dissertation is the objective of preparing and observing a mechanical object in its motional quantum ground state. In order to sense the object's zero-point motion, the probe itself must have quantum-limited sensitivity. Cavity optomechanics, the interactions between light and a mechanical object inside an optical cavity, provides an elegant means to achieve the quantum regime. In this dissertation, I provide context to the successful cavity-based optical detection of the quantum-ground-state motion of atoms-based mechanical elements; mechanical elements, consisting of the collective center-of-mass (CM) motion of ultracold atomic ensembles and prepared inside a high-finesse Fabry-Perot cavity, were dispersively probed with an average intracavity photon number as small as 0.1. I first show that cavity optomechanics emerges from the theory of cavity quantum electrodynamics when one takes into account the CM motion of one or many atoms within the cavity, and provide a simple theoretical framework to model optomechanical interactions. I then outline details regarding the apparatus and the experimental methods employed, highlighting certain fundamental aspects of optical detection along the way. Finally, I describe background information, both theoretical and experimental, to two published results on quantum cavity optomechanics that form the backbone of this dissertation. The first publication shows the observation of zero-point collective motion of several thousand atoms and quantum-limited measurement backaction on that observed motion. The second publication demonstrates that an array of near-ground-state collective atomic oscillators can be simultaneously prepared and probed, and that the motional state of one oscillator can be selectively addressed while preserving the near-zero-point motion of
Hall effect in quantum critical charge-cluster glass.
Wu, Jie; Bollinger, Anthony T; Sun, Yujie; Božović, Ivan
2016-04-19
Upon doping, cuprates undergo a quantum phase transition from an insulator to a d-wave superconductor. The nature of this transition and of the insulating state is vividly debated. Here, we study the Hall effect in La2-xSrxCuO4(LSCO) samples doped near the quantum critical point atx∼ 0.06. Dramatic fluctuations in the Hall resistance appear belowTCG∼ 1.5 K and increase as the sample is cooled down further, signaling quantum critical behavior. We explore the doping dependence of this effect in detail, by studying a combinatorial LSCO library in which the Sr content is varied in extremely fine steps,Δx∼ 0.00008. We observe that quantum charge fluctuations wash out when superconductivity emerges but can be restored when the latter is suppressed by applying a magnetic field, showing that the two instabilities compete for the ground state.
Hall effect in quantum critical charge-cluster glass
Wu, Jie; Bollinger, Anthony T.; Sun, Yujie; Božović, Ivan
2016-01-01
Upon doping, cuprates undergo a quantum phase transition from an insulator to a d-wave superconductor. The nature of this transition and of the insulating state is vividly debated. Here, we study the Hall effect in La2-xSrxCuO4 (LSCO) samples doped near the quantum critical point at x ∼ 0.06. Dramatic fluctuations in the Hall resistance appear below TCG ∼ 1.5 K and increase as the sample is cooled down further, signaling quantum critical behavior. We explore the doping dependence of this effect in detail, by studying a combinatorial LSCO library in which the Sr content is varied in extremely fine steps, Δx ∼ 0.00008. We observe that quantum charge fluctuations wash out when superconductivity emerges but can be restored when the latter is suppressed by applying a magnetic field, showing that the two instabilities compete for the ground state. PMID:27044081
Admittance of multiterminal quantum Hall conductors at kilohertz frequencies
Hernández, C.; Consejo, C.; Chaubet, C.; Degiovanni, P.
2014-03-28
We present an experimental study of the low frequency admittance of quantum Hall conductors in the [100 Hz, 1 MHz] frequency range. We show that the frequency dependence of the admittance of the sample strongly depends on the topology of the contacts connections. Our experimental results are well explained within the Christen and Büttiker approach for finite frequency transport in quantum Hall edge channels taking into account the influence of the coaxial cables capacitance. In the Hall bar geometry, we demonstrate that there exists a configuration in which the cable capacitance does not influence the admittance measurement of the sample. In this case, we measure the electrochemical capacitance of the sample and observe its dependence on the filling factor.
Density-Functional Theory of the Fractional Quantum Hall Effect.
Zhao, Jianyun; Thakurathi, Manisha; Jain, Manish; Sen, Diptiman; Jain, J K
2017-05-12
A conceptual difficulty in formulating the density-functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn-Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.
Density-Functional Theory of the Fractional Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Zhao, Jianyun; Thakurathi, Manisha; Jain, Manish; Sen, Diptiman; Jain, J. K.
2017-05-01
A conceptual difficulty in formulating the density-functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn-Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.
Few-body treatment of the quantum Hall system
NASA Astrophysics Data System (ADS)
Greene, Chris; Daily, Kevin; Wooten, Rachel
2015-03-01
The quantum Hall system is perhaps the simplest real physical system to exhibit complicated, highly-correlated quantum behavior. Our initial theoretical exploration of this problem approaches it from a few-body perspective using the adiabatic hyperspherical representation developed originally for atomic systems. Such a 2D system with interacting charged particles that move in an external magnetic field can be simulated for cold atoms using artificial vector gauge potentials. Supported by NSF.
A two fluid description of the Quantum Hall Soliton
Freivogel, Ben; Susskind, Leonard; Toumbas, Nicolaos
2015-02-03
We show that the Quantum Hall Soliton constructed in [1] is stable under small perturbations. We find that creating quasiparticles actually lowers the energy of the system, and discuss whether this indicates an instability on the time scales relevant to the problem.
Nonreciprocal quantum Hall devices with driven edge magnetoplasmons in two-dimensional materials
NASA Astrophysics Data System (ADS)
Bosco, S.; DiVincenzo, D. P.
2017-05-01
We develop a theory that describes the response of nonreciprocal devices employing two-dimensional materials in the quantum Hall regime capacitively coupled to external electrodes. As the conduction in these devices is understood to be associated to the edge magnetoplasmons (EMPs), we first investigate the EMP problem by using the linear response theory in the random phase approximation. Our model can incorporate several cases that were often treated on different grounds in literature. In particular, we analyze plasmonic excitations supported by a smooth and sharp confining potential in a two-dimensional electron gas, and in monolayer graphene, and we point out the similarities and differences in these materials. We also account for a general time-dependent external drive applied to the system. Finally, we describe the behavior of a nonreciprocal quantum Hall device: the response contains additional resonant features, which were not foreseen from previous models.
Vanishing hall coefficient in the extreme quantum limit in photocarrier-doped SrTiO3.
Kozuka, Y; Susaki, T; Hwang, H Y
2008-08-29
We explore the extreme quantum limit of photogenerated electrons in quantum paraelectric SrTiO3. This regime is distinct from conventional semiconductors, due to the large electron effective mass and large dielectric constant. At low temperature, the magnetoresistance and Hall resistivity saturate at a high magnetic field, deviating from conventional behavior. As a result, the Hall coefficient vanishes on the scale of the ratio of the Landau level splitting to the thermal energy, indicating the essential role of lowest Landau level occupancy, as limited by thermal broadening.
Band Collapse and the Quantum Hall Effect in Graphene
Bernevig, B.Andrei; Hughes, Taylor L.; Zhang, Shou-Cheng; Chen, Han-Dong; Wu, Congjun; /Santa Barbara, KITP
2010-03-16
The recent Quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall (QH) conductance in fermion systems with continuum Dirac spectrum. In this paper we take into account the lattice, and perform an exact diagonalization of the Landau problem on the hexagonal lattice. At very large magnetic fields the Dirac argument fails completely and the Hall conductance, given by the number of edge states present in the gaps of the spectrum, is dominated by lattice effects. As the field is lowered, the experimentally observed situation is recovered through a phenomenon which we call band collapse. As a corollary, for low magnetic field, graphene will exhibit two qualitatively different QHE's: at low filling, the QHE will be dominated by the 'relativistic' Dirac spectrum and the Hall conductance will be odd-integer; above a certain filling, the QHE will be dominated by a non-relativistic spectrum, and the Hall conductance will span all integers, even and odd.
Signatures of lattice geometry in quantum and topological Hall effect
NASA Astrophysics Data System (ADS)
Göbel, Börge; Mook, Alexander; Henk, Jürgen; Mertig, Ingrid
2017-06-01
The topological Hall effect (THE) of electrons in skyrmion crystals (SkXs) is strongly related to the quantum Hall effect (QHE) on lattices. This relation suggests to revisit the QHE because its Hall conductivity can be unconventionally quantized. It exhibits a jump and changes sign abruptly if the Fermi level crosses a van Hove singularity. In this Paper, we investigate the unconventional QHE features by discussing band structures, Hall conductivities, and topological edge states for square and triangular lattices; their origin are Chern numbers of bands in the SkX (THE) or of the corresponding Landau levels (QHE). Striking features in the energy dependence of the Hall conductivities are traced back to the band structure without magnetic field whose properties are dictated by the lattice geometry. Based on these findings, we derive an approximation that allows us to determine the energy dependence of the topological Hall conductivity on any two-dimensional lattice. The validity of this approximation is proven for the honeycomb lattice. We conclude that SkXs lend themselves for experiments to validate our findings for the THE and—indirectly—the QHE.
Dynamical quantum Hall effect in the parameter space.
Gritsev, V; Polkovnikov, A
2012-04-24
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase [M.V. Berry (1984), Proc. Royal. Soc. London A, 392:45], which naturally emerges in quantum adiabatic evolution. So far the applicability and measurements of the Berry phase were mostly limited to systems of weakly interacting quasi-particles, where interference experiments are feasible. Here we show how one can go beyond this limitation and observe the Berry curvature, and hence the Berry phase, in generic systems as a nonadiabatic response of physical observables to the rate of change of an external parameter. These results can be interpreted as a dynamical quantum Hall effect in a parameter space. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. We observe the quantization of this response, which we term the rotational quantum Hall effect.
Observation of the fractional quantum Hall effect in an oxide.
Tsukazaki, A; Akasaka, S; Nakahara, K; Ohno, Y; Ohno, H; Maryenko, D; Ohtomo, A; Kawasaki, M
2010-11-01
The quantum Hall effect arises from the cyclotron motion of charge carriers in two-dimensional systems. However, the ground states related to the integer and fractional quantum Hall effect, respectively, are of entirely different origin. The former can be explained within a single-particle picture; the latter arises from electron correlation effects governed by Coulomb interaction. The prerequisite for the observation of these effects is extremely smooth interfaces of the thin film layers to which the charge carriers are confined. So far, experimental observations of such quantum transport phenomena have been limited to a few material systems based on silicon, III-V compounds and graphene. In ionic materials, the correlation between electrons is expected to be more pronounced than in the conventional heterostructures, owing to a large effective mass of charge carriers. Here we report the observation of the fractional quantum Hall effect in MgZnO/ZnO heterostructures grown by molecular-beam epitaxy, in which the electron mobility exceeds 180,000 cm(2) V(-1) s(-1). Fractional states such as ν = 4/3, 5/3 and 8/3 clearly emerge, and the appearance of the ν = 2/5 state is indicated. The present study represents a technological advance in oxide electronics that provides opportunities to explore strongly correlated phenomena in quantum transport of dilute carriers.
Observation of the fractional quantum Hall effect in an oxide
NASA Astrophysics Data System (ADS)
Tsukazaki, A.; Akasaka, S.; Nakahara, K.; Ohno, Y.; Ohno, H.; Maryenko, D.; Ohtomo, A.; Kawasaki, M.
2010-11-01
The quantum Hall effect arises from the cyclotron motion of charge carriers in two-dimensional systems. However, the ground states related to the integer and fractional quantum Hall effect, respectively, are of entirely different origin. The former can be explained within a single-particle picture; the latter arises from electron correlation effects governed by Coulomb interaction. The prerequisite for the observation of these effects is extremely smooth interfaces of the thin film layers to which the charge carriers are confined. So far, experimental observations of such quantum transport phenomena have been limited to a few material systems based on silicon, III-V compounds and graphene. In ionic materials, the correlation between electrons is expected to be more pronounced than in the conventional heterostructures, owing to a large effective mass of charge carriers. Here we report the observation of the fractional quantum Hall effect in MgZnO/ZnO heterostructures grown by molecular-beam epitaxy, in which the electron mobility exceeds 180,000cm2V-1s-1. Fractional states such as ν=4/3, 5/3 and 8/3 clearly emerge, and the appearance of the ν=2/5 state is indicated. The present study represents a technological advance in oxide electronics that provides opportunities to explore strongly correlated phenomena in quantum transport of dilute carriers.
Nonlocal Polarization Feedback in a Fractional Quantum Hall Ferromagnet.
Hennel, Szymon; Braem, Beat A; Baer, Stephan; Tiemann, Lars; Sohi, Pirouz; Wehrli, Dominik; Hofmann, Andrea; Reichl, Christian; Wegscheider, Werner; Rössler, Clemens; Ihn, Thomas; Ensslin, Klaus; Rudner, Mark S; Rosenow, Bernd
2016-04-01
In a quantum Hall ferromagnet, the spin polarization of the two-dimensional electron system can be dynamically transferred to nuclear spins in its vicinity through the hyperfine interaction. The resulting nuclear field typically acts back locally, modifying the local electronic Zeeman energy. Here we report a nonlocal effect arising from the interplay between nuclear polarization and the spatial structure of electronic domains in a ν=2/3 fractional quantum Hall state. In our experiments, we use a quantum point contact to locally control and probe the domain structure of different spin configurations emerging at the spin phase transition. Feedback between nuclear and electronic degrees of freedom gives rise to memristive behavior, where electronic transport through the quantum point contact depends on the history of current flow. We propose a model for this effect which suggests a novel route to studying edge states in fractional quantum Hall systems and may account for so-far unexplained oscillatory electronic-transport features observed in previous studies.
Nonlocal Polarization Feedback in a Fractional Quantum Hall Ferromagnet
NASA Astrophysics Data System (ADS)
Hennel, Szymon; Braem, Beat A.; Baer, Stephan; Tiemann, Lars; Sohi, Pirouz; Wehrli, Dominik; Hofmann, Andrea; Reichl, Christian; Wegscheider, Werner; Rössler, Clemens; Ihn, Thomas; Ensslin, Klaus; Rudner, Mark S.; Rosenow, Bernd
2016-04-01
In a quantum Hall ferromagnet, the spin polarization of the two-dimensional electron system can be dynamically transferred to nuclear spins in its vicinity through the hyperfine interaction. The resulting nuclear field typically acts back locally, modifying the local electronic Zeeman energy. Here we report a nonlocal effect arising from the interplay between nuclear polarization and the spatial structure of electronic domains in a ν =2 /3 fractional quantum Hall state. In our experiments, we use a quantum point contact to locally control and probe the domain structure of different spin configurations emerging at the spin phase transition. Feedback between nuclear and electronic degrees of freedom gives rise to memristive behavior, where electronic transport through the quantum point contact depends on the history of current flow. We propose a model for this effect which suggests a novel route to studying edge states in fractional quantum Hall systems and may account for so-far unexplained oscillatory electronic-transport features observed in previous studies.
Symmetry-induced anyon breeding in fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Lu, Yuan-Ming; Fidkowski, Lukasz
2014-03-01
An exotic feature of the fractional quantum Hall effect is the emergence of anyons, which are quasiparticle excitations with fractional statistics. In the presence of a symmetry, such as U (1) charge conservation, it is well known that anyons can carry fractional symmetry quantum numbers. In this paper we reveal a different class of symmetry realizations, i.e., anyons can "breed" in multiples under symmetry operation. We focus on the global Ising (Z2) symmetry and show examples of these unconventional symmetry realizations in Laughlin-type fractional quantum Hall states. One remarkable consequence of such an Ising symmetry is the emergence of anyons on the Ising symmetry domain walls. We also provide a mathematical framework which generalizes this phenomenon to any Abelian topological orders.
Effect of quantum tunneling on spin Hall magnetoresistance
NASA Astrophysics Data System (ADS)
Ok, Seulgi; Chen, Wei; Sigrist, Manfred; Manske, Dirk
2017-02-01
We present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on the spin Hall magnetoresistance observed in normal metal/ferromagnetic insulator bilayers (such as Pt/Y3Fe5O12) and normal metal/ferromagnetic metal bilayers (such as Pt/Co), in which the angle of magnetization influences the magnetoresistance of the normal metal. In the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin Hall effect and subsequently the magnetoresistance, while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation. The influence of generic material properties such as spin diffusion length, layer thickness, interface coupling, and insulating gap can be quantified in a unified manner, and experiments that reveal the quantum feature of the magnetoresistance are suggested.
Effect of quantum tunneling on spin Hall magnetoresistance.
Ok, Seulgi; Chen, Wei; Sigrist, Manfred; Manske, Dirk
2017-02-22
We present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on the spin Hall magnetoresistance observed in normal metal/ferromagnetic insulator bilayers (such as Pt/Y3Fe5O12) and normal metal/ferromagnetic metal bilayers (such as Pt/Co), in which the angle of magnetization influences the magnetoresistance of the normal metal. In the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin Hall effect and subsequently the magnetoresistance, while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation. The influence of generic material properties such as spin diffusion length, layer thickness, interface coupling, and insulating gap can be quantified in a unified manner, and experiments that reveal the quantum feature of the magnetoresistance are suggested.
Mini array of quantum Hall devices based on epitaxial graphene
NASA Astrophysics Data System (ADS)
Novikov, S.; Lebedeva, N.; Hämäläinen, J.; Iisakka, I.; Immonen, P.; Manninen, A. J.; Satrapinski, A.
2016-05-01
Series connection of four quantum Hall effect (QHE) devices based on epitaxial graphene films was studied for realization of a quantum resistance standard with an up-scaled value. The tested devices showed quantum Hall plateaux RH,2 at a filling factor v = 2 starting from a relatively low magnetic field (between 4 T and 5 T) when the temperature was 1.5 K. The precision measurements of quantized Hall resistance of four QHE devices connected by triple series connections and external bonding wires were done at B = 7 T and T = 1.5 K using a commercial precision resistance bridge with 50 μA current through the QHE device. The results showed that the deviation of the quantized Hall resistance of the series connection of four graphene-based QHE devices from the expected value of 4×RH,2 = 2 h/e2 was smaller than the relative standard uncertainty of the measurement (<1 × 10-7) limited by the used resistance bridge.
Mini array of quantum Hall devices based on epitaxial graphene
Novikov, S.; Lebedeva, N.; Hämäläinen, J.; Iisakka, I.; Immonen, P.; Manninen, A. J.; Satrapinski, A.
2016-05-07
Series connection of four quantum Hall effect (QHE) devices based on epitaxial graphene films was studied for realization of a quantum resistance standard with an up-scaled value. The tested devices showed quantum Hall plateaux R{sub H,2} at a filling factor v = 2 starting from a relatively low magnetic field (between 4 T and 5 T) when the temperature was 1.5 K. The precision measurements of quantized Hall resistance of four QHE devices connected by triple series connections and external bonding wires were done at B = 7 T and T = 1.5 K using a commercial precision resistance bridge with 50 μA current through the QHE device. The results showed that the deviation of the quantized Hall resistance of the series connection of four graphene-based QHE devices from the expected value of 4×R{sub H,2} = 2 h/e{sup 2} was smaller than the relative standard uncertainty of the measurement (<1 × 10{sup −7}) limited by the used resistance bridge.
Light-induced electron localization in a quantum Hall system
NASA Astrophysics Data System (ADS)
Arikawa, T.; Hyodo, K.; Kadoya, Y.; Tanaka, K.
2017-07-01
An insulating bulk state is a prerequisite for the protection of topological edge states. In quantum Hall systems, the thermal excitation of delocalized electrons is the main route to breaking bulk insulation. In equilibrium, the only way to achieve a clear bulk gap is to use a high-quality crystal under high magnetic field at low temperature. However, bulk conduction could also be suppressed in a system driven out of equilibrium such that localized states in the Landau levels are selectively occupied. Here we report a transient suppression of bulk conduction induced by terahertz wave excitation between the Landau levels in a GaAs quantum Hall system. Strikingly, the Hall resistivity almost reaches the quantized value at a temperature where the exact quantization is normally disrupted by thermal fluctuations. The electron localization is realized by the long-range potential fluctuations, which are a unique and inherent feature of quantum Hall systems. Our results demonstrate a new means of effecting dynamical control of topology by manipulating bulk conduction using light.
Quantum anomalous Hall effect in topological insulator memory
Jalil, Mansoor B. A.; Tan, S. G.; Siu, Z. B.
2015-05-07
We theoretically investigate the quantum anomalous Hall effect (QAHE) in a magnetically coupled three-dimensional-topological insulator (3D-TI) system. We apply the generalized spin-orbit coupling Hamiltonian to obtain the Hall conductivity σ{sup xy} of the system. The underlying topology of the QAHE phenomenon is then analyzed to show the quantization of σ{sup xy} and its relation to the Berry phase of the system. Finally, we analyze the feasibility of utilizing σ{sup xy} as a memory read-out in a 3D-TI based memory at finite temperatures, with comparison to known magnetically doped 3D-TIs.
Information Causality in the Quantum and Post-Quantum Regime
Ringbauer, Martin; Fedrizzi, Alessandro; Berry, Dominic W.; White, Andrew G.
2014-01-01
Quantum correlations can be stronger than anything achieved by classical systems, yet they are not reaching the limit imposed by relativity. The principle of information causality offers a possible explanation for why the world is quantum and why there appear to be no even stronger correlations. Generalizing the no-signaling condition it suggests that the amount of accessible information must not be larger than the amount of transmitted information. Here we study this principle experimentally in the classical, quantum and post-quantum regimes. We simulate correlations that are stronger than allowed by quantum mechanics by exploiting the effect of polarization-dependent loss in a photonic Bell-test experiment. Our method also applies to other fundamental principles and our results highlight the special importance of anisotropic regions of the no-signalling polytope in the study of fundamental principles. PMID:25378182
Information causality in the quantum and post-quantum regime.
Ringbauer, Martin; Fedrizzi, Alessandro; Berry, Dominic W; White, Andrew G
2014-11-07
Quantum correlations can be stronger than anything achieved by classical systems, yet they are not reaching the limit imposed by relativity. The principle of information causality offers a possible explanation for why the world is quantum and why there appear to be no even stronger correlations. Generalizing the no-signaling condition it suggests that the amount of accessible information must not be larger than the amount of transmitted information. Here we study this principle experimentally in the classical, quantum and post-quantum regimes. We simulate correlations that are stronger than allowed by quantum mechanics by exploiting the effect of polarization-dependent loss in a photonic Bell-test experiment. Our method also applies to other fundamental principles and our results highlight the special importance of anisotropic regions of the no-signalling polytope in the study of fundamental principles.
Chiral partition functions of quantum Hall droplets
Cappelli, Andrea Viola, Giovanni; Zemba, Guillermo R.
2010-02-15
Chiral partition functions of conformal field theory describe the edge excitations of isolated Hall droplets. They are characterized by an index specifying the quasiparticle sector and transform among themselves by a finite-dimensional representation of the modular group. The partition functions are derived and used to describe electron transitions leading to Coulomb blockade conductance peaks. We find the peak patterns for Abelian hierarchical states and non-Abelian Read-Rezayi states, and compare them. Experimental observation of these features can check the qualitative properties of the conformal field theory description, such as the decomposition of the Hilbert space into sectors, involving charged and neutral parts, and the fusion rules.
Intrinsic Spin Hall Effect Induced by Quantum Phase Transition in HgCdTe Quantum Wells
Yang, Wen; Chang, Kai; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
Spin Hall effect can be induced both by the extrinsic impurity scattering and by the intrinsic spin-orbit coupling in the electronic structure. The HgTe/CdTe quantum well has a quantum phase transition where the electronic structure changes from normal to inverted. We show that the intrinsic spin Hall effect of the conduction band vanishes on the normal side, while it is finite on the inverted side. This difference gives a direct mechanism to experimentally distinguish the intrinsic spin Hall effect from the extrinsic one.
Quantum Hall effect on Riemann surfaces
NASA Astrophysics Data System (ADS)
Tejero Prieto, Carlos
2009-06-01
We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion.
Density-controlled quantum Hall ferromagnetic transition in a two-dimensional hole system
Lu, T. M.; Tracy, L. A.; Laroche, D.; ...
2017-06-01
We typically achieve Quantum Hall ferromagnetic transitions by increasing the Zeeman energy through in-situ sample rotation, while transitions in systems with pseudo-spin indices can be induced by gate control. We report here a gate-controlled quantum Hall ferromagnetic transition between two real spin states in a conventional two-dimensional system without any in-plane magnetic field. We also show that the ratio of the Zeeman splitting to the cyclotron gap in a Ge two-dimensional hole system increases with decreasing density owing to inter-carrier interactions. Below a critical density of ~2.4 × 1010 cm-2, this ratio grows greater than 1, resulting in a ferromagneticmore » ground state at filling factor ν = 2. At the critical density, a resistance peak due to the formation of microscopic domains of opposite spin orientations is observed. For such gate-controlled spin-polarizations in the quantum Hall regime the door opens in order to realize Majorana modes using two-dimensional systems in conventional, low-spin-orbit-coupling semiconductors.« less
Spin Superfluidity in the ν =0 Quantum Hall State of Graphene
NASA Astrophysics Data System (ADS)
Takei, So; Yacoby, Amir; Halperin, Bertrand I.; Tserkovnyak, Yaroslav
2016-05-01
Strong electron interactions can lead to a variety of broken-symmetry phases in monolayer graphene. In the quantum Hall regime, the interaction effect are enhanced by the formation of highly degenerate Landau levels, catalyzing the emergence of such phases. Recent magnetotransport studies show evidence that the ν =0 quantum Hall state of graphene is in an insulating canted antiferromagnetic phase with the Néel vector lying within the graphene plane. Here, we show that this Néel order can be detected via two-terminal spin transport. We find that a dynamic and inhomogeneous texture of the Néel vector can mediate nearly dissipationless (superfluid) transport of spin angular momentum polarized along the z axis, which could serve as a strong support for the antiferromagnetic scenario. The injection and detection of spin current in the ν =0 region can be achieved using the two spin-polarized edge channels of the |ν |=2 quantum Hall state. Measurements of the dependence of the spin current on the length of the ν =0 region would provide direct evidence for spin superfluidity.
Edge states in twisted bilayer graphene: quantum spin Hall and electron-hole bilayers
NASA Astrophysics Data System (ADS)
Sanchez-Yamagishi, Javier D.; Luo, Jason; Watanabe, Kenji; Taniguchi, Takashi; Jarillo-Herrero, Pablo
2015-03-01
Twisted bilayer graphene offers a unique platform for studying 1d edge states in a bilayer 2-dimensional electron gas. Despite being spaced by only 0.34 nm, a large interlayer twist decouples the layers in the bulk, while opening the door for interesting interactions at the edges. To probe this physics, we study the electronic transport through quantum Hall edge modes in twisted bilayer graphene devices. Using dual electrostatic gates, we independently control the filling factor of each layer to form different combinations of bilayer edge states while measuring their conductance. The most dramatic transport effects are observed when the layers are doped to have edge states of opposite chiralities, resulting in coexisting electron- and hole-like states. We will present evidence that, in this regime, the twisted bilayer graphene can form a quantum spin Hall state where edge states in each layer counter-propagate in opposite directions with opposite spin polarizations. This bilayer realization offers a flexible system to study quantum spin Hall edge transport as well as to build more complex 1d circuits. We will also discuss the possibility for fractional generalizations of this edge physics and our measurements of the fractional QHE in twisted bilayer graphene.
Imperfect relativistic mirrors in the quantum regime
Mendonça, J. T.; Serbeto, A.; Galvão, R. M. O.
2014-05-15
The collective backscattering of intense laser radiation by energetic electron beams is considered in the relativistic quantum regime. Exact solutions for the radiation field are obtained, for arbitrary electron pulse shapes and laser intensities. The electron beams act as imperfect nonlinear mirrors on the incident laser radiation. This collective backscattering process can lead to the development of new sources of ultra-short pulse radiation in the gamma-ray domain. Numerical examples show that, for plausible experimental conditions, intense pulses of gamma-rays, due to the double Doppler shift of the harmonics of the incident laser radiation, can be produced using the available technology, with durations less than 1 as.
``Spin-orbit" susceptibility in the quantum spin Hall systems
NASA Astrophysics Data System (ADS)
Murakami, Shuichi
2006-03-01
There are two classes of insulators showing the spin Hall effect. One is a spin Hall insulator such as PbTe while the other is a quantum spin Hall system. They are distinguished by an absence or presence of edge states. To study such insulators showing the spin Hall effect, we construct a spin analog of the Streda formula. We use the conserved spin current as proposed by Zhang et al.[cond-mat/0503505], thereby the resulting Streda formula becomes quite simple (i.e. without any s terms). As a result, the spin Hall conductivity for band insulators is proportional to a ``spin- orbit'' susceptibility, representing a response of the orbital magnetization to the Zeeman field (or equivalently a response of the spin magnetiation to the orbital magnetic field). We apply the result to real systems such as Bi1-xSbx, because in insulating Bi1-xSbx the diamagnetic susceptibility is largely enhanced due to the spin-orbit coupling.
Disorder-Induced Stabilization of the Quantum Hall Ferromagnet
NASA Astrophysics Data System (ADS)
Piot, B. A.; Desrat, W.; Maude, D. K.; Kazazis, D.; Cavanna, A.; Gennser, U.
2016-03-01
We report on an absolute measurement of the electronic spin polarization of the ν =1 integer quantum Hall state. The spin polarization is extracted in the vicinity of ν =1 (including at exactly ν =1 ) via resistive NMR experiments performed at different magnetic fields (electron densities) and Zeeman energy configurations. At the lowest magnetic fields, the polarization is found to be complete in a narrow region around ν =1 . Increasing the magnetic field (electron density) induces a significant depolarization of the system, which we attribute to a transition between the quantum Hall ferromagnet and the Skyrmion glass phase theoretically expected as the ratio between Coulomb interactions and disorder is increased. These observations account for the fragility of the polarization previously observed in high mobility 2D electron gas and experimentally demonstrate the existence of an optimal amount of disorder to stabilize the ferromagnetic state.
Fractionally charged skyrmions in fractional quantum Hall effect.
Balram, Ajit C; Wurstbauer, U; Wójs, A; Pinczuk, A; Jain, J K
2015-11-26
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.
Fractionally charged skyrmions in fractional quantum Hall effect
Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; Pinczuk, A.; Jain, J. K.
2015-11-26
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.
Quantum Hall effect in epitaxial graphene with permanent magnets
NASA Astrophysics Data System (ADS)
Parmentier, F. D.; Cazimajou, T.; Sekine, Y.; Hibino, H.; Irie, H.; Glattli, D. C.; Kumada, N.; Roulleau, P.
2016-12-01
We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, for the first time, only commercial NdFeB permanent magnets at low temperature. The relatively large and homogeneous magnetic field generated by the magnets, together with the high quality of the epitaxial graphene films, enables the formation of well-developed quantum Hall states at Landau level filling factors v = ±2, commonly observed with superconducting electro-magnets. Furthermore, the chirality of the QHE edge channels can be changed by a top gate. These results demonstrate that basic QHE physics are experimentally accessible in graphene for a fraction of the price of conventional setups using superconducting magnets, which greatly increases the potential of the QHE in graphene for research and applications.
Disclination Unbinding Transition in Quantum Hall Liquid Crystals
NASA Astrophysics Data System (ADS)
Wexler, Carlos
2002-03-01
Recent experiments [1] in the transitional region between plateaus of the quantum Hall effect have revealed a plæthora of unusual behavior in the low-temperature magnetotransport: in particular large anisotropies of the longitudinal resistivities are observed at temperatures lower than ca. 150 mK for near half filling of high (N>= 2) Landau levels (LL). the long-wavelength elastic theory for the quantum Hall smectic state starting from the Hartree-Fock approximation. Dislocations and phonons lead to an effective nematic model for T>0. This model undergoes a Kosterlitz-Thouless disclination unbinding transition from a phase with algebraic orientational order into an isotropic phase. Without the use of any fitting parameter, we obtain transition temperatures which are in qualitative agreement with recent experiments which have observed large anisotropies of the longitudinal resistivities in half-filled Landau levels, lending credence to the liquid crystal interpretation [3] of experiments. [[1
Quasiparticle Aggregation in the Fractional Quantum Hall Effect
DOE R&D Accomplishments Database
Laughlin, R. B.
1984-10-10
Quasiparticles in the Fractional Quantum Hall Effect behave qualitatively like electrons confined to the lowest landau level, and can do everything electrons can do, including condense into second generation Fractional Quantum Hall ground states. I review in this paper the reasoning leading to variational wavefunctions for ground state and quasiparticles in the 1/3 effect. I then show how two-quasiparticle eigenstates are uniquely determined from symmetry, and how this leads in a natural way to variational wavefunctions for composite states which have the correct densities (2/5, 2/7, ...). I show in the process that the boson, anyon and fermion representations for the quasiparticles used by Haldane, Halperin, and me are all equivalent. I demonstrate a simple way to derive Halperin`s multiple-valued quasiparticle wavefunction from the correct single-valued electron wavefunction. (auth)
Quantum Hall effect in epitaxial graphene with permanent magnets
Parmentier, F. D.; Cazimajou, T.; Sekine, Y.; Hibino, H.; Irie, H.; Glattli, D. C.; Kumada, N.; Roulleau, P.
2016-01-01
We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, for the first time, only commercial NdFeB permanent magnets at low temperature. The relatively large and homogeneous magnetic field generated by the magnets, together with the high quality of the epitaxial graphene films, enables the formation of well-developed quantum Hall states at Landau level filling factors v = ±2, commonly observed with superconducting electro-magnets. Furthermore, the chirality of the QHE edge channels can be changed by a top gate. These results demonstrate that basic QHE physics are experimentally accessible in graphene for a fraction of the price of conventional setups using superconducting magnets, which greatly increases the potential of the QHE in graphene for research and applications. PMID:27922114
Corrections to scaling near the quantum Hall transition
NASA Astrophysics Data System (ADS)
Evers, Ferdinand; Obuse, Hideaki; Bera, Soumya; Gruzberg, Ilya
2012-02-01
Corrections to scaling near critical points are important to understand, because they superimpose and often obscure the true asymptotics of critical scaling laws. This is true, in particular, for studies near the quantum Hall transition where recent numerical work by Slevin and Ohtsuki (Phys. Rev. B 80, 041304 (2009)) reports a very small value for the leading irrelevant scaling index |y| 0.17. We here report a numerical study of two-point conductances and two-terminal conductances at the integer quantum Hall transition within the Chalker-Coddington network. The scaling of these observables will be analyzed in the two-dimensional and the quasi-onedimensional geometries. We confirm the relation between the conductance exponents Xq and the anomalous dimensions δq known from the multifractal wavefunction analysis: Xq=2δq. For a consistent picure it is essential to carefully account for corrections to scaling due to subleading power laws and irrelevant scaling operators.
Quantum Hall effect in epitaxial graphene with permanent magnets.
Parmentier, F D; Cazimajou, T; Sekine, Y; Hibino, H; Irie, H; Glattli, D C; Kumada, N; Roulleau, P
2016-12-06
We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, for the first time, only commercial NdFeB permanent magnets at low temperature. The relatively large and homogeneous magnetic field generated by the magnets, together with the high quality of the epitaxial graphene films, enables the formation of well-developed quantum Hall states at Landau level filling factors v = ±2, commonly observed with superconducting electro-magnets. Furthermore, the chirality of the QHE edge channels can be changed by a top gate. These results demonstrate that basic QHE physics are experimentally accessible in graphene for a fraction of the price of conventional setups using superconducting magnets, which greatly increases the potential of the QHE in graphene for research and applications.
Gapless modes of fractional quantum Hall edges: a Hamiltonian study
NASA Astrophysics Data System (ADS)
Nguyen, Hoang; Joglekar, Yogesh; Murthy, Ganpathy
2004-03-01
We study the collective modes of the fractional quantum Hall edge states using the Hamiltonian formalism [1]. In this theory, the composite fermions are fully interacting; the collective modes are obtained within a conserving approximation which respects the constraints [2]. We present the gapless edge-mode dispersions at 1/3 and 2/5 filling fractions of unreconstructed and reconstructed edges. The dispersions are found to be nonlinear due to the variation of the effective magnetic field on the composite fermions. The implications of our study to the tunneling experiments into the edge of a fractional quantum Hall system [3] are discussed*. 1. R. Shankar and G. Murthy, Phys. Rev. Lett. 79, 4437 (1997). 2. G. Murthy, Phys. Rev. B 64, 195310 (2001). 3. A.M.Chang et. al., Phys. Rev. Lett. 86, 143 (2000). * Work supported by the NSF, Grant number DMR 031176.
Vortices in superconducting films: Statistics and fractional quantum Hall effect
Dziarmaga, J.
1996-03-01
We present a derivation of the Berry phase picked up during exchange of parallel vortices. This derivation is based on the Bogolubov{endash}de Gennes formalism. The origin of the Magnus force is also critically reanalyzed. The Magnus force can be interpreted as an interaction with the effective magnetic field. The effective magnetic field may be even of the order 10{sup 6}{ital T}/A. We discuss a possibility of the fractional quantum Hall effect (FQHE) in vortex systems. As the real magnetic field is varied to drive changes in vortex density, the vortex density will prefer to stay at some quantized values. The mere existence of the FQHE does not depend on vortex quantum statistics, although the pattern of the plateaux does. We also discuss how the density of anyonic vortices can lower the effective strengh of the Magnus force, what might be observable in measurements of Hall resistivity. {copyright} {ital 1996 The American Physical Society.}
Higher-Dimensional Quantum Hall Effect in String Theory
Fabinger, Michal
2002-08-08
We construct a string theory realization of the 4+1d quantum Hall effect recently discovered by Zhang and Hu. The string theory picture contains coincident D4-branes forming an S{sup 4} and having D0-branes (i.e. instantons) in their world-volume. The charged particles are modeled as string ends. Their configuration space approaches in the large n limit a CP{sup 3}, which is an S{sup 2} fibration over S{sup 4}, the extra S{sup 2} being made out of the Chan-Paton degrees of freedom. An alternative matrix theory description involves the fuzzy S{sup 4}. We also find that there is a hierarchy of quantum Hall effects in odd-dimensional spacetimes, generalizing the known cases in 2 + 1d and 4 + 1d.
Non-Abelian statistics in the fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Wen, X. G.
1991-02-01
The fractional quantum Hall states with non-Abelian statistics are studied. Those states are shown to be characterized by non-Abelian topological orders and are identified with some of the Jain states. The gapless edge states are found to be described by non-Abelian Kac-Moody algebras. It is argued that the topological orders and the associated properties are robust against any kinds of small perturbations.
Quantum Hall Effect in Bernal-stacked tetralayer graphene
NASA Astrophysics Data System (ADS)
Shi, Yanmeng; Che, Shi; Espiritu, Timothy; Pi, Ziqi; Taniguchi, Takashi; Watanabe, Kenji; Lau, Chun Ning
Bernal-stacked few layer graphene is of particular interest due to its unique tunable band structure. Here we study the electric transport of Bernal-stack tetralayer graphene that are encapsulated by boron nitride sheets. The device shows a clear Landau fan with multiple Landau level crossing features. We will present the dependence of its quantum Hall properties on electric and magnetic fields, and compare with theoretical calculations.
Quantum Hall effect in graphene decorated with disordered multilayer patches
Nam, Youngwoo; Sun, Jie Lindvall, Niclas; Kireev, Dmitry; Yurgens, August; Jae Yang, Seung; Rae Park, Chong; Woo Park, Yung
2013-12-02
Quantum Hall effect (QHE) is observed in graphene grown by chemical vapour deposition using platinum catalyst. The QHE is even seen in samples which are irregularly decorated with disordered multilayer graphene patches and have very low mobility (<500 cm{sup 2}V{sup −1}s{sup −1}). The effect does not seem to depend on electronic mobility and uniformity of the resulting material, which indicates the robustness of QHE in graphene.
New resistivity for high-mobility quantum Hall conductors
NASA Technical Reports Server (NTRS)
Mceuen, P. L.; Szafer, A.; Richter, C. A.; Alphenaar, B. W.; Jain, J. K.
1990-01-01
Measurements showing dramatic nonlocal behavior in the four-terminal resistances of a high-mobility quantum Hall conductor are presented. These measurements illustrate that the standard definition of the resistivity tensor is inappropriate, but they are in excellent agreement with a new model of the conductor that treats the edge and bulk conducting pathways independently. This model uses a single intensive parameter, analogous to a local resistivity for the bulk channel only, to characterize the system.
Scaling relations for gaps in fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Murthy, Ganpathy; Park, K.; Shankar, R.; Jain, J. K.
1998-12-01
The microscopic Hamiltonian approach of Murthy and Shankar, which has recently been used to calculate the transport gaps of quantum Hall states with fractions ν=p/(2ps+1), also implies scaling relations between gaps within a single sequence (fixed s) as well as between gaps of corresponding states in different sequences. This work tests these relations for a system of electrons in the lowest Landau level interacting with a model potential cutoff at high momenta due to sample thickness.
Gauge fields and composite fermions in bilayer quantum Hall systems
NASA Astrophysics Data System (ADS)
Cipri, Robert
When placed in a strong magnetic field, a two-dimensional electron gas can exhibit the quantum Hall effect in which a step like pattern forms in the Hall resistance, RH, which is defined to be the voltage drop perpendicular to the current driven through the plane of the sample divided by the magnitude of the current. The filling fraction nu = p/q defines the quantization condition where p and q are relatively prime integers and q is odd, with RH =h/(nu e2) where h is Planck's constant and e is the charge of the electron. At the same time the Hall resistance becomes quantized the longitudinal resistance vanishes indicating dissipationless current flow. The integer quantum Hall effect (nu = 1, 2, 3...) is simply modeled using single-particle energy levels while the many-body fractional quantum Hall effect can be understood in terms of new particles known as composite fermions, electrons bound to an even number of statistical flux quanta. In this approach, the fractional quantum Hall effect for electrons is viewed as an effective integer quantum Hall effect for composite fermions. It was pointed out by Halperin, Lee and Read that for filling fraction nu = 1/2 the external magnetic field is exactly canceled by the average of the statistical flux quanta attached to the composite fermions. As a result, the composite fermions move in zero effective magnetic field with a well-defined Fermi surface at zero temperature. This "metallic" state is compressible and does not have a quantized Hall resistance. However, when two nu = 1/2 layers are brought close together, interactions between the layers lead to a new incompressible bilayer quantum Hall state in which electrons form a exciton condensate with total filling fraction nuT = 1/2 + 1/2 = 1. Recently it has been proposed that an interesting new transition may occur in this system in which interlayer Coulomb repulsion leads to excitonic condensation not of electrons but of composite fermions which are then free to tunnel
Valley-filtered edge states and quantum valley Hall effect in gated bilayer graphene.
Zhang, Xu-Long; Xu, Lei; Zhang, Jun
2017-05-10
Electron edge states in gated bilayer graphene in the quantum valley Hall (QVH) effect regime can carry both charge and valley currents. We show that an interlayer potential splits the zero-energy level and opens a bulk gap, yielding counter-propagating edge modes with different valleys. A rich variety of valley current states can be obtained by tuning the applied boundary potential and lead to the QVH effect, as well as to the unbalanced QVH effect. A method to individually manipulate the edge states by the boundary potentials is proposed.
Effect of interedge Coulomb interactions on the transport between quantum Hall edge states
NASA Astrophysics Data System (ADS)
Moon, K.; Girvin, S. M.
1996-08-01
In a recent experiment, Milliken et al. demonstrated possible evidence for a Luttinger liquid through measurements of the tunneling conductance between edge states in the ν=1/3 quantum Hall plateau. However, at low temperatures, a discrepancy exists between the theoretical predictions based on Luttinger liquid theory and experiment. We consider the possibility that this is due to long-range Coulomb interactions, which become dominant at low temperatures. Using renormalization-group methods, we calculate the crossover behavior from Luttinger liquid to the Coulomb interaction dominated regime. The crossover behavior thus obtained seems to resolve one of the discrepancies, yielding good agreement with experiment.
Limitation of tunneling between edge states by a mesoscopic island in narrow quantum Hall conductors
NASA Astrophysics Data System (ADS)
Liu, Z. H.; Nachtwei, G.; Groß, J.; Gerhardts, R. R.; Weis, J.; von Klitzing, K.; Eberl, K.
1998-12-01
We observed current plateaus in the I- V characteristics of Corbino or quasi-Corbino devices with a narrow constriction, containing a mesoscopic island, in the quantum Hall regime. We investigated the features of the current plateaus for different filling factors, island sizes and orientations. A qualitative physical picture including the quasi-elastic inter-Landau-level tunneling and the limitation of tunneling current due to charging of the nonequilibrium electron states around the island is proposed to explain the current plateau phenomenon.
Experiments on Quantum Hall Topological Phases in Ultra Low Temperatures
Du, Rui-Rui
2015-02-14
This project is to cool electrons in semiconductors to extremely low temperatures and to study new states of matter formed by low-dimensional electrons (or holes). At such low temperatures (and with an intense magnetic field), electronic behavior differs completely from ordinary ones observed at room temperatures or regular low temperature. Studies of electrons at such low temperatures would open the door for fundamental discoveries in condensed matter physics. Present studies have been focused on topological phases in the fractional quantum Hall effect in GaAs/AlGaAs semiconductor heterostructures, and the newly discovered (by this group) quantum spin Hall effect in InAs/GaSb materials. This project consists of the following components: 1) Development of efficient sample cooling techniques and electron thermometry: Our goal is to reach 1 mK electron temperature and reasonable determination of electron temperature; 2) Experiments at ultra-low temperatures: Our goal is to understand the energy scale of competing quantum phases, by measuring the temperature-dependence of transport features. Focus will be placed on such issues as the energy gap of the 5/2 state, and those of 12/5 (and possible 13/5); resistive signature of instability near 1/2 at ultra-low temperatures; 3) Measurement of the 5/2 gaps in the limit of small or large Zeeman energies: Our goal is to gain physics insight of 5/2 state at limiting experimental parameters, especially those properties concerning the spin polarization; 4) Experiments on tuning the electron-electron interaction in a screened quantum Hall system: Our goal is to gain understanding of the formation of paired fractional quantum Hall state as the interaction pseudo-potential is being modified by a nearby screening electron layer; 5) Experiments on the quantized helical edge states under a strong magnetic field and ultralow temperatures: our goal is to investigate both the bulk and edge states in a quantum spin Hall insulator under
Realizing the farad from two ac quantum Hall resistances
NASA Astrophysics Data System (ADS)
Schurr, J.; Bürkel, V.; Kibble, B. P.
2009-12-01
Since the quantum Hall resistance (QHR) measured with alternating current (ac) has reached the state of an excellent quantum standard of impedance, we have realized a quadrature bridge with two ac QHRs to accurately calibrate capacitance standards in terms of the SI value of the von-Klitzing constant, without the need for any calculable artefact. The advantages of the realized measuring chain, experimental tests of the coaxial ac bridges involved and the achieved relative uncertainty of 6 × 10-9 (k = 1) are discussed.
Anisotropic Composite Fermions and Fractional Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Mueed, M. A.; Kamburov, Dobromir; Hasdemir, Sukret; Shayegan, Mansour; Pfeiffer, Loren; West, Ken; Baldwin, Kirk
We study the role of Fermi sea anisotropy on the transport properties of composite Fermions near Landau level filling factor ν = 1 / 2 in two-dimensional hole systems confined to GaAs quantum wells. By applying a parallel magnetic field, we tune the Fermi sea anisotropy and monitor the relative change of the transport scattering time along its principal directions. Interpreted in a simple Drude model, our results suggest that the scattering time is longer along the longitudinal direction of the Fermi sea. Furthermore, we find that the measured energy gap for the fractional quantum Hall state at ν = 2 / 3 decreases when anisotropy becomes significant.
Robust helical edge transport at ν =0 quantum Hall state
NASA Astrophysics Data System (ADS)
Gusev, G. M.; Kozlov, D. A.; Levin, A. D.; Kvon, Z. D.; Mikhailov, N. N.; Dvoretsky, S. A.
2017-07-01
Among the most interesting predictions in two-dimensional materials with a Dirac cone is the existence of the zeroth Landau level (LL), equally filled by electrons and holes with opposite chirality. The gapless edge states with helical spin structure emerge from Zeeman splitting at the LL filling factor ν =0 gapped quantum Hall (QH) state. We present observations of a giant, nonlocal, four-terminal transport in zero-gap HgTe quantum wells at the ν =0 QH state. Our experiment clearly demonstrates the existence of the robust helical edge state in a system with single-valley Dirac cone materials.
The integer quantum hall effect revisited
Michalakis, Spyridon; Hastings, Matthew
2009-01-01
For T - L x L a finite subset of Z{sup 2}, let H{sub o} denote a Hamiltonian on T with periodic boundary conditions and finite range, finite strength intetactions and a unique ground state with a nonvanishing spectral gap. For S {element_of} T, let q{sub s} denote the charge at site s and assume that the total charge Q = {Sigma}{sub s {element_of} T} q{sub s} is conserved. Using the local charge operators q{sub s}, we introduce a boundary magnetic flux in the horizontal and vertical direction and allow the ground state to evolve quasiadiabatically around a square of size one magnetic flux, in flux space. At the end of the evolution we obtain a trivial Berry phase, which we compare, via a method reminiscent of Stokes Theorem. to the Berry phase obtained from an evolution around an exponentially small loop near the origin. As a result, we show, without any averaging assumption, that the Hall conductance is quantized in integer multiples of e{sup 2}/h up to exponentially small corrections of order e{sup -L/{zeta}}, where {zeta}, is a correlation length that depends only on the gap and the range and strength of the interactions.
Koirala, Nikesh; Brahlek, Matthew; Salehi, Maryam; Wu, Liang; Dai, Jixia; Waugh, Justin; Nummy, Thomas; Han, Myung-Geun; Moon, Jisoo; Zhu, Yimei; Dessau, Daniel; Wu, Weida; Armitage, N Peter; Oh, Seongshik
2015-12-09
Material defects remain as the main bottleneck to the progress of topological insulators (TIs). In particular, efforts to achieve thin TI samples with dominant surface transport have always led to increased defects and degraded mobilities, thus making it difficult to probe the quantum regime of the topological surface states. Here, by utilizing a novel buffer layer scheme composed of an In2Se3/(Bi0.5In0.5)2Se3 heterostructure, we introduce a quantum generation of Bi2Se3 films with an order of magnitude enhanced mobilities than before. This scheme has led to the first observation of the quantum Hall effect in Bi2Se3.
Koirala, Nikesh; Han, Myung -Geun; Brahlek, Matthew; ...
2015-11-19
Material defects remain as the main bottleneck to the progress of topological insulators (TIs). In particular, efforts to achieve thin TI samples with dominant surface transport have always led to increased defects and degraded mobilities, thus making it difficult to probe the quantum regime of the topological surface states. Here, by utilizing a novel buffer layer scheme composed of an In2Se3/(Bi0.5In0.5)2Se3 heterostructure, we introduce a quantum generation of Bi2Se3 films with an order of magnitude enhanced mobilities than before. Furthermore, this scheme has led to the first observation of the quantum Hall effect in Bi2Se3.
Koirala, Nikesh; Han, Myung -Geun; Brahlek, Matthew; Salehi, Maryam; Wu, Liang; Dai, Jixia; Waugh, Justin; Nummy, Thomas; Moon, Jisoo; Zhu, Yimei; Dessau, Daniel; Wu, Weida; Armitage, N. Peter; Oh, Seongshik
2015-11-19
Material defects remain as the main bottleneck to the progress of topological insulators (TIs). In particular, efforts to achieve thin TI samples with dominant surface transport have always led to increased defects and degraded mobilities, thus making it difficult to probe the quantum regime of the topological surface states. Here, by utilizing a novel buffer layer scheme composed of an In_{2}Se_{3}/(Bi_{0.5}In_{0.5})_{2}Se_{3} heterostructure, we introduce a quantum generation of Bi_{2}Se_{3} films with an order of magnitude enhanced mobilities than before. Furthermore, this scheme has led to the first observation of the quantum Hall effect in Bi_{2}Se_{3}.
Zhou, Tong; Zhang, Jiayong; Zhao, Bao; Zhang, Huisheng; Yang, Zhongqin
2015-08-12
Electronic and topological behaviors of Sb(111) monolayers decorated with H and certain magnetic atoms are investigated by using ab initio methods. The drastic exchange field induced by the magnetic atoms, together with strong spin-orbit coupling (SOC) of Sb atoms, generates one new category of valley polarized topological insulators, called quantum spin-quantum anomalous Hall (QSQAH) insulators in the monolayer, with a band gap up to 53 meV. The strong SOC is closely related to Sb px and py orbitals, instead of pz orbitals in usual two-dimensional (2D) materials. Topological transitions from quantum anomalous Hall states to QSQAH states and then to time-reversal-symmetry-broken quantum spin Hall states are achieved by tuning the SOC strength. The behind mechanism is revealed. Our work is helpful for future valleytronic and spintronic applications in 2D materials.
Quantum spin Hall effect in nanostructures based on cadmium fluoride
Bagraev, N. T.; Guimbitskaya, O. N.; Klyachkin, L. E.; Koudryavtsev, A. A.; Malyarenko, A. M.; Romanov, V. V.; Ryskin, A. I.; Shcheulin, A. S.
2010-10-15
Tunneling current-voltage (I-V) characteristics and temperature dependences of static magnetic susceptibility and specific heat of the CdB{sub x}F{sub 2-x}/p-CdF{sub 2}-QW/CdB{sub x}F{sub 2-x} planar sandwich structures formed on the surface of an n-CdF{sub 2} crystal have been studied in order to identify superconducting properties of the CdB{sub x}F{sub 2-x} {delta} barriers confining the p-type CdF{sub 2} ultranarrow quantum well. Comparative analysis of current-voltage (I-V) characteristics and conductance-voltage dependences (measured at the temperatures, respectively, below and above the critical temperature of superconducting transition) indicates that there is an interrelation between quantization of supercurrent and dimensional quantization of holes in the p-CdF{sub 2} ultranarrow quantum well. It is noteworthy that detection of the Josephson peak of current in each hole subband is accompanied by the appearance of the spectrum of the multiple Andreev reflection (MAR). A high degree of spin polarization of holes in the edge channels along the perimeter of the p-CdF{sub 2} ultranarrow quantum well appears as a result of MAR and makes it possible to identify the quantum spin Hall effect I-V characteristics; this effect becomes pronounced in the case of detection of nonzero conductance at the zero voltage applied to the vertical gate in the Hall geometry of the experiment. Within the energy range of superconducting gap, the I-V characteristics of the spin transistor and quantum spin Hall effect are controlled by the MAR spectrum appearing as the voltage applied to the vertical gate is varied. Beyond the range of the superconducting gap, the observed I-V characteristic of the quantum spin Hall effect is represented by a quantum conductance staircase with a height of the steps equal to e{sub 2}/h; this height is interrelated with the Aharonov-Casher oscillations of longitudinal and depends on the voltage applied to the vertical gate.
Quantum Spin Hall Effect in Inverted Type II Semiconductors
Liu, Chaoxing; Hughes, Taylor L.; Qi, Xiao-Liang; Wang, Kang; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
The quantum spin Hall (QSH) state is a topologically non-trivial state of quantum matter which preserves time-reversal symmetry; it has an energy gap in the bulk, but topologically robust gapless states at the edge. Recently, this novel effect has been predicted and observed in HgTe quantum wells. In this work we predict a similar effect arising in Type-II semiconductor quantum wells made from InAs/GaSb/AlSb. Because of a rare band alignment the quantum well band structure exhibits an 'inverted' phase similar to CdTe/HgTe quantum wells, which is a QSH state when the Fermi level lies inside the gap. Due to the asymmetric structure of this quantum well, the effects of inversion symmetry breaking and inter-layer charge transfer are essential. By standard self-consistent calculations, we show that the QSH state persists when these corrections are included, and a quantum phase transition between the normal insulator and the QSH phase can be electrically tuned by the gate voltage.
Spin analogs of superconductivity and integer quantum Hall effect in an array of spin chains
NASA Astrophysics Data System (ADS)
Hill, Daniel; Kim, Se Kwon; Tserkovnyak, Yaroslav
2017-05-01
Motivated by the successful idea of using weakly coupled quantum electronic wires to realize the quantum Hall effects and the quantum spin Hall effects, we theoretically study two systems composed of weakly coupled quantum spin chains within the mean-field approximations, which can exhibit spin analogs of superconductivity and the integer quantum Hall effect. First, a certain bilayer of two arrays of interacting spin chains is mapped, via the Jordan-Wigner transformation, to an attractive Hubbard model that exhibits fermionic superconductivity, which corresponds to spin superconductivity in the original spin Hamiltonian. Secondly, an array of spin-orbit-coupled spin chains in the presence of a suitable external magnetic field is transformed to an array of quantum wires that exhibits the integer quantum Hall effect, which translates into its spin analog in the spin Hamiltonian. The resultant spin superconductivity and spin integer quantum Hall effect can be characterized by their ability to transport spin without any resistance.
Induced superconductivity in the quantum spin Hall edge
NASA Astrophysics Data System (ADS)
Hart, Sean; Ren, Hechen; Wagner, Timo; Leubner, Philipp; Mühlbauer, Mathias; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W.; Yacoby, Amir
2014-09-01
Topological insulators are a newly discovered phase of matter characterized by gapped bulk states surrounded by conducting boundary states. Since their theoretical discovery, these materials have encouraged intense efforts to study their properties and capabilities. Among the most striking results of this activity are proposals to engineer a new variety of superconductor at the surfaces of topological insulators. These topological superconductors would be capable of supporting localized Majorana fermions, particles whose braiding properties have been proposed as the basis of a fault-tolerant quantum computer. Despite the clear theoretical motivation, a conclusive realization of topological superconductivity remains an outstanding experimental goal. Here we present measurements of superconductivity induced in two-dimensional HgTe/HgCdTe quantum wells, a material that becomes a quantum spin Hall insulator when the well width exceeds dC = 6.3 nm (ref. ). In wells that are 7.5 nm wide, we find that supercurrents are confined to the one-dimensional sample edges as the bulk density is depleted. However, when the well width is decreased to 4.5 nm the edge supercurrents cannot be distinguished from those in the bulk. Our results provide evidence for supercurrents induced in the helical edges of the quantum spin Hall effect, establishing this system as a promising avenue towards topological superconductivity. In addition to directly confirming the existence of the topological edge channels, our results also provide a measurement of their widths, which range from 180 nm to 408 nm.
Hall effect in quantum critical charge-cluster glass
Bozovic, Ivan; Wu, Jie; Bollinger, Anthony T.; ...
2016-04-04
Upon doping, cuprates undergo a quantum phase transition from an insulator to a d-wave superconductor. The nature of this transition and of the insulating state is vividly debated. Here, we study the Hall effect in La2-xSrxCuO4 (LSCO) samples doped near the quantum critical point at x ≈ 0.06. Dramatic fluctuations in the Hall resistance appear below TCG ≈ 1.5 K and increase as the sample is cooled down further, signaling quantum critical behavior. We explore the doping dependence of this effect in detail, by studying a combinatorial LSCO library in which the Sr content is varied in extremely fine steps,more » Δx ≈ 0.00008. Furthermore, we observe that quantum charge fluctuations wash out when superconductivity emerges but can be restored when the latter is suppressed by applying a magnetic field, showing that the two instabilities compete for the ground state.« less
NASA Astrophysics Data System (ADS)
Gu, Yingfei; Lee, Ching Hua; Wen, Xueda; Cho, Gil Young; Ryu, Shinsei; Qi, Xiao-Liang
2016-09-01
In this paper, we study (2 +1 ) -dimensional quantum anomalous Hall states, i.e., band insulators with quantized Hall conductance, using exact holographic mapping. Exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in (3 +1 ) -dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a (3 +1 ) -dimensional topological insulator. The dual description enables a characterization of topological properties of a system by the quantum entanglement between degrees of freedom at different length scales.
Superconducting analogue of the parafermion fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Vaezi, Abolhassan
2014-03-01
Read and Rezayi Zk parafermion wavefunctions describe ν = 2 + k /(kM + 2) fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this talk, we discuss the ν = 2 / k FQH-superconductor heterostructure and through analytical and numerical calculations we argue that it can yield the superconducting analogue of the Zk parafermion FQH state. The resulting topological state has a gapless chiral edge state with Zk parafermion conformal field theory description. For instance, we find that a ν = 2 / 3 FQH in proximity to a superconductor produces a Z3 parafermion superconducting state. This state can host Fibonacci anyons capable of performing universal quantum computation through braiding operations. We finally discuss our experimental proposal for realizing parafermion superconductors. Reference: arXiv:1307.8069
Magnonic quantum Hall effect and Wiedemann-Franz law
NASA Astrophysics Data System (ADS)
Nakata, Kouki; Klinovaja, Jelena; Loss, Daniel
2017-03-01
We present a quantum Hall effect of magnons in two-dimensional clean insulating magnets at finite temperature. Through the Aharonov-Casher effect, a magnon moving in an electric field acquires a geometric phase and forms Landau levels in an electric field gradient of sawtooth form. At low temperatures, the lowest energy band being almost flat carries a Chern number associated with a Berry curvature. Appropriately defining the thermal conductance for bosons, we find that the magnon Hall conductances get quantized and show a universal thermomagnetic behavior, i.e., are independent of materials, and obey a Wiedemann-Franz law for magnon transport. We consider magnons with quadratic and linear (Dirac-like) dispersions. Finally, we show that our predictions are within experimental reach for ferromagnets and skyrmion lattices with current device and measurement techniques.
Meron-Pair Excitations in Bilayer Quantum Hall System
NASA Astrophysics Data System (ADS)
Moon, Kyungsun
Bilayer two-dimensional electron gas systems can form unusual broken symmetry states with spontaneous inter-layer phase coherence at certain filling factors. At total filling factor νT = 1, the lowest energy charged excitation of the system is theoretically suggested to be a linearly-confined meron-pair, which is topologically identical to a single skyrmion. We will review how this remarkable excitation arises and can help unravel various experimental results demonstrated in bilayer quantum Hall system. In order to detect the linearly-confined meron-pair excitation directly, we propose a gated bilayer Hall bar experiment, where the magnitude and orientation of magnetic field B‖ applied parallel to the 2D plane can be controlled. We demonstrate a strong angle-dependent transport due to the anisotropic nature of linearly-confined meron-pairs and discuss how it would be manifested in experiment.
Integer quantum Hall effect of interacting electrons in graphene
NASA Astrophysics Data System (ADS)
Yan, Xin-Zhong; Ting, C. S.
2017-02-01
By taking into account the charge and spin orderings and the exchange interactions between all the Landau levels, we investigate the integer quantum Hall effect of electrons in graphene using the mean-field theory. We find that the fourfold degeneracy of the Landau levels cannot be completely lifted by the Coulomb interactions. In particular, at fillings ν =4 n +2 with n =0 ,1 ,... , there is no splitting between the fourfold degenerated Landau levels. We show that with doping the degenerated lowest empty level can be sequentially filled one by one; the filled level is lower than the empty ones because of the Coulomb-exchange interactions. This result explains the step Δ ν =1 in the quantized Hall conductivity. We present a highly efficient method for dealing with a huge number of the Coulomb couplings between all the Landau levels of the Dirac fermions.
Hysteretic resistance spikes in quantum hall ferromagnets without domains.
Freire, Henrique J P; Egues, J Carlos
2007-07-13
We use spin-density-functional theory to study recently reported hysteretic magnetoresistance rho(xx) spikes in Mn-based 2D electron gases [Phys. Rev. Lett. 89, 266802 (2002)10.1103/PhysRevLett.89.266802]. We find hysteresis loops in our calculated Landau fan diagrams and total energies signaling quantum Hall ferromagnet phase transitions. Spin-dependent exchange-correlation effects are crucial to stabilize the relevant magnetic phases arising from distinct symmetry-broken excited- and ground-state solutions of the Kohn-Sham equations. Besides hysteretic spikes in rho(xx), we predict hysteretic dips in the Hall resistance rho(xy). Our theory, without domain walls, satisfactorily explains the recent data.
Edge states and integer quantum Hall effect in topological insulator thin films.
Zhang, Song-Bo; Lu, Hai-Zhou; Shen, Shun-Qing
2015-08-25
The integer quantum Hall effect is a topological state of quantum matter in two dimensions, and has recently been observed in three-dimensional topological insulator thin films. Here we study the Landau levels and edge states of surface Dirac fermions in topological insulators under strong magnetic field. We examine the formation of the quantum plateaux of the Hall conductance and find two different patterns, in one pattern the filling number covers all integers while only odd integers in the other. We focus on the quantum plateau closest to zero energy and demonstrate the breakdown of the quantum spin Hall effect resulting from structure inversion asymmetry. The phase diagrams of the quantum Hall states are presented as functions of magnetic field, gate voltage and chemical potential. This work establishes an intuitive picture of the edge states to understand the integer quantum Hall effect for Dirac electrons in topological insulator thin films.
Hall field-induced resistance oscillations in a tunable-density GaAs quantum well
NASA Astrophysics Data System (ADS)
Zudov, M. A.; Dmitriev, I. A.; Friess, B.; Shi, Q.; Umansky, V.; von Klitzing, K.; Smet, J.
2017-09-01
We report on Hall field-induced resistance oscillations (HIROs) in a 60-nm-wide GaAs/AlGaAs quantum well with an in situ grown back gate, which allows tuning the carrier density n . At low n , when all electrons are confined to the lowest subband (SB1), the HIRO frequency, proportional to the product of the cyclotron diameter and the Hall field, scales with n-1 /2 as expected. Remarkably, the population of the second subband (SB2) significantly enhances the HIROs, whereas their frequency now scales as n-1. We demonstrate that in this two-subband regime HIROs still originate solely from backscattering of SB1 electrons. The unusual density dependence occurs because the population of SB2 steadily increases, whereas that of SB1 remains essentially unchanged. The enhancement of the HIROs manifests an unexpected steplike increase in the quantum lifetime of SB1 electrons, which reaches a record value of 52 ps in the two-subband regime.
Competing Quantum Hall Phases in the Second Landau Level in Low Density Limit
Pan, Wei; Serafin, A.; Xia, J. S.; Liang, Y.; Sullivan, N. S.; Baldwin, K. W.; West, K. W.; Pfeiffer, L. N.; Tsui, D. C.
2015-01-01
Up to date, studies of the fractional quantum Hall effect (FQHE) states in the second Landau level have mainly been carried out in the high electron density regime, where the electron mobility is the highest. Only recently, with the advance of high quality low density MBE growth, experiments have been pushed to the low density regime [1], where the electron-electron interactions are strong and the Landau level mixing parameter, defined by κ = e^{2}/εI_{B}/ℏω_{e}, is large. Here, l_{B} = (ℏe/B)^{1/2} is the magnetic length and ω_{c} = eB/m the cyclotron frequency. All other parameters have their normal meanings. It has been shown that a large Landau level mixing effect strongly affects the electron physics in the second Landau level [2].
Interactions in quantum Hall edge channels at filling fraction 2
NASA Astrophysics Data System (ADS)
Degiovanni, Pascal; Bocquillon, Erwann; Freulon, Vincent; Grenier, Charles; Berroir, Jean-Marc; Plaçais, Bernard; Cavanna, Antonella; Jin, Yong; Fève, Gwendal
2013-03-01
Coulomb interactions play a major role in one dimensional electronic transport. They modify the nature of the elementary excitations from Landau quasiparticles in higher dimensions to collective excitations in 1D. We report here on the direct observation of the collective neutral and charge modes of the two chiral co-propagating edge channels of opposite spins of the quantum Hall effect at filling factor ν = 2 . Generating a charge density wave at frequency f in the outer channel, we measure the current induced by inter-channel Coulomb interaction in the inner channel after a 3 microns propagation length. Varying the driving frequency from 0.7 to 11 GHz, we observe damped oscillations in the induced current that results from the phase shift between the fast charge and slow neutral eigenmodes. Measuring the dispersion relation and dissipation of the neutral mode from provides quantitative information on the scattering of quantum edge magnetoplasmons. We will then comment on the consequences of these results on quasi-particle relaxation and decoherence in the ν = 2 quantum Hall edge channel system. ANR Grant 1shot (ANR-2010-BLANC-0412)
Anyons and the quantum Hall effect-A pedagogical review
Stern, Ady
2008-01-15
The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined 'anyons', may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to non-abelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation.
Quantum Hall effect in epitaxial graphene - a metrological perspective
NASA Astrophysics Data System (ADS)
Tzalenchuk, Alexander
2014-03-01
Although the QHE has been used successfully for more than two decades to realise the resistance scale, graphene has potential to supersede conventional semiconductors as the material of choice for quantum electrical metrology. The physical mechanisms giving graphene, grown on SiC in particular, an edge over the conventional semiconductors include the pinning of the filling factor over an extraordinarily broad range of magnetic field, large inter-Landau level spacing and a very short energy relaxation time. Together they lead to a very robust quantum Hall state opening an opportunity to realise the quantum resistance standard of greatly reduced cost and complexity operating at high temperatures, low magnetic fields and high signal-to-noise ratio. I will review the progress achieved in graphene engineering, physical understanding and metrology from the first accurate QHE measurements performed on exfoliated samples (with precision of 15 parts in 106) and on graphene on SiC (3 parts in 109) to a direct comparison between graphene on SiC and GaAs demonstrating equivalence of the quantised values of the Hall resistance with a relative uncertainty of 8 . 6 parts in 1011. Funded in part by the Graphene Flagship project of the European Commission and the EMRP project GraphOhm.
Lin, P.V.; Camino, F.; Goldman, V.J.
2009-12-01
We report experiments in a large, 2.5 {mu}m diameter Fabry-Perot quantum Hall interferometer with two tunneling constrictions. Interference fringes are observed as conductance oscillations as a function of applied magnetic field (the Aharonov-Bohm flux through the electron island) or a global backgate voltage (electronic charge in the island). Depletion is such that in the fractional quantum Hall regime, filling 1/3 current-carrying chiral edge channels pass through constrictions when the island filling is 2/5. The interferometer device is calibrated with fermionic electrons in the integer quantum Hall regime. In the fractional regime, we observe magnetic flux and charge periods 5h/e and 2e, respectively, corresponding to creation of ten e/5 Laughlin quasiparticles in the island. These results agree with our prior report of the superperiods in a much smaller interferometer device. The observed experimental periods are interpreted as imposed by anyonic statistical interaction of fractionally charged quasiparticles.
Observation of chiral surface states in the integer quantum Hall effect
NASA Astrophysics Data System (ADS)
Druist, David P.
1998-03-01
We demonstrate the existence of a novel, chiral 2D electron system that forms at the surface of 3D layered quantum Hall samples(D.P. Druist, P.J. Turley, K. Maranowski, E.G. Gwinn, and A.C. Gossard Phys. Rev. Lett, in press.). At low temperatures, this surface phase dominates transport, and exhibits metallic conductivity << e^2/h. We measure electrical transport in three dimensional GaAs/AlGaAs multilayer structures. When a large magnetic field is applied perpendicular to the layers, transport in the in-plane direction is well quantized (R_xy =1/integer x h/e^2, R_xx=0) at low temperatures. We also measure the vertical conductance G_zz (along the magnetic field direction, perpendicular to the layers) for a number of mesas with different sizes and shapes. Within the quantum Hall states, vertical transport is roughly activated at higher temperatures (T>200 mK). In this activated regime the vertical conductance G_zz of the different devices is proportional to device area, indicating that vertical transport is through the bulk of the mesas. At low temperatures (T<200 mK), however, G_zz is nearly temperature independent, and is proportional to mesa phperimeter. This indicates that the transport is along the surface of the mesas via a "sheath" of extended states that form from the coupled edge states in each layer. Since the edge states circulate in only one direction around the perimeter of the sample, conventional localization due to quantum interference is suppressed. This surface sheath is a novel two dimensional system that exhibits metallic (sheet) conductivity 4x10-4 e^2/h in the ν =1 quantum Hall state.
Floating Extended States in a Disordered Quantum Hall System
NASA Astrophysics Data System (ADS)
Glozman, Igor
1995-01-01
Several recent experiments, on various GaAs systems, have shown that an insulating phase at B = 0 can undergo a phase transition to the quantum Hall liquid (QHL) phase in an applied magnetic field B. The transition was generally interpreted as being consistent with the global phase diagram (GPD) of the quantum Hall effect. While the GPD is parametrized in terms of disorder and magnetic field, another canonical theory treats the field-induced delocalization phenomenon in the context of "floating" energy levels. While the two theories are not inconsistent with each other, this thesis will present experimental evidence in direct support for the latter theory. it will be demonstrated conclusively that it is indeed the levitation (or floating) of a delocalized state (as B to 0) that underlies the delocalization transition. A complete understanding of the remarkable phenomenon clearly requires a reasonable microscopic picture. Toward this end, two recent theoretical papers have suggested that Landau level mixing is at the root of the experimentally observed levitation. In fact, it has already been shown numerically that the energy of the delocalized states can shift upward due to Landau level mixing. Experimentally, a similar determination, with respect to Landau level mixing, necessitates the examination of the density of states (DOS). In order to obtain the relevant DOS information, we have conducted a systematic study of the minimum conductivity in the vicinity of the insulator-quantum Hall liquid transition. Since, at low-temperatures, hopping between localized sates is the dominant conduction mechanism for a QHL state, the minimum in conductivity should directly reflect the minimum in the DOS. Experimental evidence will be presented, through an anomalous behavior of the conductivity minimum, that Landau level mixing is indeed important and directly associated with the floating of the delocalized states.
Observation of interaction-induced modulations of a quantum Hall liquid's area
Sivan, I.; Choi, H. K.; Park, Jinhong; Rosenblatt, A.; Gefen, Yuval; Mahalu, D.; Umansky, V.
2016-01-01
Studies of electronic interferometers, based on edge-channel transport in the quantum Hall effect regime, have been stimulated by the search for evidence of abelian and non-abelian anyonic statistics of fractional charges. In particular, the electronic Fabry–Pérot interferometer has been found to be Coulomb dominated, thus masking coherent Aharonov–Bohm interference patterns: the flux trapped within the interferometer remains unchanged as the applied magnetic field is varied, barring unobservable modulations of the interference area. Here we report on conductance measurements indicative of the interferometer's area ‘breathing' with the variation of the magnetic field, associated with observable (a fraction of a flux quantum) variations of the trapped flux. This is the result of partial (controlled) screening of Coulomb interactions. Our results introduce a novel experimental tool for probing anyonic statistics. PMID:27396234
Observation of interaction-induced modulations of a quantum Hall liquid's area
NASA Astrophysics Data System (ADS)
Sivan, I.; Choi, H. K.; Park, Jinhong; Rosenblatt, A.; Gefen, Yuval; Mahalu, D.; Umansky, V.
2016-07-01
Studies of electronic interferometers, based on edge-channel transport in the quantum Hall effect regime, have been stimulated by the search for evidence of abelian and non-abelian anyonic statistics of fractional charges. In particular, the electronic Fabry-Pérot interferometer has been found to be Coulomb dominated, thus masking coherent Aharonov-Bohm interference patterns: the flux trapped within the interferometer remains unchanged as the applied magnetic field is varied, barring unobservable modulations of the interference area. Here we report on conductance measurements indicative of the interferometer's area `breathing' with the variation of the magnetic field, associated with observable (a fraction of a flux quantum) variations of the trapped flux. This is the result of partial (controlled) screening of Coulomb interactions. Our results introduce a novel experimental tool for probing anyonic statistics.
Scanning nuclear electric resonance microscopy using quantum-Hall-effect breakdown
Hashimoto, K. Tomimatsu, T.; Shirai, S.; Taninaka, S.; Nagase, K.; Sato, K.; Hirayama, Y.
2016-07-15
We present a scanning nuclear-spin resonance (NSR) method that incorporates resistive detection with electric-field induced NSR locally excited by a scanning metallic probe. In the quantum-Hall effect breakdown regime, NSR intensity mapping at both the fundamental NSR frequency f{sub 75As} and twice the frequency 2f{sub 75As} demonstrates the capability to probe the distribution of nuclear polarization, particularly in a semiconductor quantum well. We find that f{sub 75As} NSR excitation drives not only local NSR but also spatially overlapped nonlocal NSR, which suppresses the maximum intensity of local NSR, while the 2f{sub 75As} NSR yields purely local excitation conferring a larger intensity.
Vortex equations governing the fractional quantum Hall effect
Medina, Luciano
2015-09-15
An existence theory is established for a coupled non-linear elliptic system, known as “vortex equations,” describing the fractional quantum Hall effect in 2-dimensional double-layered electron systems. Via variational methods, we prove the existence and uniqueness of multiple vortices over a doubly periodic domain and the full plane. In the doubly periodic situation, explicit sufficient and necessary conditions are obtained that relate the size of the domain and the vortex numbers. For the full plane case, existence is established for all finite-energy solutions and exponential decay estimates are proved. Quantization phenomena of the magnetic flux are found in both cases.
Composite Fermion Theory for Bosonic Quantum Hall States on Lattices
NASA Astrophysics Data System (ADS)
Möller, G.; Cooper, N. R.
2009-09-01
We study the ground states of the Bose-Hubbard model in a uniform magnetic field, motivated by the physics of cold atomic gases on lattices at high vortex density. Mapping the bosons to composite fermions (CF) leads to the prediction of quantum Hall fluids that have no counterpart in the continuum. We construct trial states for these phases and test numerically the predictions of the CF model. We establish the existence of strongly correlated phases beyond those in the continuum limit and provide evidence for a wider scope of the composite fermion approach beyond its application to the lowest Landau level.
Four-Dimensional Quantum Hall Effect with Ultracold Atoms.
Price, H M; Zilberberg, O; Ozawa, T; Carusotto, I; Goldman, N
2015-11-06
We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms. Based on contemporary technology, motion along a synthetic fourth dimension can be accomplished through controlled transitions between internal states of atoms arranged in a 3D optical lattice. From a semiclassical analysis, we identify the linear and nonlinear quantized current responses of our 4D model, relating these to the topology of the Bloch bands. We then propose experimental protocols, based on current or center-of-mass-drift measurements, to extract the topological second Chern number. Our proposal sets the stage for the exploration of novel topological phases in higher dimensions.
Jack polynomial fractional quantum Hall states and their generalizations
NASA Astrophysics Data System (ADS)
Baratta, Wendy; Forrester, Peter J.
2011-02-01
In the study of fractional quantum Hall states, a certain clustering condition involving up to four integers has been identified. We give a simple proof that particular Jack polynomials with α=-(r-1)/(k+1), (r-1) and (k+1) relatively prime, and with partition given in terms of its frequencies by [n0k0k0k⋯0m] satisfy this clustering condition. Our proof makes essential use of the fact that these Jack polynomials are translationally invariant. We also consider nonsymmetric Jack polynomials, symmetric and nonsymmetric generalized Hermite and Laguerre polynomials, and Macdonald polynomials from the viewpoint of the clustering.
Covariant effective action for a Galilean invariant quantum Hall system
Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.
2016-09-16
Here, we construct effective field theories for gapped quantum Hall systems coupled to background geometries with local Galilean invariance i.e. Bargmann spacetimes. Along with an electromagnetic field, these backgrounds include the effects of curved Galilean spacetimes, including torsion and a gravitational field, allowing us to study charge, energy, stress and mass currents within a unified framework. A shift symmetry specific to single constituent theories constraints the effective action to couple to an effective background gauge field and spin connection that is solved for by a self-consistent equation, providing a manifestly covariant extension of Hoyos and Son’s improvement terms to arbitrary order in m.
Unconventional fractional quantum Hall effect in monolayer and bilayer graphene
Jacak, Janusz; Jacak, Lucjan
2016-01-01
The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained. Experimentally observed hierarchy of FQHE in the first and second Landau levels in monolayer graphene and in the zeroth Landau level in bilayer graphene is beyond the conventional composite fermion interpretation but fits to the presented nonlocal topology commensurability condition. PMID:27877866
Quantum anomalous Hall effect in stable dumbbell stanene
NASA Astrophysics Data System (ADS)
Zhang, Huisheng; Zhang, Jiayong; Zhao, Bao; Zhou, Tong; Yang, Zhongqin
2016-02-01
Topological property of the dumbbell (DB) stanene, more stable than the stanene with a honeycomb lattice, is investigated by using ab initio methods. The magnetic DB stanene demonstrates an exotic quantum anomalous Hall (QAH) effect due to inversion of the Sn spin-up px,y and spin-down pz states. The QAH gap is found to be opened at Γ point rather than the usual K and K' points, beneficial to observe the effect in experiments. When a 3% tensile strain is applied, a large nontrivial gap (˜50 meV) is achieved. Our results provide another lighthouse for realizing QAH effects in two-dimensional systems.
Testing the Topological Nature of the Fractional Quantum Hall Edge
Jolad, Shivakumar; Jain, Jainendra K.
2009-03-20
We carry out numerical diagonalization for much larger systems than before by restricting the fractional quantum Hall (FQH) edge excitations to a basis that is exact for a short-range interaction and very accurate for the Coulomb interaction. This enables us to perform substantial tests of the predicted universality of the edge physics. Our results suggest the possibility that the behavior of the FQH edge is intrinsically nonuniversal, even in the absence of edge reconstruction, and therefore may not bear a sharp and unique relation to the nature of the bulk FQH state.
Gaussian free fields at the integer quantum Hall plateau transition
NASA Astrophysics Data System (ADS)
Bondesan, R.; Wieczorek, D.; Zirnbauer, M. R.
2017-05-01
In this work we put forward an effective Gaussian free field description of critical wavefunctions at the transition between plateaus of the integer quantum Hall effect. To this end, we expound our earlier proposal that powers of critical wave intensities prepared via point contacts behave as pure scaling fields obeying an Abelian operator product expansion. Our arguments employ the framework of conformal field theory and, in particular, lead to a multifractality spectrum which is parabolic. We also derive a number of old and new identities that hold exactly at the lattice level and hinge on the correspondence between the Chalker-Coddington network model and a supersymmetric vertex model.
Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase
NASA Astrophysics Data System (ADS)
Zhu, W.; Liu, Zhao; Haldane, F. D. M.; Sheng, D. N.
2016-12-01
Multicomponent quantum Hall systems with internal degrees of freedom provide a fertile ground for the emergence of exotic quantum liquids. Here, we investigate the possibility of non-Abelian topological order in the half-filled fractional quantum Hall (FQH) bilayer system driven by the tunneling effect between two layers. By means of the state-of-the-art density-matrix renormalization group, we unveil "fingerprint" evidence of the non-Abelian Moore-Read Pfaffian state emerging in the intermediate-tunneling regime, including the ground-state degeneracy on the torus geometry and the topological entanglement spectroscopy (entanglement spectrum and topological entanglement entropy) on the spherical geometry, respectively. Remarkably, the phase transition from the previously identified Abelian (331) Halperin state to the non-Abelian Moore-Read Pfaffian state is determined to be continuous, which is signaled by the continuous evolution of the universal part of the entanglement spectrum, and discontinuities in the excitation gap and the derivative of the ground-state energy. Our results not only provide a "proof-of-principle" demonstration of realizing a non-Abelian state through coupling different degrees of freedom, but also open up a possibility in FQH bilayer systems for detecting different chiral p -wave pairing states.
The transport mechanism of the integer quantum Hall effect
NASA Astrophysics Data System (ADS)
Hui, Tan; LiMing, W.; Liang, Shi-Dong
2016-11-01
The integer quantum Hall effect (IQHE) is analysed using a mechanism of the electron transport in the form of semi-classic wave packages in this paper. Due to the confinement of the edges of a slab the Landau levels of electrons in a strong magnetic field go up at large wave-vectors to form energy bands. The slopes of the energy bands give the group velocities of electron wave packages and thus contribute to the current. Certain magnetic fields separate the electron transport in the slab into two branches with opposite and large wave vectors, which are localized at the two edges of the slab, respectively. In this case back scattering of electrons is prohibited due to the localization of these two branches. Thus the slab exhibits zero longitudinal resistance and plateaus of Hall resistance. When the Fermi level is sweeping over a Landau level at some magnetic fields, however, the electron waves locate around the central axis of the slab and overlap each other thus back scattering of electrons takes place frequently. Then longitudinal resistance appears and the Hall resistance goes up from one plateau to a new one. This transport mechanism is much clearer and more intuitive than the conventional explanations to the IQHE.
On transport in quantum Hall systems with constrictions
NASA Astrophysics Data System (ADS)
Lal, S.
2007-10-01
We study edge transport in a simple model of a constricted quantum Hall system with a lowered local filling factor. The current backscattered from the constriction is explained from a matching of the properties of the edge-current excitations in the constriction (ν2) and bulk (ν1) regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model, finding that a competition between two tunneling process, related by a quasiparticle-quasihole symmetry, determines the fate of the low-bias transmission conductance. A novel generalisation of the Kane-Fisher quantum impurity model is found, describing transitions from a weak-coupling theory at partial transmission to strong-coupling theories for perfect transmission and reflection as well as a new symmetry dictated fixed point. These results provide satisfactory explanations for recent experimental results at filling factors of 1/3 and 1.
Matrix model for non-Abelian quantum Hall states
NASA Astrophysics Data System (ADS)
Dorey, Nick; Tong, David; Turner, Carl
2016-08-01
We propose a matrix quantum mechanics for a class of non-Abelian quantum Hall states. The model describes electrons which carry an internal SU(p ) spin. The ground states of the matrix model include spin-singlet generalizations of the Moore-Read and Read-Rezayi states and, in general, lie in a class previously introduced by Blok and Wen. The effective action for these states is a U(p ) Chern-Simons theory. We show how the matrix model can be derived from quantization of the vortices in this Chern-Simons theory and how the matrix model ground states can be reconstructed as correlation functions in the boundary WZW model.
Deformed Calogero-Sutherland model and fractional quantum Hall effect
NASA Astrophysics Data System (ADS)
Atai, Farrokh; Langmann, Edwin
2017-01-01
The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.
Crossover between magnetic and electric edges in quantum Hall systems
NASA Astrophysics Data System (ADS)
Nogaret, Alain; Mondal, Puja; Kumar, Ankip; Ghosh, Sankalpa; Beere, Harvey; Ritchie, David
2017-08-01
We report on the transition from magnetic edge to electric edge transport in a split magnetic gate device which applies a notch magnetic field to a two-dimensional electron gas. The gate bias allows tuning the overlap of magnetic and electric edge wave functions on the scale of the magnetic length. Conduction at the magnetic edges, in the two-dimensional bulk, is found to compete with conduction at the electric edges until the magnetic edges become depleted. Current lines then move to the electrostatic edges as in the conventional quantum Hall picture. The conductivity was modeled using the quantum Boltzmann equation in the exact hybrid potential. The theory predicts the features of the bulk-edge crossover, in good agreement with experiment.
Anisotropic composite fermions and fractional quantum Hall effect
NASA Astrophysics Data System (ADS)
Mueed, M. A.; Kamburov, D.; Hasdemir, S.; Pfeiffer, L. N.; West, K. W.; Baldwin, K. W.; Shayegan, M.
2016-05-01
We study the role of anisotropy on the transport properties of composite fermions near Landau level filling factor ν =1 /2 in two-dimensional holes confined to a GaAs quantum well. By applying a parallel magnetic field, we tune the composite fermion Fermi sea anisotropy and monitor the relative change of the transport scattering time at ν =1 /2 along the principal directions. Interpreted in a simple Drude model, our results suggest that the scattering time is longer along the longitudinal direction of the composite fermion Fermi sea. Furthermore, the measured energy gap for the fractional quantum Hall state at ν =2 /3 decreases when anisotropy becomes significant. The decrease, however, might partly stem from the charge distribution becoming bilayerlike at very large parallel magnetic fields.
Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States
NASA Astrophysics Data System (ADS)
Mueed, M. A.; Kamburov, D.; Pfeiffer, L. N.; West, K. W.; Baldwin, K. W.; Shayegan, M.
2016-12-01
Via the application of a parallel magnetic field, we induce a single-layer to bilayer transition in two-dimensional electron systems confined to wide GaAs quantum wells and study the geometric resonance of composite fermions (CFs) with a periodic density modulation in our samples. The measurements reveal that CFs exist close to bilayer quantum Hall states, formed at Landau level filling factors ν =1 and 1 /2 . Near ν =1 , the geometric resonance features are consistent with half the total electron density in the bilayer system, implying that CFs prefer to stay in separate layers and exhibit a two-component behavior. In contrast, close to ν =1 /2 , CFs appear single-layer-like (single component) as their resonance features correspond to the total density.
Edge physics of the quantum spin Hall insulator from a quantum dot excited by optical absorption.
Vasseur, Romain; Moore, Joel E
2014-04-11
The gapless edge modes of the quantum spin Hall insulator form a helical liquid in which the direction of motion along the edge is determined by the spin orientation of the electrons. In order to probe the Luttinger liquid physics of these edge states and their interaction with a magnetic (Kondo) impurity, we consider a setup where the helical liquid is tunnel coupled to a semiconductor quantum dot that is excited by optical absorption, thereby inducing an effective quantum quench of the tunneling. At low energy, the absorption spectrum is dominated by a power-law singularity. The corresponding exponent is directly related to the interaction strength (Luttinger parameter) and can be computed exactly using boundary conformal field theory thanks to the unique nature of the quantum spin Hall edge.
NASA Astrophysics Data System (ADS)
Liou, Shiuan-Fan; Hu, Zi-Xiang; Yang, Kun
2017-06-01
We use exact diagonalization to study the quantum phases and phase transitions when a single species of fermionic atoms at a Landau level filling factor νf=1 in a rotating trap interact through a p -wave Feshbach resonance. We show that under a weak pairing interaction, the system undergoes a second-order quantum phase transition from a νf=1 fermionic integer quantum Hall (FIQH) state at positive detuning, to a νb=1/4 bosonic fractional quantum Hall (BFQH) state at negative detuning. However, when the pairing interaction increases, a new phase between them emerges, corresponding to a fraction of fermionic atoms staying in a coherent superposition of a bosonic molecule state and an unbound pair. The phase transition from the FIQH phase to the new phase is of second order and that from the new phase to BFQH phase is of first order.
2. QUANTUM HALL EFFECT: The problem of Coulomb interactions in the theory of the quantum Hall effect
NASA Astrophysics Data System (ADS)
Baranov, M. A.; Pruisken, A. M. M.; Škoric, B.
2001-10-01
We summarize the main ingredients of a unifying theory for abelian quantum Hall states. This theory combines the Finkel'stein approach to localization and interaction effects with the topological concept of an instanton vacuum as well as Chern-Simons gauge theory. We elaborate on the meaning of a new symmetry (Script F invariance) for systems with an infinitely ranged interaction potential. We address the renormalization of the theory and present the main results in terms of a scaling diagram of the conductances.
Space charge saturated sheath regime and electron temperature saturation in Hall thrusters
NASA Astrophysics Data System (ADS)
Raitses, Y.; Staack, D.; Smirnov, A.; Fisch, N. J.
2005-07-01
Existing electron-wall interaction models predict that secondary electron emission in Hall thrusters is significant and that the near-wall sheaths are space charge saturated. The experimental electron-wall collision frequency is computed using plasma parameters measured in a laboratory Hall thruster. In spite of qualitative similarities between the measured and predicted dependencies of the maximum electron temperature on the discharge voltage, the deduced electron-wall collision frequency for high discharge voltages is much lower than the theoretical value obtained for space charge saturated sheath regime, but larger than the wall recombination frequency. The observed electron temperature saturation appears to be directly associated with a decrease of the Joule heating rather than with the enhancement of the electron energy loss at the walls due to a strong secondary electron emission. Another interesting experimental result is related to the near-field plasma plume, where electron energy balance appears to be independent on the magnetic field.
NASA Astrophysics Data System (ADS)
Lonchakov, A. T.; Bobin, S. B.; Deryushkin, V. V.; Okulov, V. I.; Govorkova, T. E.; Neverov, V. N.; Pamyatnykh, E. A.; Paranchich, L. D.
2017-04-01
Quantum oscillations of the anomalous component of Hall resistance with an amplitude exceeding the amplitude of the Shubnikov-de Haas oscillations of transverse magnetoresistance are observed in mercury selenide crystals doped with low concentrations of cobalt impurity. In accordance with the predictions of the Hall effect theory for systems with spontaneous spin polarization of hybridized donor electrons, the observed oscillations correspond to magnetic quantum oscillations caused by the thermodynamic anomalous Hall effect.
Thickness Dependence of the Quantum Anomalous Hall Effect in Magnetic Topological Insulator Films.
Feng, Xiao; Feng, Yang; Wang, Jing; Ou, Yunbo; Hao, Zhenqi; Liu, Chang; Zhang, Zuocheng; Zhang, Liguo; Lin, Chaojing; Liao, Jian; Li, Yongqing; Wang, Li-Li; Ji, Shuai-Hua; Chen, Xi; Ma, Xucun; Zhang, Shou-Cheng; Wang, Yayu; He, Ke; Xue, Qi-Kun
2016-08-01
The evolution of the quantum anomalous Hall effect with the thickness of Cr-doped (Bi,Sb)2 Te3 magnetic topological insulator films is studied, revealing how the effect is caused by the interplay of the surface states, band-bending, and ferromagnetic exchange energy. Homogeneity in ferromagnetism is found to be the key to high-temperature quantum anomalous Hall material.
Mach-Zehnder interferometry of fractional quantum Hall edge states
NASA Astrophysics Data System (ADS)
Levkivskyi, Ivan P.; Boyarsky, Alexey; Fröhlich, Jürg; Sukhorukov, Eugene V.
2009-07-01
We propose direct experimental tests of the effective models of fractional quantum Hall edge states. We first recall a classification of effective models based on the requirement of anomaly cancellation and illustrate the general classification with the example of a quantum Hall fluid at filling factor ν=2/3 . We show that, in this example, it is impossible to describe the edge states with only one chiral channel and that there are several inequivalent models of the edge states with two fields. We focus our attention on the four simplest models of the edge states of a fluid with ν=2/3 and evaluate charges and scaling dimensions of quasiparticles. We study transport through an electronic Mach-Zehnder interferometer and show that scaling properties of the Fourier components of Aharonov-Bohm oscillations in the current provide information about the electric charges and scaling dimensions of quasiparticles. Thus, Mach-Zehnder interferometers can be used to discriminate between different effective models of fluids corresponding to the same filling factor. They, therefore, can be used to test fundamental postulates underlying the low-energy effective theory of edge states. An important ingredient of our analysis is the tunneling Hamiltonian of quasiparticles, the form of which is discussed in detail.
Fractionally charged skyrmions in fractional quantum Hall effect
Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; ...
2015-11-26
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeemanmore » energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.« less
Quantum spin Hall effect in twisted bilayer graphene
NASA Astrophysics Data System (ADS)
Finocchiaro, F.; Guinea, F.; San-Jose, P.
2017-06-01
Motivated by a recent experiment (Sanchez-Yamagishi et al 2016 Nat. Nanotechnol. 214) reporting evidence of helical spin-polarized edge states in layer-biased twisted bilayer graphene under a magnetic flux, we study the possibility of stabilising a quantum spin Hall (QSH) phase in such a system, without Zeeman or spin-orbit couplings, and with a QSH gap induced instead by electronic interactions. We analyse how magnetic flux, electric field, interlayer rotation angle, and interactions (treated at a mean field level) combine to produce a pseudo-QSH with broken time-reversal symmetry, and spin-polarized helical edge states. The effect is a consequence of a robust interaction-induced ferrimagnetic ordering of the quantum Hall ground state under an interlayer bias, provided the two rotated layers are effectively decoupled at low energies. We discuss in detail the electronic structure and the constraints on system parameters, such as the angle, interactions and magnetic flux, required to reach the pseudo-QSH phase. We find, in particular, that purely local electronic interactions are not sufficient to account for the experimental observations, which demand at least nearest-neighbour interactions to be included.
Quantum anomalous Hall effect in magnetic topological insulators
Wang, Jing; Lian, Biao; Zhang, Shou -Cheng
2015-08-25
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimensions (2D) and three-dimensions (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. We present the phase diagram in thin films of a magnetic topological insulator and review the basic mechanism of ferromagnetic order in magnetically doped topological insulators. We also review the recent experimental observation of the QAH effect. Furthermore, we discuss more recent theoretical work on the coexistence of the helical and chiral edge states, multi-channel chiral edge states, the theory of the plateau transition, and the thickness dependence in the QAH effect.
Chiral ladders and the edges of quantum Hall insulators
NASA Astrophysics Data System (ADS)
Hügel, Dario; Paredes, Belén
2014-02-01
The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as readily realizable bridges between one-dimensional spin-orbit (time-reversal) topological insulators and two-dimensional quantum Hall insulators. We reveal three instances of their promising potential: (i) they realize spin-orbit coupling, with the left-right leg degree of freedom playing the role of an effective spin, (ii) their energy bands and eigenstates exactly reproduce the topological chiral edge modes of two-dimensional Chern insulators, and (iii) they can be tailored to realize a topological phase transition from a trivial to a topological insulating phase. We propose realistic schemes to observe the chiral and topological properties of ladder systems with current optical lattice-based experiments. Our findings open a door to the exploration of the physics of the edges of quantum Hall insulators and to the realization of spin-orbit coupling and topological superfluid phases with ultracold atomic gases.
Quantum anomalous Hall effect in magnetic topological insulators
Wang, Jing; Lian, Biao; Zhang, Shou -Cheng
2015-08-25
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimensions (2D) and three-dimensions (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. We presentmore » the phase diagram in thin films of a magnetic topological insulator and review the basic mechanism of ferromagnetic order in magnetically doped topological insulators. We also review the recent experimental observation of the QAH effect. Furthermore, we discuss more recent theoretical work on the coexistence of the helical and chiral edge states, multi-channel chiral edge states, the theory of the plateau transition, and the thickness dependence in the QAH effect.« less
Quantum Hall drag of exciton condensate in graphene
NASA Astrophysics Data System (ADS)
Liu, Xiaomeng; Watanabe, Kenji; Taniguchi, Takashi; Halperin, Bertrand I.; Kim, Philip
2017-08-01
An exciton condensate is a Bose-Einstein condensate of electron and hole pairs bound by the Coulomb interaction. In an electronic double layer (EDL) subject to strong magnetic fields, filled Landau states in one layer bind with empty states of the other layer to form an exciton condensate. Here we report exciton condensation in a bilayer graphene EDL separated by hexagonal boron nitride. Driving current in one graphene layer generates a near-quantized Hall voltage in the other layer, resulting in coherent exciton transport. Owing to the strong Coulomb coupling across the atomically thin dielectric, quantum Hall drag in graphene appears at a temperature ten times higher than previously observed in a GaAs EDL. The wide-range tunability of densities and displacement fields enables exploration of a rich phase diagram of Bose-Einstein condensates across Landau levels with different filling factors and internal quantum degrees of freedom. The observed robust exciton condensation opens up opportunities to investigate various many-body exciton phases.
NASA Astrophysics Data System (ADS)
Huang, Chun-Feng; Tsai, I.-H.
It is well-established how the quantum interference induces strong localization leading to quantum Hall effect at high enough magnetic fields. Decreasing the magnetic fields, however, the localization strength can be reduced and the semiclassical magneto-oscillations following Shubnikov-de Haas formula appear in most quantum Hall systems. To understand the transport properties as the localization strength becomes weak, our team has investigated the magneto-resistance in some quantum Hall systems at low magnetic fields. Under the semiclassical transport, the crossing points in Hall plateaus showed Landau-band quantization and microwave-induced heating demonstrated the band-edge equivalence important to Landau-level addition transformation. We note that such equivalence is consistent with the edge universality based on the random matrices of Wigner type, and the Landau-band quantization can be explained by considering geometric phase effects. From our study, some quantum Hall features can survive as the semiclassical transport reveals the insufficient localization.
Glushkov, V V; Lobanova, I I; Ivanov, V Yu; Voronov, V V; Dyadkin, V A; Chubova, N M; Grigoriev, S V; Demishev, S V
2015-12-18
Separating between the ordinary Hall effect and anomalous Hall effect in the paramagnetic phase of Mn_{1-x}Fe_{x}Si reveals an ordinary Hall effect sign inversion associated with the hidden quantum critical (QC) point x^{*}∼0.11. The effective hole doping at intermediate Fe content leads to verifiable predictions in the field of fermiology, magnetic interactions, and QC phenomena in Mn_{1-x}Fe_{x}Si. The change of electron and hole concentrations is considered as a "driving force" for tuning the QC regime in Mn_{1-x}Fe_{x}Si via modifying the Ruderman-Kittel-Kasuya-Yosida exchange interaction within the Heisenberg model of magnetism.
NASA Astrophysics Data System (ADS)
Tuegel, Thomas I.; Hughes, Taylor L.
2015-10-01
The Hall viscosity describes a nondissipative response to strain in systems with broken time-reversal symmetry. We develop a method for computing the Hall viscosity of lattice systems in strong magnetic fields based on momentum transport, which we compare to the method of momentum polarization used by Tu et al. [Phys. Rev. B 88, 195412 (2013), 10.1103/PhysRevB.88.195412] and Zaletel et al. [Phys. Rev. Lett. 110, 236801 (2013), 10.1103/PhysRevLett.110.236801] for noninteracting systems. We compare the Hall viscosity of square-lattice tight-binding models in magnetic field to the continuum integer quantum Hall effect (IQHE) showing agreement when the magnetic length is much larger than the lattice constant, but deviation as the magnetic field strength increases. We also relate the Hall viscosity of relativistic electrons in magnetic field (the Dirac IQHE) to the conventional IQHE. The Hall viscosity of the lattice Dirac model in magnetic field agrees with the continuum Dirac Hall viscosity when the magnetic length is much larger than the lattice constant. We also show that the Hall viscosity of the lattice model deviates further from the continuum model if the C4 symmetry of the square lattice is broken to C2, but the deviation is again minimized as the magnetic length increases.
Coalescence of magnetic islands in the low-resistivity, Hall-MHD regime.
Knoll, D A; Chacón, L
2006-04-07
The coalescence of magnetic islands in the low-resistivity eta, Hall-MHD regime is studied. The interaction between the ion inertial length d(i) and the dynamically evolving current sheet scale length deltaJ is established. Initially, d(i) < deltaJ. If eta is such that deltaJ dynamically thins down to d(i) prior to the well-known sloshing phenomena, then sloshing is avoided. This results in eta independent peak reconnection rates. However, if d(i) is small enough that deltaJ cannot be thinned down to this scale prior to sloshing, then sloshing proceeds as in the resistive MHD model.
NASA Astrophysics Data System (ADS)
Hui, Hoi-Yin; Sau, Jay D.
2017-01-01
Time-reversal invariance places strong constraints on the properties of the quantum spin Hall edge. One such restriction is the inevitability of dissipation in a Josephson junction between two superconductors formed on such an edge without the presence of interaction. Interactions and spin-conservation breaking are key ingredients for the realization of the dissipationless ac Josephson effect on such quantum spin Hall edges. We present a simple quantum impurity model that allows us to create a dissipationless fractional Josephson effect on a quantum spin Hall edge. We then use this model to substantiate a general argument that shows that any such nondissipative Josephson effect must necessarily be 8 π periodic.
NASA Astrophysics Data System (ADS)
Ji, Wei-xiao; Zhang, Chang-wen; Ding, Meng; Zhang, Bao-min; Li, Ping; Li, Feng; Ren, Miao-juan; Wang, Pei-ji; Zhang, Run-wu; Hu, Shu-jun; Yan, Shi-shen
2016-08-01
Bismuth (Bi) has attracted a great deal of attention for its strongest spin-orbit coupling (SOC) strength among main group elements. Although quantum anomalous Hall (QAH) state is predicted in half-hydrogenated Bi honeycomb monolayers Bi2H, the experimental results are still missing. Halogen atoms (X = F, Cl and Br) were also frequently used as modifications, but Bi2X films show a frustrating metallic character that masks the QAH effects. Here, first-principle calculations are performed to predict the full-cyanided bismuthene (Bi2(CN)2) as 2D topological insulator supporting quantum spin Hall state with a record large gap up to 1.10 eV, and more importantly, half-cyanogen saturated bismuthene (Bi2(CN)) as a Chern insulator supporting a valley-polarized QAH state, with a Curie temperature to be 164 K, as well as a large gap reaching 0.348 eV which could be further tuned by bi-axial strain and SOC strength. Our findings provide an appropriate and flexible material family candidate for spintronic and valleytronic devices.
Terahertz Imaging of cyclotron emission from quantum Hall conductors
NASA Astrophysics Data System (ADS)
Komiyama, Susumu
2006-03-01
Microscopy of extremely weak terahertz (THz) waves via photon-counting method is reported. A quantum-dot photon detector [1] is incorporated into a scanning terahertz microscope [2]. By using a quantum Hall detector [3] as well, measurements cover the intensity dynamic range more than five orders of magnitude. The minimum intensity reaches as lo as 10̂-21^ watt (one photon per one second). Applying the measurement system to the study of semiconductor quantum Hall (QH) devices, we image cyclotron radiation emitted by non-equilibrium electrons generated in QH electron systems. Owing to the unprecedented sensitivity, a variety of new features of electron kinetics are unveiled [4]. It is stressed that the present approach is in marked contrast to the THz- wave applications recently discussed extensively in a wide variety of fields including clinic, security, and environment. In the vast majority of those applications, room-temperature operation is implicit. The intensity of treated THz radiation is hence well beyond the level of 300K black body radiation (roughly 10̂-7 watts or 10̂14 photons/s per square centimeter in a 1/10 relative band width). From the scientific viewpoint, however, detecting extremely weak THz waves from an object without external illumination such as applied in the present work is of strong importance, because the microscopic kinetics of an object can be probed only in such a passive method. Besides semiconductor electric devices studied here, we will also discuss possible applications of the present method for molecular dynamics, micro thermography, and cell activities.. [1] S. Komiyama et al., Nature 403, 405 (2000). [2] K. Ikushima et al.,. Rev. Sci. Instrum. 74, 4209 (2003). [3] Y.Kawano et al., J. Appl. Phys. 89, 4037 (2001). [4] K.Ikushima et al., Phys. Rev. Lett. 93, 146804 (2004).
Scanning gate spectroscopy of a quantum Hall island near a quantum point contact
NASA Astrophysics Data System (ADS)
Hackens, Benoit; Martins, Frederico; Faniel, Sebastien; Bayot, Vincent; Rosenow, Bernd; Desplanque, Ludovic; Wallart, Xavier; Pala, Marco; Sellier, Hermann; Huant, Serge
2013-03-01
We report on low temperature (100 mK) scanning gate experiments performed at high magnetic field (around 10 T) on a mesoscopic device patterned in an InGaAs/InAlAs heterostructure. Magnetotransport measurements yield signatures of ultra-small Quantum Hall Islands (QHI) formed by closed quantum Hall edge states and connected to propagating edge channels through tunnel barriers. Scanning gate microscopy and scanning gate spectroscopy are used to locate and probe a single QHI near a quantum point contact. The presence of Coulomb diamonds in the local spectroscopy confirms that Coulomb blockade governs transport across the QHI. Varying the microscope tip bias as well as current bias across the device, we uncover the QHI discrete energy spectrum arising from electronic confinement and we extract estimates of the gradient of the confining potential and of the edge state velocity.
Edge mode velocities in the quantum Hall effect from a dc measurement
NASA Astrophysics Data System (ADS)
Zucker, Philip; Feldman, D. E.
Because of the bulk gap, low energy physics in the quantum Hall effect is confined to the edges of the 2D electron liquid. The velocities of edge modes are key parameters of edge physics. They were determined in several quantum Hall systems from time-resolved measurements and high-frequency ac transport. We propose a way to extract edge velocities from dc transport in a point contact geometry defined by narrow gates. The width of the gates assumes two different sizes at small and large distances from the point contact. The Coulomb interaction across the gates depends on the gate width and affects the conductance of the contact. The conductance exhibits two different temperature dependencies at high and low temperatures. The transition between the two regimes is determined by the edge velocity. An interesting feature of the low-temperature I - V curve is current oscillations as a function of the voltage. The oscillations emerge due to charge reflection from the interface of the regions defined by the narrow and wide sections of the gates. This work is available at arXiv:1510.01725 This work was supported by the NSF under Grant No. DMR-1205715.
Jain, Jainendra
2011-07-15
The fractional quantum Hall effect (FQHE) is one of the most amazing collective states discovered in modern times. A remarkably detailed and accurate understanding of its nonperturbative physics has been achieved in terms of a new class of exotic particles called composite fermions. I will begin with a brief review of the composite fermion theory and its outstanding successes. The rest of the talk will be concerned with fractional quantum Hall effect in graphene, observed recently. I will present results of theoretical studies that demonstrate that composite fermions are formed in graphene as well, but the spin and valley degeneracies and the linear dispersion of electrons produce interesting new physics relative to that in the usual two-dimensional GaAs systems. Composite fermion theory allows detailed predictions about FQHE in graphene in regimes when either or both of the spin and valley degeneracies are broken. I will discuss the relevance of our theory to recent experiments. This work on FQHE in graphene has been performed in collaboration with Csaba Toke.
NASA Astrophysics Data System (ADS)
Zhang, Gu-Feng; Li, Yi; Wu, Congjun
2014-08-01
We construct a minimal four-band model for the two-dimensional (2D) topological insulators and quantum anomalous Hall insulators based on the px- and py-orbital bands in the honeycomb lattice. The multiorbital structure allows the atomic spin-orbit coupling which lifts the degeneracy between two sets of on-site Kramers doublets jz=±3/2 and jz=±1/2. Because of the orbital angular momentum structure of Bloch-wave states at Γ and K(K') points, topological gaps are equal to the atomic spin-orbit coupling strengths, which are much larger than those based on the mechanism of the s-p band inversion. In the weak and intermediate regime of spin-orbit coupling strength, topological gaps are the global gap. The energy spectra and eigen wave functions are solved analytically based on Clifford algebra. The competition among spin-orbit coupling λ, sublattice asymmetry m, and the Néel exchange field n results in band crossings at Γ and K(K ') points, which leads to various topological band structure transitions. The quantum anomalous Hall state is reached under the condition that three gap parameters λ, m, and n satisfy the triangle inequality. Flat bands also naturally arise which allow a local construction of eigenstates. The above mechanism is related to several classes of solid state semiconducting materials.
Bismuthene on a SiC substrate: A candidate for a high-temperature quantum spin Hall material
NASA Astrophysics Data System (ADS)
Reis, F.; Li, G.; Dudy, L.; Bauernfeind, M.; Glass, S.; Hanke, W.; Thomale, R.; Schäfer, J.; Claessen, R.
2017-07-01
Quantum spin Hall materials hold the promise of revolutionary devices with dissipationless spin currents but have required cryogenic temperatures owing to small energy gaps. Here we show theoretically that a room-temperature regime with a large energy gap may be achievable within a paradigm that exploits the atomic spin-orbit coupling. The concept is based on a substrate-supported monolayer of a high-atomic number element and is experimentally realized as a bismuth honeycomb lattice on top of the insulating silicon carbide substrate SiC(0001). Using scanning tunneling spectroscopy, we detect a gap of ~0.8 electron volt and conductive edge states consistent with theory. Our combined theoretical and experimental results demonstrate a concept for a quantum spin Hall wide-gap scenario, where the chemical potential resides in the global system gap, ensuring robust edge conductance.
Quantum Hall states stabilized in semi-magnetic bilayers of topological insulators
NASA Astrophysics Data System (ADS)
Yoshimi, R.; Yasuda, K.; Tsukazaki, A.; Takahashi, K. S.; Nagaosa, N.; Kawasaki, M.; Tokura, Y.
2015-10-01
By breaking the time-reversal symmetry in three-dimensional topological insulators with the introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect or quantum Hall effect, when the chemical potential locates inside the gap. Further breaking of inversion symmetry is possible by employing magnetic topological insulator heterostructures that host non-degenerate top and bottom surface states. Here we demonstrate the tailored-material approach for the realization of robust quantum Hall states in the bilayer system, in which the cooperative or cancelling combination of the anomalous and ordinary Hall responses from the respective magnetic and non-magnetic layers is exemplified. The appearance of quantum Hall states at filling factor 0 and +1 can be understood by the relationship of energy band diagrams for the two independent surface states. The designable heterostructures of magnetic topological insulator may explore a new arena for intriguing topological transport and functionality.
Quantum Hall states stabilized in semi-magnetic bilayers of topological insulators
Yoshimi, R.; Yasuda, K.; Tsukazaki, A.; Takahashi, K. S.; Nagaosa, N.; Kawasaki, M.; Tokura, Y.
2015-01-01
By breaking the time-reversal symmetry in three-dimensional topological insulators with the introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect or quantum Hall effect, when the chemical potential locates inside the gap. Further breaking of inversion symmetry is possible by employing magnetic topological insulator heterostructures that host non-degenerate top and bottom surface states. Here we demonstrate the tailored-material approach for the realization of robust quantum Hall states in the bilayer system, in which the cooperative or cancelling combination of the anomalous and ordinary Hall responses from the respective magnetic and non-magnetic layers is exemplified. The appearance of quantum Hall states at filling factor 0 and +1 can be understood by the relationship of energy band diagrams for the two independent surface states. The designable heterostructures of magnetic topological insulator may explore a new arena for intriguing topological transport and functionality. PMID:26497065
Quantum Hall states stabilized in semi-magnetic bilayers of topological insulators.
Yoshimi, R; Yasuda, K; Tsukazaki, A; Takahashi, K S; Nagaosa, N; Kawasaki, M; Tokura, Y
2015-10-26
By breaking the time-reversal symmetry in three-dimensional topological insulators with the introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect or quantum Hall effect, when the chemical potential locates inside the gap. Further breaking of inversion symmetry is possible by employing magnetic topological insulator heterostructures that host non-degenerate top and bottom surface states. Here we demonstrate the tailored-material approach for the realization of robust quantum Hall states in the bilayer system, in which the cooperative or cancelling combination of the anomalous and ordinary Hall responses from the respective magnetic and non-magnetic layers is exemplified. The appearance of quantum Hall states at filling factor 0 and +1 can be understood by the relationship of energy band diagrams for the two independent surface states. The designable heterostructures of magnetic topological insulator may explore a new arena for intriguing topological transport and functionality.
Quantum Zeno Effect in the Strong Measurement Regime of Circuit Quantum Electrodynamics
2016-05-17
New J. Phys. 18 (2016) 053031 doi:10.1088/1367-2630/18/5/053031 PAPER Quantum Zeno effect in the strongmeasurement regime of circuit quantum ...Keywords: quantumZeno effect, quantum jumps, superconducting qubit, circuit QED, random telegraph signals Abstract Weobserve the quantumZeno effect...where the act ofmeasurement slows the rate of quantum state transitions—in a superconducting qubit using linear circuit quantum electrodynamics readout
Spacetime-noncommutativity regime of loop quantum gravity
NASA Astrophysics Data System (ADS)
Amelino-Camelia, Giovanni; Da Silva, Malú Maira; Ronco, Michele; Cesarini, Lorenzo; Lecian, Orchidea Maria
2017-01-01
A recent study by Bojowald and Paily [M. Bojowald and G. M. Paily, Phys. Rev. D 87, 044044 (2013)., 10.1103/PhysRevD.87.044044] provided a path toward the identification of an effective quantum-spacetime picture of loop quantum gravity, applicable in the "Minkowski regime," the regime where the large-scale (coarse-grained) spacetime metric is flat. A pivotal role in the analysis is played by loop-quantum-gravity-based modifications to the hypersurface deformation algebra, which leave a trace in the Minkowski regime. We here show that the symmetry-algebra results reported by Bojowald and Paily are consistent with a description of spacetime in the Minkowski regime given in terms of the κ -Minkowski noncommutative spacetime, whose relevance for the study of the quantum-gravity problem had already been proposed for independent reasons.
Manipulating edge transport in quantum anomalous Hall insulators
NASA Astrophysics Data System (ADS)
Kandala, Abhinav
The quantum anomalous Hall (QAH) effect provides a path to obtain dissipation-less, one-dimensional (1D) edge states at zero magnetic field. It's recent experimental realization in magnetic topological insulator thin films lies at the overlap of several areas of condensed matter physics: dilute magnetic semiconductors, low dimensional electron transport and topologically non-trivial material systems. In this talk, we demonstrate how careful compositional and electrical tuning of epitaxial films of Cr-doped (Bi,Sb)2Te3 enables access to a robust zero-field quantized Hall effect, despite sample roughness and low carrier mobility. In samples that show near-dissipation-less transport, we manipulate the intermixing between edge states and dissipative channels via a tilted-field crossover from ballistic 1D edge transport to diffusive transport. This crossover manifests in a gate-tunable giant anisotropic magneto-resistance effect that we use as a quantitative probe of dissipation in our systems. Finally, we discuss experiments with mesoscopic channels of QAH insulator thin films, and discuss the effect of their modified magnetic anisotropy on edge transport. This work was carried out in collaboration with A. Richardella, C-X Liu, M. Liu, W. Wang, N. P. Ong, and N. Samarth. Funded by ARO/MURI, DARPA and ONR.
Steady States of the Inhomogenous Microwave Irradiated Quantum Hall Gas
NASA Astrophysics Data System (ADS)
Auerbach, Assa; Finkler, Ilya; Halperin, Bertrand; Yacoby, Amir
2005-03-01
To explain the observation of Zero-Resistance states (ZRS) in Microwave irradiated Quantum Hall gases[1], it has been proposed[2] that under appropriate conditions the sample will break into domains of photogenerated fields. In the absence of disorder induced pinning, motion of domain walls results in a ZRS state. In order to treat the effects of long wavelength disorder, we construct a Lyapunov functional for systems with uniform Hall conductivity. We use it to derive stability conditions on the domain structure and to compute the conductance. We show that weak white noise disorder does not destroy the ZRS although it produces current fluctuations. In contrast, separable and correlated disorder pin the domain walls, and produce a finite conductance and a photovoltage as demonstrated by one dimensional, and simple two dimensional, potentials.1. R.G. Mani et.al. Nature, 420, 646 (2002); M.A. Zudov et.al., Phys. Rev. Lett. 90, 046807 (2003).2. A.V. Andreev, I.L. Aleiner, and A.J. Millis, PRL 91, 056803 (2003).
Quantum transport in graphene Hall bars: Effects of side gates
NASA Astrophysics Data System (ADS)
Petrović, M. D.; Peeters, F. M.
2017-05-01
Quantum electron transport in side-gated graphene Hall bars is investigated in the presence of quantizing external magnetic fields. The asymmetric potential of four side-gates distorts the otherwise flat bands of the relativistic Landau levels, and creates new propagating states in the Landau spectrum (i.e. snake states). The existence of these new states leads to an interesting modification of the bend and Hall resistances, with new quantizing plateaus appearing in close proximity of the Landau levels. The electron guiding in this system can be understood by studying the current density profiles of the incoming and outgoing modes. From the fact that guided electrons fully transmit without any backscattering (similarly to edge states), we are able to analytically predict the values of the quantized resistances, and they match the resistance data we obtain with our numerical (tight-binding) method. These insights in the electron guiding will be useful in predicting the resistances for other side-gate configurations, and possibly in other system geometries, as long as there is no backscattering of the guided states.
Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Yang, Bo; Hu, Zi-Xiang; Lee, Ching Hua; Papić, Z.
2017-04-01
We generalize the notion of Haldane pseudopotentials to anisotropic fractional quantum Hall (FQH) systems that are physically realized, e.g., in tilted magnetic field experiments or anisotropic band structures. This formalism allows us to expand any translation-invariant interaction over a complete basis, and directly reveals the intrinsic metric of incompressible FQH fluids. We show that purely anisotropic pseudopotentials give rise to new types of bound states for small particle clusters in the infinite plane, and can be used as a diagnostic of FQH nematic order. We also demonstrate that generalized pseudopotentials quantify the anisotropic contribution to the effective interaction potential, which can be particularly large in models of fractional Chern insulators.
Geometry of quantum Hall states: Gravitational anomaly and transport coefficients
Can, Tankut; Laskin, Michael; Wiegmann, Paul B.
2015-11-15
We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iterating a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.
Time-reversal-breaking induced quantum spin Hall effect.
Luo, Wei; Shao, D X; Deng, Ming-Xun; Deng, W Y; Sheng, L
2017-02-21
We show that quantum spin Hall (QSH) effect does not occur in a square lattice model due to cancellation of the intrinsic spin-orbit coupling coming from different hopping paths. However, we show that QSH effect can be induced by the presence of staggered magnetic fluxes alternating directions square by square. When the resulting Peierls phase takes a special value , the system has a composite symmetry ΘΡ- with Θ the time-reversal operator and Ρ- transforming the Peierls phase from γ to γ - , which protects the gapless edge states. Once the phase deviates from , the edge states open a gap, as the composite symmetry is broken. We further investigate the effect of a Zeeman field on the QSH state, and find that the edge states remain gapless for . This indicates that the QSH effect is immune to the magnetic perturbation.
Topological spin texture in a quantum anomalous Hall insulator.
Wu, Jiansheng; Liu, Jie; Liu, Xiong-Jun
2014-09-26
The quantum anomalous Hall (QAH) effect has been recently discovered in an experiment using a thin-film topological insulator with ferromagnetic ordering and strong spin-orbit coupling. Here we investigate the spin degree of freedom of a QAH insulator and uncover the fundamental phenomenon that the edge states exhibit a topologically stable spin texture in the boundary when a chiral-like symmetry is present. This result shows that edge states are chiral in both the orbital and spin degrees of freedom, and the chiral edge spin texture corresponds to the bulk topological states of the QAH insulator. We also study the potential applications of the edge spin texture in designing topological-state-based spin devices, which might be applicable to future spintronic technologies.
Covariant effective action for a Galilean invariant quantum Hall system
Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.
2016-09-16
Here, we construct effective field theories for gapped quantum Hall systems coupled to background geometries with local Galilean invariance i.e. Bargmann spacetimes. Along with an electromagnetic field, these backgrounds include the effects of curved Galilean spacetimes, including torsion and a gravitational field, allowing us to study charge, energy, stress and mass currents within a unified framework. A shift symmetry specific to single constituent theories constraints the effective action to couple to an effective background gauge field and spin connection that is solved for by a self-consistent equation, providing a manifestly covariant extension of Hoyos and Son’s improvement terms to arbitrarymore » order in m.« less
Time-reversal-breaking induced quantum spin Hall effect
NASA Astrophysics Data System (ADS)
Luo, Wei; Shao, D. X.; Deng, Ming-Xun; Deng, W. Y.; Sheng, L.
2017-02-01
We show that quantum spin Hall (QSH) effect does not occur in a square lattice model due to cancellation of the intrinsic spin-orbit coupling coming from different hopping paths. However, we show that QSH effect can be induced by the presence of staggered magnetic fluxes alternating directions square by square. When the resulting Peierls phase takes a special value , the system has a composite symmetry ΘΡ- with Θ the time-reversal operator and Ρ- transforming the Peierls phase from γ to γ - , which protects the gapless edge states. Once the phase deviates from , the edge states open a gap, as the composite symmetry is broken. We further investigate the effect of a Zeeman field on the QSH state, and find that the edge states remain gapless for . This indicates that the QSH effect is immune to the magnetic perturbation.
Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene
NASA Astrophysics Data System (ADS)
Kim, Youngwook; Park, Jaesung; Song, Intek; Ok, Jong Mok; Jo, Younjung; Watanabe, Kenji; Taniquchi, Takashi; Choi, Hee Cheul; Lee, Dong Su; Jung, Suyong; Kim, Jun Sung
2016-12-01
Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers.
Quantum Hall exciton condensation at full spin polarization.
Finck, A D K; Eisenstein, J P; Pfeiffer, L N; West, K W
2010-01-08
Using Coulomb drag as a probe, we explore the excitonic phase transition in quantum Hall bilayers at nu(T) = 1 as a function of Zeeman energy E(Z). The critical layer separation (d/l)(c) for exciton condensation initially increases rapidly with E(Z), but then reaches a maximum and begins a gentle decline. At high E(Z), where both the excitonic phase at small d/l and the compressible phase at large d/l are fully spin polarized, we find that the width of the transition, as a function of d/l, is much larger than at small E(Z) and persists in the limit of zero temperature. We discuss these results in the context of two models in which the system contains a mixture of the two fluids.
Quantum spin-Hall effect and topologically invariant Chern numbers.
Sheng, D N; Weng, Z Y; Sheng, L; Haldane, F D M
2006-07-21
We present a topological description of the quantum spin-Hall effect (QSHE) in a two-dimensional electron system on a honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. We show that the topology of the band insulator can be characterized by a 2 x 2 matrix of first Chern integers. The nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM). A spin Chern number is derived from the CNM, which is conserved in the presence of finite disorder scattering and spin nonconserving Rashba coupling. By using the Laughlin gedanken experiment, we numerically calculate the spin polarization and spin transfer rate of the conducting edge states and determine a phase diagram for the QSHE.
Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene
Kim, Youngwook; Park, Jaesung; Song, Intek; Ok, Jong Mok; Jo, Younjung; Watanabe, Kenji; Taniquchi, Takashi; Choi, Hee Cheul; Lee, Dong Su; Jung, Suyong; Kim, Jun Sung
2016-01-01
Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers. PMID:27905496
Time-reversal-breaking induced quantum spin Hall effect
Luo, Wei; Shao, D. X.; Deng, Ming-Xun; Deng, W. Y.; Sheng, L.
2017-01-01
We show that quantum spin Hall (QSH) effect does not occur in a square lattice model due to cancellation of the intrinsic spin-orbit coupling coming from different hopping paths. However, we show that QSH effect can be induced by the presence of staggered magnetic fluxes alternating directions square by square. When the resulting Peierls phase takes a special value , the system has a composite symmetry ΘΡ− with Θ the time-reversal operator and Ρ− transforming the Peierls phase from γ to γ − , which protects the gapless edge states. Once the phase deviates from , the edge states open a gap, as the composite symmetry is broken. We further investigate the effect of a Zeeman field on the QSH state, and find that the edge states remain gapless for . This indicates that the QSH effect is immune to the magnetic perturbation. PMID:28220858
Pseudo Magnetic Faraday and Quantum Hall Effect In Oscillating Graphene
NASA Astrophysics Data System (ADS)
Bhagat, Anita; Mullen, Kieran
When a graphene layer is stressed, the strain changes the phase between sites in a tight binding model of the system. This phase can be viewed as a pseudo-magnetic vector potential. The corresponding pseudo-magnetic field has been experimentally verified in static cases. We examine the case of oscillating graphene ribbons and explore two new effects. The first is to investigate an oscillating pseudo-magnetic field that produces a quantum Hall effect: we calculate the I-V characteristic of an oscillating graphene nanoribbon as a function of frequency, and amplitude in both the oscillations and the applied driving voltage. Second, the time dependent pseudo-magnetic field should produce a pseudo-Faraday effect driving electrons in different valleys in opposite directions. In both cases, we make explicit calculations for experiment. This project was supported in part by the US National Science Foundation under Grant DMR-1310407.
Inducing superconducting correlation in quantum Hall edge states
NASA Astrophysics Data System (ADS)
Lee, Gil-Ho; Huang, Ko-Fan; Efetov, Dmitri K.; Wei, Di S.; Hart, Sean; Taniguchi, Takashi; Watanabe, Kenji; Yacoby, Amir; Kim, Philip
2017-07-01
The quantum Hall (QH) effect supports a set of chiral edge states at the boundary of a two-dimensional system. A superconductor (SC) contacting these states can provide correlations of the quasiparticles in the dissipationless edge states. Here we fabricated highly transparent and nanometre-scale SC junctions to graphene. We demonstrate that the QH edge states can couple via superconducting correlations through the SC electrode narrower than the superconducting coherence length. We observe that the chemical potential of the edge state exhibits a sign reversal across the SC electrode. This provides direct evidence of conversion of the incoming electron to the outgoing hole along the chiral edge state, termed crossed Andreev conversion (CAC). We show that CAC can successfully describe the temperature, bias and SC electrode width dependences. This hybrid SC/QH system could provide a novel route to create isolated non-Abelian anyonic zero modes, in resonance with the chiral edge states.
Theory of activated transport in bilayer quantum Hall systems.
Roostaei, B; Mullen, K J; Fertig, H A; Simon, S H
2008-07-25
We analyze the transport properties of bilayer quantum Hall systems at total filling factor nu=1 in drag geometries as a function of interlayer bias, in the limit where the disorder is sufficiently strong to unbind meron-antimeron pairs, the charged topological defects of the system. We compute the typical energy barrier for these objects to cross incompressible regions within the disordered system using a Hartree-Fock approach, and show how this leads to multiple activation energies when the system is biased. We then demonstrate using a bosonic Chern-Simons theory that in drag geometries current in a single layer directly leads to forces on only two of the four types of merons, inducing dissipation only in the drive layer. Dissipation in the drag layer results from interactions among the merons, resulting in very different temperature dependences for the drag and drive layers, in qualitative agreement with experiment.
Bosonization, coherent states and semiclassical quantum Hall skyrmions.
Dutta, Sreedhar B; Shankar, R
2008-07-09
We bosonize (2+1)-dimensional fermionic theory using coherent states. The gauge-invariant subspace of boson-Chern-Simons Hilbert space is mapped to fermionic Hilbert space. This subspace is then equipped with a coherent state basis. These coherent states are labelled by a dynamic spinor field. The label manifold could be assigned a physical meaning in terms of density and spin density. A path-integral representation of the evolution operator in terms of these physical variables is given. The corresponding classical theory when restricted to LLL is described by spin fluctuations alone and is found to be the NLSM with Hopf term. The formalism developed here is suitable to study quantum Hall skyrmions semiclassically and/or beyond the hydrodynamic limit. The effects of Landau level mixing or the presence of slowly varying external fields can also be easily incorporated.
Investigating dissipation in the quantum anomalous Hall effect
NASA Astrophysics Data System (ADS)
Fox, Eli; Bestwick, Andrew; Goldhaber-Gordon, David; Feng, Yang; Ou, Yunbo; He, Ke; Wang, Yayu; Xue, Qi-Kun; Kou, Xufeng; Pan, Lei; Wang, Kang
In the quantum anomalous Hall effect, a magnetic exchange gap in a 3D topological insulator gives rise to dissipationless chiral edge states. Though the effect has recently been realized in a family of ferromagnetically-doped (Bi,Sb)2Te3 topological insulator thin films, experiments to date have found non-vanishing longitudinal resistance, contrary to initial theoretical expectations. Proposed sources of this dissipation include extra gapless or activated quasi-helical edge states, thermally activated 2D conduction, and variable-range hopping. Here, we discuss transport measurements of Corbino disk and non-local geometries to identify the mechanism of non-ideal behavior. This work supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award No. 19-7503.
The quantum anomalous Hall effect in kagomé lattices.
Zhang, Zhi-Yong
2011-09-14
The quantum anomalous Hall (QAH) effect in kagomé lattices is investigated in the presence of both Rashba spin-orbit coupling and an exchange field. In addition to the gap at the Dirac points as found in graphene, a new topological energy gap is opened at the Γ point. With the Fermi energy lying in the first gap, the Chern number = 2 as in graphene, whereas with it lying in the second one, = 1. The distribution of Berry curvature is obtained to reveal the nontrivial topological properties in momentum space. For stripes with 'armchair' and 'zigzag' edges, the topological characteristics of gapless edge states on the genus g = 2 Riemann surface are studied. The obtained nonzero winding numbers also demonstrate the QAH effe
On fractional quantum Hall solitons in ABJM-like theory
NASA Astrophysics Data System (ADS)
Belhaj, Adil
2011-11-01
Using D-brane physics, we study fractional quantum Hall solitons (FQHS) in ABJM-like theory in terms of type IIA dual geometries. In particular, we discuss a class of Chern-Simons (CS) quivers describing FQHS systems at low energy. These CS quivers come from R-R gauge fields interacting with D6-branes wrapped on 4-cycles, which reside within a blown up CP3 projective space. Based on the CS quiver method and mimicking the construction of del Pezzo surfaces in terms of CP2, we first give a model which corresponds to a single layer model of FQHS system, then we propose a multi-layer system generalizing the doubled CS field theory, which is used in the study of topological defect in graphene.
Unified Fock space representation of fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Di Gioacchino, Andrea; Molinari, Luca Guido; Erba, Vittorio; Rotondo, Pietro
2017-06-01
Many bosonic (fermionic) fractional quantum Hall states, such as Laughlin, Moore-Read, and Read-Rezayi wave functions, belong to a special class of orthogonal polynomials: the Jack polynomials (times a Vandermonde determinant). This fundamental observation allows one to point out two different recurrence relations for the coefficients of the permanent (Slater) decomposition of the bosonic (fermionic) states. Here we provide an explicit Fock space representation for these wave functions by introducing a two-body squeezing operator which represents them as a Jastrow operator applied to reference states, which are, in general, simple periodic one-dimensional patterns. Remarkably, this operator representation is the same for bosons and fermions, and the different nature of the two recurrence relations is an outcome of particle statistics.
Edge states and integer quantum Hall effect in topological insulator thin films
NASA Astrophysics Data System (ADS)
Zhang, Song-Bo; Lu, Hai-Zhou; Shen, Shun-Qing
The integer quantum Hall effect is a topological state of quantum matter in two dimensions, and has recently been observed in three-dimensional topological insulator thin films. In this report, I will talk about the Landau levels and edge states of surface Dirac fermions in topological insulators under a strong magnetic field. We examine the formation of the quantum plateaux of the Hall conductance and find two different patterns, in one pattern the filling number covers all integers while only odd integers in the other. We focus on the quantum plateau closest to zero energy and demonstrate the breakdown of the quantum spin Hall effect as a result of the interplay of magnetic field and structure inversion asymmetry. We also reveal that the edge states exist only for the integer Hall conductance while no edge-state solution can be found for the ''half-integer'' Hall conductance. The addition of top and bottom surface Dirac fermions always form well-defined edge states, and gives an integer quantum Hall effect. This work establishes an intuitive picture of the edge states to understand the integer quantum Hall effect for Dirac electrons in topological insulator thin films.
Gapless Andreev bound states in the quantum spin Hall insulator HgTe
NASA Astrophysics Data System (ADS)
Bocquillon, Erwann; Deacon, Russell S.; Wiedenmann, Jonas; Leubner, Philipp; Klapwijk, Teunis M.; Brüne, Christoph; Ishibashi, Koji; Buhmann, Hartmut; Molenkamp, Laurens W.
2016-08-01
In recent years, Majorana physics has attracted considerable attention because of exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here, we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a 2D topological insulator that exhibits the quantum spin Hall (QSH) effect. The a.c. Josephson effect demonstrates that the supercurrent has a 4π periodicity in the superconducting phase difference, as indicated by a doubling of the voltage step for multiple Shapiro steps. In addition, this response like that of a superconducting quantum interference device to a perpendicular magnetic field shows that the 4π-periodic supercurrent originates from states located on the edges of the junction. Both features appear strongest towards the QSH regime, and thus provide evidence for induced topological superconductivity in the QSH edge states.
Gapless Andreev bound states in the quantum spin Hall insulator HgTe
NASA Astrophysics Data System (ADS)
Bocquillon, Erwann; Deacon, Russell S.; Wiedenmann, Jonas; Leubner, Philipp; Klapwijk, Teunis M.; Brüne, Christoph; Ishibashi, Koji; Buhmann, Hartmut; Molenkamp, Laurens W.
2017-02-01
In recent years, Majorana physics has attracted considerable attention because of exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here, we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a 2D topological insulator that exhibits the quantum spin Hall (QSH) effect. The a.c. Josephson effect demonstrates that the supercurrent has a 4π periodicity in the superconducting phase difference, as indicated by a doubling of the voltage step for multiple Shapiro steps. In addition, this response like that of a superconducting quantum interference device to a perpendicular magnetic field shows that the 4π-periodic supercurrent originates from states located on the edges of the junction. Both features appear strongest towards the QSH regime, and thus provide evidence for induced topological superconductivity in the QSH edge states.
Influence of quantum Hall effect on wave refraction in ferrite-semiconductor superlattices
NASA Astrophysics Data System (ADS)
Tarkhanyan, Roland H.; Niarchos, Dimitris G.
2008-12-01
Peculiarities of wave refraction are investigated in periodic structures consisting of alternating layers of ferromagnetic insulator and GaAs-AlGaAs-type semiconductor bilayers. It is shown that in quantum Hall effect conditions, the refractive indices and consequently the refraction angles of the propagating waves are quantized.Two different geometries of the refracting plane are considered: (I) parallel and (II) perpendicular to the quantizing magnetic field. It is shown that in the first case, negative refraction through the lateral surface of the structure is possible. A frequency region is found where the refraction is negative for all angles of incidence and regardless of the sign of permittivity tensor components. Analytical expressions for both phase and group refractive indices are obtained.In the second case, one of the propagating waves (in the birefringent regime) is backward. Despite this, and unlike in the case of non-quantizing magnetic fields, negative refraction is impossible.
Lee, Y; Tran, D; Myhro, K; Velasco, J; Gillgren, N; Poumirol, J M; Smirnov, D; Barlas, Y; Lau, C N
2016-01-13
Using transport measurements, we investigate multicomponent quantum Hall (QH) ferromagnetism in dual-gated rhombohedral trilayer graphene (r-TLG) in which the real spin, orbital pseudospin, and layer pseudospins of the lowest Landau level form spontaneous ordering. We observe intermediate QH plateaus, indicating a complete lifting of the degeneracy of the zeroth Landau level (LL) in the hole-doped regime. In charge neutral r-TLG, the orbital degeneracy is broken first, and the layer degeneracy is broken last and only in the presence of an interlayer potential U⊥. In the phase space of U⊥ and filling factor ν, we observe an intriguing "hexagon" pattern, which is accounted for by a model based on crossings between symmetry-broken LLs.
Robust large-gap quantum spin Hall insulators in chemically decorated arsenene films
NASA Astrophysics Data System (ADS)
Wang, Dongchao; Chen, Li; Shi, Changmin; Wang, Xiaoli; Cui, Guangliang; Zhang, Pinhua; Chen, Yeqing
2016-03-01
Based on first-principles calculations, we propose one new category of two-dimensional topological insulators (2D TIs) in chemically functionalized (-CH3 and -OH) arsenene films. The results show that the surface decorated arsenene (AsCH3 and AsOH) films are intrinsic 2D TIs with sizeable bulk gap. The bulk energy gaps are 0.184 eV, and 0.304 eV in AsCH3 and AsOH films, respectively. Such large bulk gaps make them suitable to realize quantum spin Hall effect in an experimentally accessible temperature regime. Topologically helical edge states in these systems are desirable for dissipationless transport. Moreover, we find that the topological properties in these systems are robust against mechanical deformation by exerting biaxial strain. These novel 2D TIs with large bulk gaps are potential candidate in future electronic devices with ultralow dissipation.
Scaling in the quantum Hall regime of graphene Corbino devices
Peters, Eva C.; Burghard, Marko; Giesbers, A. J. M.; Kern, Klaus
2014-05-19
The scaling behavior of graphene devices in Corbino geometry was investigated through temperature dependent conductivity measurements under magnetic field. Evaluation of the Landau level width as a function of temperature yielded a relatively low temperature exponent of κ = 0.16 ± 0.05. Furthermore, an unusually large value close to 7.6 ± 0.9 was found for the universal scaling constant γ, while the determined inelastic scattering exponent of p = 2 is consistent with established scattering mechanisms in graphene. The deviation of the scaling parameters from values characteristic of conventional two-dimensional electron gases is attributed to an inhomogeneous charge carrier distribution in the Corbino devices. Direct evidence for the presence of the latter could be gained by spatially resolved photocurrent microscopy away from the charge neutrality point of the devices.
Bending strain engineering in quantum spin hall system for controlling spin currents
NASA Astrophysics Data System (ADS)
Huang, Bing; Jin, Kyung-Hwan; Cui, Bin; Zhai, Feng; Mei, Jiawei; Liu, Feng
2017-06-01
Quantum spin Hall system can exhibit exotic spin transport phenomena, mediated by its topological edge states. Here the concept of bending strain engineering to tune the spin transport properties of a quantum spin Hall system is demonstrated. We show that bending strain can be used to control the spin orientation of counter-propagating edge states of a quantum spin system to generate a non-zero spin current. This physics mechanism can be applied to effectively tune the spin current and pure spin current decoupled from charge current in a quantum spin Hall system by control of its bending curvature. Furthermore, the curved quantum spin Hall system can be achieved by the concept of topological nanomechanical architecture in a controllable way, as demonstrated by the material example of Bi/Cl/Si(111) nanofilm. This concept of bending strain engineering of spins via topological nanomechanical architecture affords a promising route towards the realization of topological nano-mechanospintronics.
Bending strain engineering in quantum spin hall system for controlling spin currents.
Huang, Bing; Jin, Kyung-Hwan; Cui, Bin; Zhai, Feng; Mei, Jiawei; Liu, Feng
2017-06-16
Quantum spin Hall system can exhibit exotic spin transport phenomena, mediated by its topological edge states. Here the concept of bending strain engineering to tune the spin transport properties of a quantum spin Hall system is demonstrated. We show that bending strain can be used to control the spin orientation of counter-propagating edge states of a quantum spin system to generate a non-zero spin current. This physics mechanism can be applied to effectively tune the spin current and pure spin current decoupled from charge current in a quantum spin Hall system by control of its bending curvature. Furthermore, the curved quantum spin Hall system can be achieved by the concept of topological nanomechanical architecture in a controllable way, as demonstrated by the material example of Bi/Cl/Si(111) nanofilm. This concept of bending strain engineering of spins via topological nanomechanical architecture affords a promising route towards the realization of topological nano-mechanospintronics.
High-temperature intrinsic quantum anomalous Hall effect in rare Earth monohalide
NASA Astrophysics Data System (ADS)
Wu, Menghao
2017-06-01
Although the quantum anomalous Hall effect was verified in 2013, presently its experimental realization is limited to doped magnetic topological insulators under extremely low temperature, while its theoretical existence is limited within doped or functionalized materials, or heterostructures. Based on first-principles calculations, LaCl and LaBr monolayer and bulk forms, which were fabricated in 1980s (Mattausch et al 1980 Z. Anorg. Allg. Chem. 466 7-22 Araujo and Corbett 1981 Inorg. Chem. 20 3082-6), are both revealed to exhibit intrinsic 2D/3D quantum anomalous Hall effect with energy gaps up to 36 meV. These simple binary compounds are also revealed to be ferromagnets with high Curie temperature, which guarantees that the quantum anomalous Hall effect survives at ambient condictions. Besides holding promise for low-dissipation electronics and quantum computing, this proposal realizes 3D quantum anomalous Hall effect.
Using custom potentials to access quantum Hall states in rotating Bose gases
NASA Astrophysics Data System (ADS)
Morris, Alexis G.; Feder, David L.
2007-03-01
The exact ground states of zero-temperature rotating Bose gases confined in quasi-two-dimensional harmonic traps are studied numerically, for small numbers of alkali atoms. As the rotation frequency increases, the interacting Bose gas undergoes a series of transitions from one quantum Hall state to another. We have investigated the possibility of facilitating access to specific quantum Hall states through the addition of customized potentials to the existing trapping potential. For the right choice of potential, we show that creation of predetermined quantum Hall states in rotating Bose gases should be possible using current experimental setups. (Research supported by NSERC, iCORE and CFI)
Scalable quantum memory in the ultrastrong coupling regime.
Kyaw, T H; Felicetti, S; Romero, G; Solano, E; Kwek, L-C
2015-03-02
Circuit quantum electrodynamics, consisting of superconducting artificial atoms coupled to on-chip resonators, represents a prime candidate to implement the scalable quantum computing architecture because of the presence of good tunability and controllability. Furthermore, recent advances have pushed the technology towards the ultrastrong coupling regime of light-matter interaction, where the qubit-resonator coupling strength reaches a considerable fraction of the resonator frequency. Here, we propose a qubit-resonator system operating in that regime, as a quantum memory device and study the storage and retrieval of quantum information in and from the Z2 parity-protected quantum memory, within experimentally feasible schemes. We are also convinced that our proposal might pave a way to realize a scalable quantum random-access memory due to its fast storage and readout performances.
Scalable quantum memory in the ultrastrong coupling regime
Kyaw, T. H.; Felicetti, S.; Romero, G.; Solano, E.; Kwek, L.-C.
2015-01-01
Circuit quantum electrodynamics, consisting of superconducting artificial atoms coupled to on-chip resonators, represents a prime candidate to implement the scalable quantum computing architecture because of the presence of good tunability and controllability. Furthermore, recent advances have pushed the technology towards the ultrastrong coupling regime of light-matter interaction, where the qubit-resonator coupling strength reaches a considerable fraction of the resonator frequency. Here, we propose a qubit-resonator system operating in that regime, as a quantum memory device and study the storage and retrieval of quantum information in and from the Z2 parity-protected quantum memory, within experimentally feasible schemes. We are also convinced that our proposal might pave a way to realize a scalable quantum random-access memory due to its fast storage and readout performances. PMID:25727251
Terahertz Quantum Plasmonics of Nanoslot Antennas in Nonlinear Regime.
Kim, Joon-Yeon; Kang, Bong Joo; Park, Joohyun; Bahk, Young-Mi; Kim, Won Tae; Rhie, Jiyeah; Jeon, Hyeongtag; Rotermund, Fabian; Kim, Dai-Sik
2015-10-14
Quantum tunneling in plasmonic nanostructures has presented an interesting aspect of incorporating quantum mechanics into classical optics. However, the study has been limited to the subnanometer gap regime. Here, we newly extend quantum plasmonics to gap widths well over 1 nm by taking advantage of the low-frequency terahertz regime. Enhanced electric fields of up to 5 V/nm induce tunneling of electrons in different arrays of ring-shaped nanoslot antennas of gap widths from 1.5 to 10 nm, which lead to a significant nonlinear transmission decrease. These observations are consistent with theoretical calculations considering terahertz-funneling-induced electron tunneling across the gap.
Fibonacci Anyons From Abelian Bilayer Quantum Hall States
NASA Astrophysics Data System (ADS)
Vaezi, Abolhassan; Barkeshli, Maissam
2014-12-01
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this Letter, we consider a simple bilayer fractional quantum Hall system with the 1 /3 Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous "Fibonacci" anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν =2 /3 in bilayers, as past experiments may not have definitively ruled them out.
Measuring Fractional Statistics with Fabry-Perot Quantum Hall Interferometers
NASA Astrophysics Data System (ADS)
Goldman, Vladimir J.
2008-03-01
Laughlin quasiparticles are the elementary excitations of a highly-correlated fractional quantum Hall electron fluid. They have fractional charge and obey fractional statistics. The quasiparticles can propagate quantum-coherently in chiral edge channels, and constructively or destructively interfere. Unlike electrons, the interference condition for Laughlin quasiparticles has a non-vanishing statistical contribution that can be observed experimentally. Two kinds of interferometer devices have been realized. In the primary-filling interferometer, the entire device has filling 1/3, and the e/3 edge channel quasiparticles encircle identical e/3 island quasiparticles. Here the flux period is h/e, same as for electrons, but the back-gate charge period is e/3. In the second kind of interferometer, a lower density edge channel at filling 1/3 forms around a higher density island at filling 2/5, so that e/3 edge quasiparticles encircle e/5 island quasiparticles. Here we observe superperiodic oscillations with 5h/e flux and 2e charge periods, both corresponding to excitation of ten island quasiparticles. These periods can be understood as imposed by the anyonic braiding statistics of Laughlin quasiparticles. This work was done in collaboration with Fernando E. Camino, Ping Lin and Wei Zhou.
Configuration interaction matrix elements for the quantum Hall effect
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Macek, Joseph
2015-03-01
In the spherical model of the quantum Hall system, the two-body matrix elements and pseudopotentials can be found analytically in terms of a general scalar pair interaction potential by expressing the pair interaction as a weighted sum over Legendre polynomials. For non-infinite systems, only a finite set of terms in the potential expansion contribute to the interactions; the contributing terms define an effective spatial potential for the system. The connection between the effective spatial potential and the pseudopotential is one-to-one for finite systems, and any completely defined model pseudopotential can be analytically inverted to give a unique corresponding spatial potential. This technique of inverting the pseudopotential to derive effective spatial potentials may be of use for developing accurate model spatial potentials for quantum Monte Carlo simulations. We demonstrate the technique and the corresponding spatial potentials for a few example model pseudopotentials. Supported by Office of Basic Energy Sciences, U.S. DOE, Grant DE-FG02-02ER15283 to the University of Tennessee.
Critical integer quantum Hall topology in the integrable Maryland model
NASA Astrophysics Data System (ADS)
Ganeshan, Sriram; Kechedzhi, Kostyantyn
2014-03-01
One-dimensional tight binding models such as Aubry-Andre-Harper (AAH) model (with onsite cosine potential) and the integrable Maryland model (with onsite tangent potential) have been the subjects of extensive theoretical research in localization studies. AAH can be directly mapped onto the two-dimensional Hofstadter model that manifests the integer quantum Hall topology on a lattice. However, no such connection has been made for the Maryland model (MM). In this talk, we present a generalized model that contains AAH and MM as the limiting cases with the MM lying precisely at a topological quantum phase transition (TQPT) point. A remarkable feature of this critical point is that the 1D MM retains well-defined energy gaps whereas the equivalent 2D model becomes gapless, signifying the 2D nature of the TQPT. The criticality allows us to associate topological invariants with the Maryland model in a restricted mathematical sense at the special filling factors that are adiabatically connected to the spectral gaps in the 1D Aubry-Andre-Harper model. Our theory presented in this work establishes deep and unexpected mathematical connections between 2D topological models and a family of 1D incommensurate localization models. This work is supported by JQI-NSF-PFC, Microsoft Q and JQI-ARO-MU.
Theory of Transport Phenomena in Coherent Quantum Hall Bilayers
NASA Astrophysics Data System (ADS)
MacDonald, Allan H.; Chen, Hua; Sodemann, Inti
2015-03-01
We will describe a theory that allows to understand the anomalous transport properties of the excitonic condensate state occurring in quantum quantum Hall bilayers in terms of a picture in which the condensate phase is nearly uniform across the sample, and the strength of condensate coupling to interlayer tunneling processes is substantially reduced compared to the predictions of disorder-free microscopic mean-field theory. These ingredients provide a natural explanation for recently established I-V characteristics which feature a critical current above which the tunneling resistance abruptly increases and a non-local interaction between interlayer tunneling at the inner and outer edges of Corbino rings. We propose a microscopic picture in which disorder is the main agent responsible for the reduction of the effective interlayer tunneling strength. IS is supported by the Pappalardo Fellowship in Physics. HC and AHM are supported by DOE Division of Materials Sciences and Engineering Grant DE-FG03- 02ER45958 and Welch Foundation Grant TBF1473.
Fibonacci anyons from Abelian bilayer quantum Hall states.
Vaezi, Abolhassan; Barkeshli, Maissam
2014-12-05
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this Letter, we consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous "Fibonacci" anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν=2/3 in bilayers, as past experiments may not have definitively ruled them out.
Selective Equilibration of Spin-Polarized Quantum Hall Edge States in Graphene
NASA Astrophysics Data System (ADS)
Amet, F.; Williams, J. R.; Watanabe, K.; Taniguchi, T.; Goldhaber-Gordon, D.
2014-05-01
We report on transport measurements of dual-gated, single-layer graphene devices in the quantum Hall regime, allowing for independent control of the filling factors in adjoining regions. Progress in device quality allows us to study scattering between edge states when the fourfold degeneracy of the Landau level is lifted by electron correlations, causing edge states to be spin and/or valley polarized. In this new regime, we observe a dramatic departure from the equilibration seen in more disordered devices: edge states with opposite spins propagate without mixing. As a result, the degree of equilibration inferred from transport can reveal the spin polarization of the ground state at each filling factor. In particular, the first Landau level is shown to be spin polarized at half filling, providing an independent confirmation of a conclusion of Young et al. [Nat. Phys. 8, 550 (2012)]. The conductance in the bipolar regime is strongly suppressed, indicating that copropagating edge states, even with the same spin, do not equilibrate along PN interfaces. We attribute this behavior to the formation of an insulating ν =0 stripe at the PN interface.
Liu, Zhao; Bhatt, R N
2016-11-11
We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a suitably averaged entanglement entropy with respect to disorder-the magnitude of its disorder derivative appears to diverge in the thermodynamic limit. We also study the level statistics of the entanglement spectrum as a function of disorder. However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction of level repulsion only deep in the Anderson insulating phase.
Optical probes of excitonic phases in quantum Hall bilayers at νT=1*
NASA Astrophysics Data System (ADS)
Pellegrini, Vittorio
2009-03-01
In this talk we discuss our recent inelastic light scattering results that shed light on the interplay between incompressible and compressible quantum phases of electron bilayers at total filling factor νT = 1. In the regime of finite values of tunneling gaps, we observe a quantum phase transformation between composite fermion (CF) metal and incompressible excitonic states as the tunneling gap is reduced. We show that the transition becomes discontinuous (first-order) by impacts of different terms of the electron-electron interactions that prevail on weak residual disorder [1]. The evidence is based on precise determinations of the excitonic order parameter and of measurements of CF spin excitations by resonant inelastic light scattering close to the phase boundary [2,3]. While there is marked softening of low-lying excitations, our experiments underpin the roles of competing order parameters linked to quasi-particle correlations in removing the divergence of quantum fluctuations [4]. In the regime of vanishingly small tunneling gaps we show that the abrupt disappearing of CF spin excitations below the spin-wave indicates the emergence of the inter-layer correlated quantum Hall state in the vicinity of νT = 1 and when the temperature is lowered below a critical value [5]. Finally, the evolution of the spin-wave mode as a function of the Zeeman energy suggests the occurrence of a spin transition [5]. * Work done in collaboration with: B. Karmakar, A. Pinczuk, L.N. Pfeiffer, K.W. West.[4pt] [1] B. Karmakar, submitted; [2] S. Luin, et al. Phys. Rev. Lett. 94, 146804 (2005); [3] B. Karmakar et al. Solid State Communications 143, 499 (2007); [4] J. Schliemann, S. M. Girvin and A. H. MacDonald, Phys. Rev. Lett. 86, 1849 (2001); [5] B. Karmakar et al. unpublished.
Understanding the physics of a possible non-Abelian fractional quantum hall effect state.
Pan, Wei; Crawford, Matthew; Tallakulam, Madhu; Ross, Anthony Joseph, III
2010-10-01
We wish to present in this report experimental results from a one-year Senior Council Tier-1 LDRD project that focused on understanding the physics of a possible non-Abelian fractional quantum Hall effect state. We first give a general introduction to the quantum Hall effect, and then present the experimental results on the edge-state transport in a special fractional quantum Hall effect state at Landau level filling {nu} = 5/2 - a possible non-Abelian quantum Hall state. This state has been at the center of current basic research due to its potential applications in fault-resistant topological quantum computation. We will also describe the semiconductor 'Hall-bar' devices we used in this project. Electron physics in low dimensional systems has been one of the most exciting fields in condensed matter physics for many years. This is especially true of quantum Hall effect (QHE) physics, which has seen its intellectual wealth applied in and has influenced many seemingly unrelated fields, such as the black hole physics, where a fractional QHE-like phase has been identified. Two Nobel prizes have been awarded for discoveries of quantum Hall effects: in 1985 to von Klitzing for the discovery of integer QHE, and in 1998 to Tsui, Stormer, and Laughlin for the discovery of fractional QHE. Today, QH physics remains one of the most vibrant research fields, and many unexpected novel quantum states continue to be discovered and to surprise us, such as utilizing an exotic, non-Abelian FQHE state at {nu} = 5/2 for fault resistant topological computation. Below we give a briefly introduction of the quantum Hall physics.
Robust fractional quantum Hall effect in the N=2 Landau level in bilayer graphene
NASA Astrophysics Data System (ADS)
Diankov, Georgi; Liang, Chi-Te; Amet, François; Gallagher, Patrick; Lee, Menyoung; Bestwick, Andrew J.; Tharratt, Kevin; Coniglio, William; Jaroszynski, Jan; Watanabe, Kenji; Taniguchi, Takashi; Goldhaber-Gordon, David
2016-12-01
The fractional quantum Hall effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most fractional quantum Hall studies have focussed on the lowest Landau level, whose fractional states are successfully explained by the composite fermion model. In the widely studied GaAs-based system, the composite fermion picture is thought to become unstable for the N≥2 Landau level, where competing many-body phases have been observed. Here we report magneto-resistance measurements of fractional quantum Hall states in the N=2 Landau level (filling factors 4<|ν|<8) in bilayer graphene. In contrast with recent observations of particle-hole asymmetry in the N=0/N=1 Landau levels of bilayer graphene, the fractional quantum Hall states we observe in the N=2 Landau level obey particle-hole symmetry within the fully symmetry-broken Landau level. Possible alternative ground states other than the composite fermions are discussed.
Robust fractional quantum Hall effect in the N=2 Landau level in bilayer graphene.
Diankov, Georgi; Liang, Chi-Te; Amet, François; Gallagher, Patrick; Lee, Menyoung; Bestwick, Andrew J; Tharratt, Kevin; Coniglio, William; Jaroszynski, Jan; Watanabe, Kenji; Taniguchi, Takashi; Goldhaber-Gordon, David
2016-12-21
The fractional quantum Hall effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most fractional quantum Hall studies have focussed on the lowest Landau level, whose fractional states are successfully explained by the composite fermion model. In the widely studied GaAs-based system, the composite fermion picture is thought to become unstable for the N≥2 Landau level, where competing many-body phases have been observed. Here we report magneto-resistance measurements of fractional quantum Hall states in the N=2 Landau level (filling factors 4<|ν|<8) in bilayer graphene. In contrast with recent observations of particle-hole asymmetry in the N=0/N=1 Landau levels of bilayer graphene, the fractional quantum Hall states we observe in the N=2 Landau level obey particle-hole symmetry within the fully symmetry-broken Landau level. Possible alternative ground states other than the composite fermions are discussed.
Helical edge states and fractional quantum Hall effect in a graphene electron-hole bilayer.
Sanchez-Yamagishi, Javier D; Luo, Jason Y; Young, Andrea F; Hunt, Benjamin M; Watanabe, Kenji; Taniguchi, Takashi; Ashoori, Raymond C; Jarillo-Herrero, Pablo
2017-02-01
Helical 1D electronic systems are a promising route towards realizing circuits of topological quantum states that exhibit non-Abelian statistics. Here, we demonstrate a versatile platform to realize 1D systems made by combining quantum Hall (QH) edge states of opposite chiralities in a graphene electron-hole bilayer at moderate magnetic fields. Using this approach, we engineer helical 1D edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong non-local transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Unlike other approaches used for realizing helical states, the graphene electron-hole bilayer can be used to build new 1D systems incorporating fractional edge states. Indeed, we are able to tune the bilayer devices into a regime hosting fractional and integer edge states of opposite chiralities, paving the way towards 1D helical conductors with fractional quantum statistics.
Statistical theory of relaxation of high-energy electrons in quantum Hall edge states
NASA Astrophysics Data System (ADS)
Lunde, Anders Mathias; Nigg, Simon E.
2016-07-01
We investigate theoretically the energy exchange between the electrons of two copropagating, out-of-equilibrium edge states with opposite spin polarization in the integer quantum Hall regime. A quantum dot tunnel coupled to one of the edge states locally injects electrons at high energy. Thereby a narrow peak in the energy distribution is created at high energy above the Fermi level. A second downstream quantum dot performs an energy-resolved measurement of the electronic distribution function. By varying the distance between the two dots, we are able to follow every step of the energy exchange and relaxation between the edge states, even analytically under certain conditions. In the absence of translational invariance along the edge, e.g., due to the presence of disorder, energy can be exchanged by non-momentum-conserving two-particle collisions. For weakly broken translational invariance, we show that the relaxation is described by coupled Fokker-Planck equations. From these we find that relaxation of the injected electrons can be understood statistically as a generalized drift-diffusion process in energy space for which we determine the drift velocity and the dynamical diffusion parameter. Finally, we provide a physically appealing picture in terms of individual edge-state heating as a result of the relaxation of the injected electrons.
Helical edge states and fractional quantum Hall effect in a graphene electron-hole bilayer
NASA Astrophysics Data System (ADS)
Sanchez-Yamagishi, Javier D.; Luo, Jason Y.; Young, Andrea F.; Hunt, Benjamin M.; Watanabe, Kenji; Taniguchi, Takashi; Ashoori, Raymond C.; Jarillo-Herrero, Pablo
2017-02-01
Helical 1D electronic systems are a promising route towards realizing circuits of topological quantum states that exhibit non-Abelian statistics. Here, we demonstrate a versatile platform to realize 1D systems made by combining quantum Hall (QH) edge states of opposite chiralities in a graphene electron-hole bilayer at moderate magnetic fields. Using this approach, we engineer helical 1D edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong non-local transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Unlike other approaches used for realizing helical states, the graphene electron-hole bilayer can be used to build new 1D systems incorporating fractional edge states. Indeed, we are able to tune the bilayer devices into a regime hosting fractional and integer edge states of opposite chiralities, paving the way towards 1D helical conductors with fractional quantum statistics.
Helical edge states and fractional quantum Hall effect in a graphene electron-hole bilayer
NASA Astrophysics Data System (ADS)
Sanchez-Yamagishi, Javier D.; Luo, Jason Y.; Young, Andrea F.; Hunt, Benjamin M.; Watanabe, Kenji; Taniguchi, Takashi; Ashoori, Raymond C.; Jarillo-Herrero, Pablo
2016-10-01
Helical 1D electronic systems are a promising route towards realizing circuits of topological quantum states that exhibit non-Abelian statistics. Here, we demonstrate a versatile platform to realize 1D systems made by combining quantum Hall (QH) edge states of opposite chiralities in a graphene electron-hole bilayer at moderate magnetic fields. Using this approach, we engineer helical 1D edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong non-local transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Unlike other approaches used for realizing helical states, the graphene electron-hole bilayer can be used to build new 1D systems incorporating fractional edge states. Indeed, we are able to tune the bilayer devices into a regime hosting fractional and integer edge states of opposite chiralities, paving the way towards 1D helical conductors with fractional quantum statistics.
Magnetic Topological Insulators and Quantum Anomalous Hall Effect
NASA Astrophysics Data System (ADS)
Kou, Xufeng
The engineering of topological surface states is a key to realize applicable devices based on topological insulators (TIs). Among various proposals, introducing magnetic impurities into TIs has been proven to be an effective way to open a surface gap and integrate additional ferromagnetism with the original topological order. In this Dissertation, we study both the intrinsic electrical and magnetic properties of the magnetic TI thin films grown by molecular beam epitaxy. By doping transition element Cr into the host tetradymite-type V-VI semiconductors, we achieve robust ferromagnetic order with a strong perpendicular magnetic anisotropy. With additional top-gating capability, we realize the electric-field-controlled ferromagnetism in the magnetic TI systems, and demonstrate such magneto-electric effects can be effectively manipulated, depending on the interplays between the band topology, magnetic exchange coupling, and structural engineering. Most significantly, we report the observation of quantum anomalous Hall effect (QAHE) in the Cr-doped (BiSb)2Te3 samples where dissipationless chiral edge conduction is realized in the macroscopic millimeter-size devices without the presence of any external magnetic field, and the stability of the quantized Hall conductance of e2/h is well-maintained as the film thickness varies across the 2D hybridization limit. With additional quantum confinement, we discover the metal-to-insulator switching between two opposite QAHE states, and reveal the universal QAHE phase diagram in the thin magnetic TI samples. In addition to the uniform magnetic TIs, we further investigate the TI/Cr-doped TI bilayer structures prepared by the modulation-doped growth method. By controlling the magnetic interaction profile, we observe the Dirac hole-mediated ferromagnetism and develop an effective way to manipulate its strength. Besides, the giant spin-orbit torque in such magnetic TI-based heterostructures enables us to demonstrate the current
Quantum Hall transitions: An exact theory based on conformal restriction
NASA Astrophysics Data System (ADS)
Bettelheim, E.; Gruzberg, I. A.; Ludwig, A. W. W.
2012-10-01
We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, and for other two-dimensional disordered systems, based on the theory of “conformal restriction.” This is a mathematical theory that was recently developed within the context of the Schramm-Loewner evolution which describes the “stochastic geometry” of fractal curves and other stochastic geometrical fractal objects in two-dimensional space. Observables elucidating the connection with the plateau transition include the so-called point-contact conductances (PCCs) between points on the boundary of the sample, described within the language of the Chalker-Coddington network model for the transition. We show that the disorder-averaged PCCs are characterized by a classical probability distribution for certain geometric objects in the plane (which we call pictures), occurring with positive statistical weights, that satisfy the crucial so-called restriction property with respect to changes in the shape of the sample with absorbing boundaries; physically, these are boundaries connected to ideal leads. At the transition point, these geometrical objects (pictures) become fractals. Upon combining this restriction property with the expected conformal invariance at the transition point, we employ the mathematical theory of “conformal restriction measures” to relate the disorder-averaged PCCs to correlation functions of (Virasoro) primary operators in a conformal field theory (of central charge c=0). We show how this can be used to calculate these functions in a number of geometries with various boundary conditions. Since our results employ only the conformal restriction property, they are equally applicable to a number of other critical disordered electronic systems in two spatial dimensions, including for example the spin quantum Hall effect, the thermal metal phase in symmetry class D, and classical diffusion in two
Real-Space Renormalization-Group Approach to the Integer Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Cain, Philipp; Römer, Rudolf A.
We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, Pc(G), with very high accuracy. The RG flow of P(G) at energies away from the transition yields a value of the critical exponent ν that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as RL and RH is given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD). This distribution is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with ν = 2.37±0.02. Away from the transition it crosses over towards the Poisson distribution. We next investigate the plateau-to-insulator transition at strong magnetic fields. For a fully quantum coherent situation, we find a quantized Hall insulator with RH≈h/e2 up to RL 20h/e2 when interpreting the results in terms of most probable value of the distribution function P(RH). Upon further increasing RL→∞, the Hall insulator with diverging Hall resistance R H∝ R Lκ is seen. The crossover between these two regimes depends on the precise nature of the averaging procedure for the distributions P(RL) and P(RH). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition. Inhomogeneities are modeled by a smooth random potential with a correlator which falls off with distance as a power law r-α. Similar to the classical percolation, we observe an enhancement of ν with decreasing α. These results exemplify the surprising fact that a small RG unit, containing only five nodes, accurately captures most of the correlations responsible for the localization
NASA Astrophysics Data System (ADS)
Yoshioka, Daijiro
1998-01-01
A theory of transport in the quantum-Hall regime is developed for separately contacted double-layer electron systems. Inter-layer tunneling provides a channel for equilibration of the distribution functions in the two layers at the edge states. Resistances and transresistances for various configurations of the electrodes are calculated as functions of the inter-layer tunneling amplitude. Induced current in one of the layer by a current in the other is also calculated. It is shown that reflection at the leads causes change in the results for some electrode configurations. The results obtained in this work is consistent with recent experiments.
Conformal field theory approach to Abelian and non-Abelian quantum Hall quasielectrons.
Hansson, T H; Hermanns, M; Regnault, N; Viefers, S
2009-04-24
The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.
Quantum Plasma Effects in the Classical Regime
Brodin, G.; Marklund, M.; Manfredi, G.
2008-05-02
For quantum effects to be significant in plasmas it is often assumed that the temperature over density ratio must be small. In this paper we challenge this assumption by considering the contribution to the dynamics from the electron spin properties. As a starting point we consider a multicomponent plasma model, where electrons with spin-up and spin-down are regarded as different fluids. By studying the propagation of Alfven wave solitons we demonstrate that quantum effects can survive in a relatively high-temperature plasma. The consequences of our results are discussed.
Simulation of an optomechanical quantum memory in the nonlinear regime
NASA Astrophysics Data System (ADS)
Teh, R. Y.; Kiesewetter, S.; Reid, M. D.; Drummond, P. D.
2017-07-01
Optomechanical systems cooled to the quantum level provide a promising mechanism for a high-fidelity quantum memory that is faithful to a given temporal mode structure, and can be recovered synchronously. We carry out full, probabilistic quantum simulation of a quantum optomechanical memory, including nonlinear effects that are usually ignored. This is achieved using both the approximate truncated Wigner and the exact positive P phase-space representations. By considering the nonlinear quantum optomechanical Hamiltonian, our simulations allow us to probe the regime where the linearization approximation fails to hold. We show evidence for large spectral overlap between the quantum signal and the transfer field in typical optomechanical quantum memory experiments. Methods for eliminating this overlap to accurately recover the quantum signal are discussed. This allows us to give a complete model for the quantum storage of a coherent state. We treat the mode matching that is necessary to accurately retrieve the stored quantum state, by including the internal dynamics of the mechanical system as well as the optical system. We also include the finite switching time of the control transfer field. The fidelity for the storage of a coherent state is computed numerically using currently realistic experimental parameters in the electromechanical case. We find the expected fidelity is lower than required to demonstrate true quantum state transfers. Significant improvements in the quality factor of the cavity and mechanical systems will, however, increase the fidelity beyond the quantum threshold.
Particle-hole symmetry and Luttinger liquids in a quantum Hall circuit
NASA Astrophysics Data System (ADS)
Roddaro, Stefano
2006-03-01
I shall present recent experimental results on edge-state transport through quantum point contacts in the quantum Hall (QH) regime. Finite-bias backscattering measurements between edge channels at filling factor ν=1 will be presented at different temperatures. Transport through the constriction displays a non-linear Luttinger-like behavior even in the integer QH regime in contrast with the linear tunneling predicted for integer edge states [1,2]. Both zero-bias enhancement and suppression of the inter-edge tunneling will be shown in a controllable way as a function of gate bias [2,3,4]. The observed evolution is connected to the local charge depletion in the constriction region and offers new insight into the link between QH charge-conjugation and Luttinger liquid description of edge channels [2]. I shall discuss the relevance of these experimental results in the context of the dynamics of the highly-correlated edge channels in the fractional QH regime [5]. Finally I shall demonstrate how charge-conjugation can be exploited in the design of new QH circuits where the transport properties of the hole component of a partially filled Landau level can be directly addressed. [1] X.-G. Wen, Phys. Rev. Lett. 62, 2206 (1990); P. Fendley et al. Phys. Rev. Lett. 74, 3005 (1995). [2] S. Roddaro, V. Pellegrini, F. Beltram, L. N. Pfeiffer, K. W. West, Phys. Rev. Lett. 95, 156804 (2005). [3] S. Roddaro, V. Pellegrini, F. Beltram, G. Biasiol, L. Sorba., Phys. Rev. Lett. 93, 046801 (2004). [4] S. Roddaro, V. Pellegrini, F. Beltram, G. Biasiol, L. Sorba, R. Raimondi, G. Vignale, Phys. Rev. Lett. 90, 046805 (2003). [5] A. M. Chang, Rev. Mod. Phys. 75, 1449 (2003).
Spectral classification of coupling regimes in the quantum Rabi model
NASA Astrophysics Data System (ADS)
Rossatto, Daniel Z.; Villas-Bôas, Celso J.; Sanz, Mikel; Solano, Enrique
2017-07-01
The quantum Rabi model is in the scientific spotlight due to the recent theoretical and experimental progress. Nevertheless, a full-fledged classification of its coupling regimes remains as a relevant open question. We propose a spectral classification dividing the coupling regimes into three regions based on the validity of perturbative criteria on the quantum Rabi model, which allows us the use of exactly solvable effective Hamiltonians. These coupling regimes are (i) the perturbative ultrastrong coupling regime which comprises the Jaynes-Cummings model, (ii) a region where nonperturbative ultrastrong and nonperturbative deep strong coupling regimes coexist, and (iii) the perturbative deep strong coupling regime. We show that this spectral classification depends not only on the ratio between the coupling strength and the natural frequencies of the unperturbed parts, but also on the energy to which the system can access. These regimes additionally discriminate the completely different behaviors of several static physical properties, namely the total number of excitations, the photon statistics of the field, and the cavity-qubit entanglement. Finally, we explain the dynamical properties which are traditionally associated with the deep strong coupling regime, such as the collapses and revivals of the state population, in the frame of the proposed spectral classification.
Energy level spacing distribution at the quantum Hall transition
NASA Astrophysics Data System (ADS)
Roemer, Rudolf A.; Cain, Philipp; Raikh, Mikhail E.; Schreiber, Michael
2002-03-01
We apply the renormalization group (RG) approach to study the energy level statistics at the integer quantum Hall transition. Within the RG approach the macroscopic array of saddle points of the Chalker-Coddington network is replaced by a fragment consisting of only five saddle points. Previously we have demonstrated that the RG approach reproduces the distribution of the power transmission coefficients at the transition, P(T), with very high accuracy.(P. Cain, M.E. Raikh, R.A. Roemer, M. Schreiber, Phys. Rev. B 64), 235326-9 (2001). To assess the level statistics we analyze the phases of the transmission coefficients. We find that, at the transition, the level spacing distribution (LSD) is close to that for the unitary ensemble with well-pronounced level repulsion. We emphasize that a metal-like LSD emerges when the fixed point distribution P(T) is used. We check that away from the transition the LSD crosses over towards the Poisson distribution.
Quantum anomalous Hall effect in ferromagnetic transition metal halides
NASA Astrophysics Data System (ADS)
Huang, Chengxi; Zhou, Jian; Wu, Haiping; Deng, Kaiming; Jena, Puru; Kan, Erjun
2017-01-01
The quantum anomalous Hall (QAH) effect is a novel topological spintronic phenomenon arising from inherent magnetization and spin-orbit coupling. Various theoretical and experimental efforts have been devoted in search of intrinsic QAH insulators. However, up to now, it has only been observed in Cr or V doped (Bi,Sb ) 2T e3 film in experiments with very low working temperature. Based on the successful synthesis of transition metal halides, we use first-principles calculations to predict that the Ru I3 monolayer is an intrinsic ferromagnetic QAH insulator with a topologically nontrivial global band gap of 11 meV. This topologically nontrivial band gap at the Fermi level is due to its crystal symmetry, thus the QAH effect is robust. Its Curie temperature, estimated to be ˜360 K using Monte Carlo simulation, is above room temperature and higher than most two-dimensional ferromagnetic thin films. The inclusion of Hubbard U in the Ru-d electrons does not affect this result. We also discuss the manipulation of its exchange energy and nontrivial band gap by applying in-plane strain. Our work adds an experimentally feasible member to the QAH insulator family, which is expected to have broad applications in nanoelectronics and spintronics.
Quantum anomalous Hall effect in stanene on a nonmagnetic substrate
NASA Astrophysics Data System (ADS)
Zhang, Huisheng; Zhou, Tong; Zhang, Jiayong; Zhao, Bao; Yao, Yugui; Yang, Zhongqin
2016-12-01
Since the quantum anomalous Hall (QAH) effect was realized in magnetic topological insulators, research on the effect has become a hot topic. The very harsh realizing requirements of the effect in experiments, however, hinder its practical applications. Based on ab initio methods, we find that nonmagnetic Pb I2 films are ideal substrates for the two-dimensional honeycomb stanene. The QAH effect with a pretty large band gap (up to 90 meV) can be achieved in the functionalized stanene /Pb I2 heterostructure. Despite van der Waals interactions in the heterostructure, band inversions are found to be happening between Sn (s and px ,y ) and Pb (px ,y) orbitals, playing a key role in determining the nontrivial topology and the large band gap of the system. Having no magnetic atoms is imperative to triggering the QAH effect. A very stable rudimentary device having QAH effects is proposed based on the Sn /Pb I2 heterostructure. Our results demonstrate that QAH effects can be easily realized in the Sn /Pb I2 heterostructures in experiments.
Coulomb drag and tunneling studies in quantum Hall bilayers
NASA Astrophysics Data System (ADS)
Nandi, Debaleena
The bilayer quantum Hall state at total filling factor νT=1, where the total electron density matches the degeneracy of the lowest Landau level, is a prominent example of Bose-Einstein condensation of excitons. A macroscopically ordered state is realized where an electron in one layer is tightly bound to a "hole" in the other layer. If exciton transport were the only bulk transportmechanism, a current driven in one layer would spontaneously generate a current of equal magnitude and opposite sign in the other layer. The Corbino Coulomb drag measurements presented in this thesis demonstrate precisely this phenomenon. Excitonic superfluidity has been long sought in the νT=1 state. The tunneling between the two electron gas layers exihibit a dc Josephson-like effect. A simple model of an over-damped voltage biased Josephson junction is in reasonable agreement with the observed tunneling I -- V. At small tunneling biases, it exhibits a tunneling "supercurrent". The dissipation is carefully studied in this tunneling "supercurrent" and found to remain small but finite.
Proximity enhanced quantum spin Hall state in graphene
Kou, Liangzhi; Hu, Feiming; Yan, Binghai; Wehling, Tim; Felser, Claudia; Frauenheim, Thomas; Chen, Changfeng
2015-02-23
Graphene is the first model system of two-dimensional topological insulator (TI), also known as quantum spin Hall (QSH) insulator. The QSH effect in graphene, however, has eluded direct experimental detection because of its extremely small energy gap due to the weak spin–orbit coupling. Here we predict by ab initio calculations a giant (three orders of magnitude) proximity induced enhancement of the TI energy gap in the graphene layer that is sandwiched between thin slabs of Sb_{2}Te_{3} (or MoTe_{2}). This gap (1.5 meV) is accessible by existing experimental techniques, and it can be further enhanced by tuning the interlayer distance via compression. We reveal by a tight-binding study that the QSH state in graphene is driven by the Kane–Mele interaction in competition with Kekulé deformation and symmetry breaking. As a result, the present work identifies a new family of graphene-based TIs with an observable and controllable bulk energy gap in the graphene layer, thus opening a new avenue for direct verification and exploration of the long-sought QSH effect in graphene.
Quantum spin Hall phase in 2D trigonal lattice
Wang, Z. F.; Jin, Kyung-Hwan; Liu, Feng
2016-01-01
The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, px, py) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin–orbit coupling (SOC)-induced s–p band inversion or p–p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ∼73 meV, facilitating the possible room-temperature measurement. Our results will extend the search for substrate supported QSH materials to new lattice and orbital types. PMID:27599580
Stochastic geometry in disordered systems, applications to quantum Hall transitions
NASA Astrophysics Data System (ADS)
Gruzberg, Ilya
2012-02-01
A spectacular success in the study of random fractal clusters and their boundaries in statistical mechanics systems at or near criticality using Schramm-Loewner Evolutions (SLE) naturally calls for extensions in various directions. Can this success be repeated for disordered and/or non-equilibrium systems? Naively, when one thinks about disordered systems and their average correlation functions one of the very basic assumptions of SLE, the so called domain Markov property, is lost. Also, in some lattice models of Anderson transitions (the network models) there are no natural clusters to consider. Nevertheless, in this talk I will argue that one can apply the so called conformal restriction, a notion of stochastic conformal geometry closely related to SLE, to study the integer quantum Hall transition and its variants. I will focus on the Chalker-Coddington network model and will demonstrate that its average transport properties can be mapped to a classical problem where the basic objects are geometric shapes (loosely speaking, the current paths) that obey an important restriction property. At the transition point this allows to use the theory of conformal restriction to derive exact expressions for point contact conductances in the presence of various non-trivial boundary conditions.
Emergence and mechanism in the fractional quantum Hall effect
NASA Astrophysics Data System (ADS)
Bain, Jonathan
2016-11-01
For some authors, an adequate notion of emergence must include an account of a mechanism by means of which emergent behavior is realized. This appeal to mechanism is problematic in the case of the fractional quantum Hall effect (FQHE). There is a consensus among physicists that the FQHE exhibits emergent phenomena, but there are at least four alternative explanations of the latter that, arguably, appeal to ontologically distinct mechanisms, both at the microphysics level and at the level of general organizing principles. In light of this underdetermination of mechanism, one is faced with the following options: (I) deny that emergence is present in the FQHE; (II) argue for the priority of one mechanistic explanation over the others; or (III) temper the desire for a mechanism-centric account of emergence. I will argue that there are good reasons to reject (I) and (II) and accept (III). In particular, I will suggest that a law-centric account of emergence does just fine in explaining the emergent phenomena associated with the FQHE.
Quantum spin Hall phase in 2D trigonal lattice
Wang, Z. F.; Jin, Kyung -Hwan; Liu, Feng
2016-09-07
The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, px, py) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin–orbit coupling (SOC)-induced s–p band inversion or p–p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown tomore » be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ~73 meV, facilitating the possible room-temperature measurement. Finally, our results will extend the search for substrate supported QSH materials to new lattice and orbital types.« less
Quantum spin Hall phase in 2D trigonal lattice
Wang, Z. F.; Jin, Kyung -Hwan; Liu, Feng
2016-09-07
The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, p_{x}, p_{y}) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin–orbit coupling (SOC)-induced s–p band inversion or p–p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ~73 meV, facilitating the possible room-temperature measurement. Finally, our results will extend the search for substrate supported QSH materials to new lattice and orbital types.
A bifunctional spin detector made of quantum anomalous Hall insulator
NASA Astrophysics Data System (ADS)
Shi, Zhangsheng; Wu, Jiansheng
2016-10-01
The spin selection of the topological boundary states (TBS) which are protected by the chiral-like symmetry in quantum anomalous Hall insulator (QAHI) can be used to construct a bifunctional spin detector (SD). Such device made of QAHIs in parallel with opposite chirality can divide an incoming spin-polarized current into two outgoing currents. The agreement between numerical and analytical calculation proves that the SD device functions as both spin filter and spin separator well in reflecting the spin polarization of source material from the ratio of two currents. The monotonic relation of spin polarization and current ratio suggests that using such kind of device, the spin polarization can be obtained directly. We also find that such device has a broad working energy region attributed by the TBS within the bulk gap. Combining with the result that the current ratio is barely dependent on the coupling between candidate materials and device, it is reasonable to apply this technique with a stable measuring accuracy. Furthermore, the features such as having simple geometry, being manipulated without external magnetic field, and the prospect of working at room temperature make this proposed device seem promising in developing future low-power-consumption spintronic device.
Proximity enhanced quantum spin Hall state in graphene
Kou, Liangzhi; Hu, Feiming; Yan, Binghai; ...
2015-02-23
Graphene is the first model system of two-dimensional topological insulator (TI), also known as quantum spin Hall (QSH) insulator. The QSH effect in graphene, however, has eluded direct experimental detection because of its extremely small energy gap due to the weak spin–orbit coupling. Here we predict by ab initio calculations a giant (three orders of magnitude) proximity induced enhancement of the TI energy gap in the graphene layer that is sandwiched between thin slabs of Sb2Te3 (or MoTe2). This gap (1.5 meV) is accessible by existing experimental techniques, and it can be further enhanced by tuning the interlayer distance viamore » compression. We reveal by a tight-binding study that the QSH state in graphene is driven by the Kane–Mele interaction in competition with Kekulé deformation and symmetry breaking. As a result, the present work identifies a new family of graphene-based TIs with an observable and controllable bulk energy gap in the graphene layer, thus opening a new avenue for direct verification and exploration of the long-sought QSH effect in graphene.« less
Forward scattering approximation and bosonization in integer quantum Hall systems
Rosenau da Costa, M. Westfahl, H.; Caldeira, A.O.
2008-03-15
In this work, we present a model and a method to study integer quantum Hall (IQH) systems. Making use of the Landau levels structure we divide these two-dimensional systems into a set of interacting one-dimensional gases, one for each guiding center. We show that the so-called strong field approximation, used by Kallin and Halperin and by MacDonald, is equivalent, in first order, to a forward scattering approximation and analyze the IQH systems within this approximation. Using an appropriate variation of the Landau level bosonization method we obtain the dispersion relations for the collective excitations and the single-particle spectral functions. For the bulk states, these results evidence a behavior typical of non-normal strongly correlated systems, including the spin-charge splitting of the single-particle spectral function. We discuss the origin of this behavior in the light of the Tomonaga-Luttinger model and the bosonization of two-dimensional electron gases.
Collective modes at the fractional quantum Hall edge
NASA Astrophysics Data System (ADS)
Joglekar, Yogesh; Murthy, Ganpathy
2002-03-01
The fractional quantum Hall edge has been a continuing source of new ideas [1] and experimental results [2] for some time. Most theoretical approaches start with an effective bosonic theory [1] in which all fermions have been integrated out (an exception is the approach based on Chern-Simons theory [3]). Our approach is based on the lowest Landau level Hamiltonian theory of the FQHE [4]. In this theory, composite fermions are fully interacting, and We obtain the collective modes using a conserving approximation which respects the constraints. We present the edge-mode dispersions for various simple fractions. 1. X.-G.Wen, Phys. Rev. Lett. 64, 2206 (1990); A.Lopez and E.Fradkin, Phys. Rev. B 59, 15323 (1999); U. Zulicke and A.H.MacDonald, Phys. Rev. B 60, 2837 (1999); D.-H.Lee and X.-G.Wen, cond-mat/9809160. 2. A.M.Chang et al, Phys. Rev. Lett. 86, 143 (2000). 3. L.S.Levitov, A.V.Shytov, and B.I.Halperin, Phys. Rev. B 64, 075322 (2001). 4. R. Shankar and G. Murthy, Phys. Rev. Lett. 79, 4437 (1997).
Giant quantum Hall plateaus generated by charge transfer in epitaxial graphene
Alexander-Webber, J. A.; Huang, J.; Maude, D. K.; Janssen, T. J. B. M.; Tzalenchuk, A.; Antonov, V.; Yager, T.; Lara-Avila, S.; Kubatkin, S.; Yakimova, R.; Nicholas, R. J.
2016-01-01
Epitaxial graphene has proven itself to be the best candidate for quantum electrical resistance standards due to its wide quantum Hall plateaus with exceptionally high breakdown currents. However one key underlying mechanism, a magnetic field dependent charge transfer process, is yet to be fully understood. Here we report measurements of the quantum Hall effect in epitaxial graphene showing the widest quantum Hall plateau observed to date extending over 50 T, attributed to an almost linear increase in carrier density with magnetic field. This behaviour is strong evidence for field dependent charge transfer from charge reservoirs with exceptionally high densities of states in close proximity to the graphene. Using a realistic framework of broadened Landau levels we model the densities of donor states and predict the field dependence of charge transfer in excellent agreement with experimental results, thus providing a guide towards engineering epitaxial graphene for applications such as quantum metrology. PMID:27456765
Quantum phase transitions and the ν=5/2 fractional Hall state in wide quantum wells.
Papić, Z; Haldane, F D M; Rezayi, E H
2012-12-28
We study the nature of the ν=5/2 quantum Hall state in wide quantum wells under the mixing of electronic subbands and Landau levels. A general method is introduced to analyze the Moore-Read pfaffian state and its particle-hole conjugate, the anti-pfaffian state, under periodic boundary conditions in a "quartered" Brillouin zone scheme containing both even and odd numbers of electrons. By examining the rotational quantum numbers on the torus, we show spontaneous breaking of the particle-hole symmetry can be observed in finite-size systems. In the presence of electronic-subband and Landau-level mixing, the particle-hole symmetry is broken in such a way that the anti-pfaffian state is unambiguously favored, and becomes more robust in the vicinity of a transition to the compressible phase, in agreement with recent experiments.
Nambu-Goldstone modes and the Josephson supercurrent in the bilayer quantum Hall system
NASA Astrophysics Data System (ADS)
Hama, Yusuke; Tsitsishvili, George; Ezawa, Zyun F.
2013-05-01
An interlayer phase coherence develops spontaneously in the bilayer quantum Hall system at the filling factor ν = 1. On the other hand, the spin and pseudospin degrees of freedom are entangled coherently in the canted antiferromagnetic phase of the bilayer quantum Hall system at the filling factor ν = 2. There emerges a complex Nambu-Goldstone mode with a linear dispersion in the zero tunneling-interaction limit for both cases. Then its phase field provokes a Josephson supercurrent in each layer, which is dissipationless as in a superconductor. We study what kind of phase coherence the Nambu-Goldstone mode develops in association with the Josephson supercurrent and its effect on the Hall resistance in the bilayer quantum Hall system at ν = 1, 2, by employing the Grassmannian formalism.
Polaronic quantum diffusion in dynamic localization regime
NASA Astrophysics Data System (ADS)
Yao, Yao
2017-04-01
We investigate the quantum dynamics in a disordered electronic lattice by the time-dependent density matrix renormalization group algorithm. The on-site energy in the lattice follows the Fibonacci sequence and the electron off-diagonally couples to a sub-Ohmic phonon bath. It is found that the slope of the inverse participation ratio versus the coupling strength undergoes a sudden change that indicates a transition from static to dynamic localization, and that the generated polarons coherently diffuse via hopping-like processes, evidenced by the saturated entanglement entropy, providing a novel scenario for a transportation mechanism in strongly disordered systems. Moreover, the mean-square displacement is revealed to be insensitive to the coupling strength, implying the quantum diffusion behavior survives the energy disorder that prevails in real organic materials.
Photon mirror acceleration in the quantum regime
NASA Astrophysics Data System (ADS)
Mendonça, J. T.; Fedele, R.
2014-12-01
Reflection of an electron beam by an intense laser pulse is considered. This is the so-called photon mirror configuration for laser acceleration in vacuum, where the energy of the incident electron beam is nearly double-Doppler shifted due to reflection on the laser pulse front. A wave-electron optical description for electron reflection and resonant backscattering, due to both linear electric field force and quadratic ponderomotive force, is provided beyond the paraxial approximation. This is done by assuming that the single electron of the beam is spin-less and therefore its motion can be described by a quantum scalar field whose spatiotemporal evolution is governed by the Klein-Gordon equation (Klein-Gordon field). Our present model, not only confirms the classical results but also shows the occurrence of purely quantum effects, such as partial reflection of the incident electron beam and enhanced backscattering due to Bragg resonance.
Photon mirror acceleration in the quantum regime
Mendonça, J. T.; Fedele, R.
2014-12-15
Reflection of an electron beam by an intense laser pulse is considered. This is the so-called photon mirror configuration for laser acceleration in vacuum, where the energy of the incident electron beam is nearly double-Doppler shifted due to reflection on the laser pulse front. A wave-electron optical description for electron reflection and resonant backscattering, due to both linear electric field force and quadratic ponderomotive force, is provided beyond the paraxial approximation. This is done by assuming that the single electron of the beam is spin-less and therefore its motion can be described by a quantum scalar field whose spatiotemporal evolution is governed by the Klein-Gordon equation (Klein-Gordon field). Our present model, not only confirms the classical results but also shows the occurrence of purely quantum effects, such as partial reflection of the incident electron beam and enhanced backscattering due to Bragg resonance.
Ultracold Molecules: Physics in the Quantum Regime
Doyle, John
2014-11-17
Our research encompasses approaches to the trapping of diatomic molecules at low temperature plus the cooling and detection of polyatomic molecules in the kelvin temperature regime. We have cooled and trapped CaF and/or CaH molecules, loaded directly from a molecular beam. As part of this work, we are continuing to develop an important trapping technique, optical loading from a buffer-gas beam. This method was invented in our lab. We are also studying cold polyatomic molecules and their interactions with cold atoms.
Interference of e/3 quasiparticles encircling 2/5 fractional quantum Hall island
NASA Astrophysics Data System (ADS)
Lin, Ping V.; Camino, F. E.; Goldman, V. J.
2010-03-01
We report experiments in a large, 2.5 micron Fabry-Perot interferometer fabricated from a GaAs/AlGaAs heterostructure. Device is defined by etch trenches; front gates deposited in the trenches allow to tune the device. Tunneling in the two constrictions closes an Aharonov-Bohm path around the 2D electron island. Quantized plateaus in RXX and RXY allow to find out both: the bulk and the constriction filling. Etch trench depletion is such that in the fractional quantum Hall regime we obtain the situation when 1/3 chiral edge channels pass through the constrictions and encircle an island of the 2/5 FQH fluid. In this regime the magnetic field oscillation period is 5.4±0.3 of the integer filling 1 period. In this large device magnetic field period well approximates the flux period. We thus conclude that the flux period is 5h/e, and the corresponding back-gate period is 2e. These results agree with our previous reports of these superperiods in smaller size devices [1]. The experimental superperiods are interpreted as imposed by the anyonic statistics of the fractionally charged e/3 and e/5 quasiparticles. [1] F. E. Camino et al., PRB 72, 075342 (2005); W. Zhou et al., PRB 73, 245322 (2006).
Non-abelian fractional quantum hall effect for fault-resistant topological quantum computation.
Pan, Wei; Thalakulam, Madhu; Shi, Xiaoyan; Crawford, Matthew; Nielsen, Erik; Cederberg, Jeffrey George
2013-10-01
Topological quantum computation (TQC) has emerged as one of the most promising approaches to quantum computation. Under this approach, the topological properties of a non-Abelian quantum system, which are insensitive to local perturbations, are utilized to process and transport quantum information. The encoded information can be protected and rendered immune from nearly all environmental decoherence processes without additional error-correction. It is believed that the low energy excitations of the so-called =5/2 fractional quantum Hall (FQH) state may obey non-Abelian statistics. Our goal is to explore this novel FQH state and to understand and create a scientific foundation of this quantum matter state for the emerging TQC technology. We present in this report the results from a coherent study that focused on obtaining a knowledge base of the physics that underpins TQC. We first present the results of bulk transport properties, including the nature of disorder on the 5/2 state and spin transitions in the second Landau level. We then describe the development and application of edge tunneling techniques to quantify and understand the quasiparticle physics of the 5/2 state.
Two-flux composite fermion series of the fractional quantum Hall states in strained Si.
Lai, K; Pan, W; Tsui, D C; Lyon, S; Mühlberger, M; Schäffler, F
2004-10-08
Magnetotransport properties are investigated in a high-mobility two-dimensional electron system in the strained Si quantum well of a (100) Si(0.75)Ge(0.25)/Si/Si(0.75)Ge0.25 heterostructure, at temperatures down to 30 mK and in magnetic fields up to 45 T. We observe around nu=1/2 the two-flux composite fermion (CF) series of the fractional quantum Hall effect (FQHE) at nu=2/3, 3/5, 4/7, and at nu=4/9, 2/5, 1/3. Among these FQHE states, the nu=1/3, 4/7, and 4/9 states are seen for the first time in the Si/SiGe system. Interestingly, of the CF series, the 3/5 state is weaker than the nearby 4/7 state and the 3/7 state is conspicuously missing, resembling the observation in the IQHE regime that the nu=3 is weaker than the nearby nu=4 state. Our results can be quantitatively understood in the picture of CF's with the valley degree of freedom.
Mesoscopic Transport in Electrostatically Defined Spin-Full Channels in Quantum Hall Ferromagnets
NASA Astrophysics Data System (ADS)
Kazakov, Aleksandr; Simion, George; Lyanda-Geller, Yuli; Kolkovsky, Valery; Adamus, Zbigniew; Karczewski, Grzegorz; Wojtowicz, Tomasz; Rokhinson, Leonid P.
2017-07-01
In this work, we use electrostatic control of quantum Hall ferromagnetic transitions in CdMnTe quantum wells to study electron transport through individual domain walls (DWs) induced at a specific location. These DWs are formed due to the hybridization of two counterpropagating edge states with opposite spin polarization. Conduction through DWs is found to be symmetric under magnetic field direction reversal, consistent with the helical nature of these DWs. We observe that long domain walls are in the insulating regime with a localization length of 4 - 6 μ m . In shorter DWs, the resistance saturates to a nonzero value at low temperatures. Mesoscopic resistance fluctuations in a magnetic field are investigated. The theoretical model of transport through impurity states within the gap induced by spin-orbit interactions agrees well with the experimental data. Helical DWs have the required symmetry for the formation of synthetic p -wave superconductors. The achieved electrostatic control of a single helical domain wall is a milestone on the path to their reconfigurable network and ultimately to a demonstration of the braiding of non-Abelian excitations.
Characterization and modelling of one-dimensional states in a bent quantum Hall system
NASA Astrophysics Data System (ADS)
Steinke, L.; Schuh, D.; Bichler, M.; Abstreiter, G.; Grayson, M.
2007-03-01
We study the transport properties of a one-dimensional (1D) wire state at the corner of a 90^o bent quantum Hall (QH) system. Such a system is formed in a corner-overgrown bent quantum well [1] by applying a tilted magnetic field B. The corner geometry itself serves as a sharp QH boundary and hosts strongly coupled 1D forward and reverse movers with no barrier in between. At different magnetic fields we measure a different conductance behavior of the 1D wire, depending on the QH filling factor ν. In the integer QH regime, at equal filling factors ν= 1 and ν= 2 on both facets of the bent 2D system, we observe an insulating phase where the wire conductance decreases rapidly with decreasing temperature T and DC bias Voltage VDC. The integer filling factors ν>2 show a critical behavior with only weak dependence on T and VDC. Spin-unresolved Hartree calculations of the dispersions of the corner states illustrate possible origins of the two observed phases [2]. The calculations also provide an insight into the electronic states in the bent QH system, which has no analogue in a planar structure. [1] M. Grayson, D. Schuh, M. Huber, M. Bichler, and G. Abstreiter, APL 86,); [2] M. Grayson, L. Steinke, D. Schuh, M. Bichler, L. Hoeppel, J. Smet, K. v. Klitzing, D. K. Maude, and G. Abstreiter, submitted;
NASA Astrophysics Data System (ADS)
Men'shov, V. N.; Tugushev, V. V.; Chulkov, E. V.
2016-10-01
We theoretically study how magnetic modulation can be used to manipulate the transport properties of heterostructures formed by a thin film of a three-dimensional topological insulator sandwiched between slabs of a normal insulator. Employing the k • p scheme, in the framework of a continual approach, we argue that electron states of the system are spin-polarized when ultrathin magnetic insertions are incorporated into the film. We demonstrate that (i) the spin-polarization magnitude depends strongly on the magnetic insertion position in the film and (ii) there is the optimal insertion position to realize quantum anomalous Hall effect, which is a function of the material parameters, the film thickness and the topological insulator/normal insulator interface potential. For the heterostructure with a pair of symmetrically placed magnetic insertions, we calculate a phase diagram that shows a series of transitions between distinct quantum regimes of transverse conductivity. We provide consistent interpretation of recent experimental findings in the context of our results.
NASA Astrophysics Data System (ADS)
Abanin, D. A.; Skachko, I.; Du, X.; Andrei, E. Y.; Levitov, L. S.
2010-03-01
Fractional quantum Hall effect (FQHE), observed recently in suspended graphene (SG) [1], was found to persist up to temperatures much higher than in previously studied systems, such as GaAs. This suggests strong electron interactions in SG. Can the interaction strength be inferred from the measurements? The best results on FQHE were obtained on micron-size SG flakes, where only two-terminal measurements could be performed. This talk will address the problem of determining transport coefficients from the two-terminal conductance in the FQHE regime. A general approach, which relies on the conformal invariance of two-dimensional magnetotransport, is used to extract σxx and σxy. From the temperature dependence of σxx we estimate the energy gap of quasiparticle excitations in the ν= 1/3 state. The gap value, which is found to be well above that measured in GaAs systems [2], is compared to theoretical predictions. Our approach provides a new tool for the studies of quantum transport in suspended graphene and other nanoscale systems. [1] X. Du et al, Nature 462, 192 (2009); K. Bolotin et al, ibid., 196 (2009). [2] G. S. Boebinger et al, Phys. Rev. Lett. 55, 1606 (1985).
Quantum Hall effect in HgTe quantum wells at nitrogen temperatures
Kozlov, D. A. Kvon, Z. D.; Mikhailov, N. N.; Dvoretskii, S. A.; Weishäupl, S.; Krupko, Y.; Portal, J.-C.
2014-09-29
We report on the observation of quantized Hall plateaus in a system of two-dimensional Dirac fermions, implemented in a 6.6 nm HgTe quantum well at magnetic fields up to 34 T at nitrogen temperatures. The activation energies determined from the temperature dependence of the longitudinal resistivity are found to be almost equal for the filling factors ν of 1 and 2. This indicates that the large values of the g-factor (about 30–40) remain unchanged at very strong magnetic fields.
Notion of time and the semiclassical regime of quantum gravity
Castagnino, M.A.; Mazzitelli, F.D. Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab 1, 1428 Buenos Aires )
1990-07-15
Using the notion of {ital probabilistic} {ital time} introduced in a previous work, we analyze the perturbed minisuperspace models of quantum gravity. For Robertson-Walker minisuperspace we show that it is possible to derive the so-called self-consistent cosmology in the semiclassical regime. The generalization to models with several semiclassical variables is also discussed.
Charge-density-wave stripe state in fractional quantum spin Hall effects
NASA Astrophysics Data System (ADS)
Li, Wei; Chen, Yan
2016-02-01
By means of finite-size exact diagonalization, we theoretically study the effect of an inter-spin interaction in a fractional quantum spin Hall system, and demonstrate that the charge-density-wave stripe state can be realized in a fractional quantum spin Hall system by tuning the strength of an inter-spin interaction, which clarifies the nature of the puzzling mysterious phase emerging in previous studies. The experimental realization of such exotic quantum state as well as its evolution in optical lattices are also discussed. These results may provide insights into the future studies of fractional topological insulators.
Observation of a fractional quantum hall state at nu = 1/4 in a wide GaAs quantum well.
Luhman, D R; Pan, W; Tsui, D C; Pfeiffer, L N; Baldwin, K W; West, K W
2008-12-31
We report the observation of an even-denominator fractional quantum Hall state at nu = 1/4 in a high quality, wide GaAs quantum well. The sample has a quantum well width of 50 nm and an electron density of n(e) = 2.55 x 10(11) cm(-2). We have performed transport measurements at T - 35 mK in magnetic fields up to 45 T. When the sample is perpendicular to the applied magnetic field, the diagonal resistance displays a kink at nu = 1/4. Upon tilting the sample to an angle of theta = 20.3 degrees a clear fractional quantum Hall state emerges at nu = 1/4 with a plateau in the Hall resistance and a strong minimum in the diagonal resistance.
Universal transport signatures of topological superconductivity in quantum spin Hall architectures
NASA Astrophysics Data System (ADS)
Lee, Shu-Ping; Aasen, David; Karzig, Torsten; Alicea, Jason
2015-03-01
Interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to ``engineered'' topological superconductivity. Given exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce power-law-localized ``parafermion'' excitations at a superconductor/quantum spin Hall junction. NSF Grant DMR-1341822. (2) Institute for Quantum Information and Matter, an NSF physics frontier center with support from the Moore Foundation.
Electron-Positron Pair Production in the Deep Quantum Regime
Thompson, Kathleen A
1998-10-06
Electron-positron pair production via real and virtual photons is significant to the design of linear colliders, especially in the deep quantum regime (i.e., beamstrahlung parameter Upsilon >> 1). In this regime, pair production via a virtual photon (the trident process) can become comparable in rate to pair production via a real beamstrahlung photon. We derive characteristics of the e+e- pairs produced via the trident process, using the quasi-classical approach of Baier, Katkov, and Strakhovenko. We have also examined some of the implications of e+e- pair production for the design of very high energy (several TeV in the center of mass) linear colliders in the deep quantum regime.
NASA Astrophysics Data System (ADS)
Kleinbaum, Ethan I.
Electrons confined to two dimensions, cooled to cryogenic temperatures, and placed in a strong perpendicular magnetic field exhibit a set of ground states referred to as the fractional quantum Hall states (FQHS). The FQHSs forming in the region called the second Landau level are some of the most exciting states as several theories predict that they are very different from the well understood FQHS in the lowest Landau level. Nonetheless, the nature of these FQHSs continue to evade understanding. In this thesis, a unique ultra-low temperature setup is used to examine the FQHSs of the second Landau level in regimes which have not been studied previously. Additionally, a new instrument was developed for future studies of these exciting FQHSs. In Chapter 2, I describe measurements in a high quality sample in the region of the second Landau level referred to as the upper spin branch at a factor of two lower temperatures than previous measurements in this region. In this region we find a new FQHS at the filling factor nu = 3+1/3. A quantitative study of this new and other FQHS in the upper spin branch reveals a surprising relationship: the relative magnitudes of the energy gaps of the nu = 3+1/3 and 3+1/5 states are reversed when compared to the counterpart states in the lower spin branch at nu = 2+1/3 and 2+1/5. We demonstrate that this reversal is only found to occur in the upper spin branch and cannot be understood within the existing theories. Our results suggest the possibility of new types of FQHSs in this region. In Chapter 3, I examine the even denominator FQHSs at nu = 5/2 and nu = 7/2 in a series of samples with intentionally added alloy disorder. The energy gap of both of these states is suppressed with increased alloy content. Unexpectedly, in contrast to samples with no added disorder, in samples with intentionally added alloy disorder we find that the measured energy gap of the nu = 5/2 FQHS displays a strong correlation with the mobility. Of further
Single electron probes of fractional quantum hall states
NASA Astrophysics Data System (ADS)
Venkatachalam, Vivek
When electrons are confined to a two dimensional layer with a perpendicular applied magnetic field, such that the ratio of electrons to flux quanta (nu) is a small integer or simple rational value, these electrons condense into remarkable new phases of matter that are strikingly different from the metallic electron gas that exists in the absence of a magnetic field. These phases, called integer or fractional quantum Hall (IQH or FQH) states, appear to be conventional insulators in their bulk, but behave as a dissipationless metal along their edge. Furthermore, electrical measurements of such a system are largely insensitive to the detailed geometry of how the system is contacted or even how large the system is... only the order in which contacts are made appears to matter. This insensitivity to local geometry has since appeared in a number of other two and three dimensional systems, earning them the classification of "topological insulators" and prompting an enormous experimental and theoretical effort to understand their properties and perhaps manipulate these properties to create robust quantum information processors. The focus of this thesis will be two experiments designed to elucidate remarkable properties of the metallic edge and insulating bulk of certain FQH systems. To study such systems, we can use mesoscopic devices known as single electron transistors (SETs). These devices operate by watching single electrons hop into and out of a confining box and into a nearby wire (for measurement). If it is initially unfavorable for an electron to leave the box, it can be made favorable by bringing another charge nearby, modifying the energy of the confined electron and pushing it out of the box and into the nearby wire. In this way, the SET can measure nearby charges. Alternatively, we can heat up the nearby wire to make it easier for electrons to enter and leave the box. In this way, the SET is a sensitive thermometer. First, by operating the SET as an
Reprint of : Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor
NASA Astrophysics Data System (ADS)
Arrachea, Liliana; von Oppen, Felix
2016-08-01
The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer-Büttiker theory. Scattering theory provides a microscopic derivation of the Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.
Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor
NASA Astrophysics Data System (ADS)
Arrachea, Liliana; von Oppen, Felix
2015-11-01
The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer-Büttiker theory. Scattering theory provides a microscopic derivation of the Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.
NASA Astrophysics Data System (ADS)
Ganeshan, Sriram; Kechedzhi, K.; Das Sarma, S.
2014-07-01
One-dimensional tight binding models such as the Aubry-André-Harper (AAH) model (with an on-site cosine potential) and the integrable Maryland model (with an on-site tangent potential) have been the subject of extensive theoretical research in localization studies. AAH can be directly mapped onto the two-dimensional (2D) Hofstadter model which manifests the integer quantum Hall topology on a lattice. However, such a connection needs to be made for the Maryland model (MM). Here we describe a generalized model that contains AAH and MM as the limiting cases with the MM lying precisely at a topological quantum phase transition (TQPT) point. A remarkable feature of this critical point is that the one-dimensional MM retains well defined energy gaps whereas the equivalent 2D model becomes gapless, signifying the 2D nature of the TQPT.
NASA Astrophysics Data System (ADS)
Zhang, Ying-Tao; Hou, Zhe; Xie, X. C.; Sun, Qing-Feng
2017-06-01
We investigate the quantum tunneling and Andreev reflection in a top-gated quantum anomalous Hall insulator proximity coupled with a superconductor junction. A quantized perfect crossed Andreev reflection with its coefficient being integer 1 is obtained and all other scattering processes (the normal reflection, normal tunneling, and local Andreev reflection) are completely suppressed when the topological superconductor phase with Chern number N =1 is realized. This perfect crossed Andreev reflection originates from the tunneling of the chiral Majorana edge states, and the phase of tunneling amplitude only being 0 and π plays a decisive role. Furthermore, because of the chiral characteristic of the Majorana edge states, the perfect crossed Andreev reflection is robust against the disorder and can work in a wide range of system parameters.
NASA Astrophysics Data System (ADS)
Chang, Cui-Zu; Zhao, Weiwei; Li, Jian; Jain, J. K.; Liu, Chaoxing; Moodera, Jagadeesh S.; Chan, Moses H. W.
2016-09-01
Fundamental insight into the nature of the quantum phase transition from a superconductor to an insulator in two dimensions, or from one plateau to the next or to an insulator in the quantum Hall effect, has been revealed through the study of its scaling behavior. Here, we report on the experimental observation of a quantum phase transition from a quantum-anomalous-Hall insulator to an Anderson insulator in a magnetic topological insulator by tuning the chemical potential. Our experiment demonstrates the existence of scaling behavior from which we extract the critical exponent for this quantum phase transition. We expect that our work will motivate much further investigation of many properties of quantum phase transition in this new context.
Chang, Cui-Zu; Zhao, Weiwei; Li, Jian; Jain, J K; Liu, Chaoxing; Moodera, Jagadeesh S; Chan, Moses H W
2016-09-16
Fundamental insight into the nature of the quantum phase transition from a superconductor to an insulator in two dimensions, or from one plateau to the next or to an insulator in the quantum Hall effect, has been revealed through the study of its scaling behavior. Here, we report on the experimental observation of a quantum phase transition from a quantum-anomalous-Hall insulator to an Anderson insulator in a magnetic topological insulator by tuning the chemical potential. Our experiment demonstrates the existence of scaling behavior from which we extract the critical exponent for this quantum phase transition. We expect that our work will motivate much further investigation of many properties of quantum phase transition in this new context.
NASA Astrophysics Data System (ADS)
Huang, Huaqing; Wang, Zhaoyou; Luo, Nannan; Liu, Zhirong; Lü, Rong; Wu, Jian; Duan, Wenhui
2015-08-01
We theoretically investigate the electronic properties of the interface between quantum spin Hall (QSH) and quantum anomalous Hall (QAH) insulators. A robust chiral gapless state, which substantially differs from edge states of QSH or QAH insulators, is predicted at the QSH/QAH interface using an effective Hamiltonian model. We systematically reveal distinctive properties of interface states between QSH and single-valley QAH, multivalley high-Chern-number QAH and valley-polarized QAH insulators based on tight-binding models using the interface Green's function method. As an example, first-principles calculations are conducted for the interface states between fully and semihydrogenated bismuth (111) thin films, verifying the existence of interface states in realistic material systems. Due to the physically protected junction structure, the interface state is expected to be more stable and insensitive than topological boundary states against edge defects and chemical decoration. Hence our results of the interface states provide a promising route towards enhancing the performance and stability of low-dissipation electronics in real environment.
Evolution of quantum entanglement with disorder in fractional quantum Hall liquids
NASA Astrophysics Data System (ADS)
Liu, Zhao; Bhatt, R. N.
2017-09-01
We present a detailed study of the ground-state entanglement in disordered fractional quantum Hall liquids. We consider electrons at various filling fractions f in the lowest Landau level, with Coulomb interactions. At f =1 /3 ,1 /5 , and 2 /5 where an incompressible ground-state manifold exists at zero disorder, we observe a pronounced minimum in the derivative of entanglement entropy with respect to disorder. At each filling, the position of this minimum is stable against increasing system size, but its magnitude grows monotonically and appears to diverge in the thermodynamic limit. We consider this behavior of the entropy derivative as a compelling signal of the expected disorder-driven phase transition from a topological fractional quantum Hall phase to an insulating phase. On the contrary, at f =1 /2 where a compressible composite fermion sea is present at zero disorder, the entropy derivative exhibits much greater, almost chaotic, finite-size effects, without a clear phase transition signal for system sizes within our exact diagonalization limit. However, the dependence of entanglement entropy with system size changes with increasing disorder, consistent with the expectation of a phase transition from a composite fermion sea to an insulator. Finally, we consider f =1 /7 where compressible Wigner crystals are quite competitive at zero disorder, and analyze the level statistics of entanglement spectrum at f =1 /3 .
Quantum Hall effect in a quantum point contact at Landau filling fraction ν=52
NASA Astrophysics Data System (ADS)
Miller, Jeffrey; Radu, Iuliana; Zumbühl, Dominik; Levenson-Falk, Eli; Kastner, Marc; Marcus, Charles; Pfeiffer, Loren; West, Ken
2007-03-01
We study the transport properties of quantum point contacts (QPC) fabricated on a GaAs/AlGaAs two dimensional electron gas that exhibits excellent bulk fractional quantum Hall effect, including a strong plateau in the Hall resistance at Landau level filling fraction ν= 52. We find that the ν=52 plateau is identifiable in point contacts with lithographic separations as small as 0.8 microns, but is not present in a 0.5 micron QPC. We study the temperature and dc-current-bias dependence of the ν=52 plateau---as well as neighboring fractional and integer plateaus---in the QPC. We also discuss our method to study the QPC at one filling fraction while the bulk remains at a higher filling fraction. Research supported in part by Microsoft Corporation, Project Q, and HCRP at Harvard University, and ARO (W911NF-05-1-0062), the NSEC program of the NSF (PHY-0117795) and NSF (DMR-0353209) at MIT.
Fermi surface of underdoped cuprate revealed by quantum oscillations and Hall effect
NASA Astrophysics Data System (ADS)
Proust, Cyril
2008-03-01
Despite twenty years of research, the phase diagram of high temperature superconductors remains enigmatic. A central issue is the origin of the differences in the physical properties of these copper oxides doped to opposite sides of the superconducting region. In the overdoped regime, the material behaves as a reasonably conventional metal, with a large Fermi surface [1]. The underdoped regime, however, is highly anomalous and appears to have no coherent Fermi surface, but only disconnected `Fermi arcs' [2]. We have reported the observation of quantum oscillations in the electrical resistance of the oxygen-ordered copper oxides YBa2Cu3O6.5 [3] and YBa2Cu4O8 [4], establishing the existence of a coherent closed Fermi surface at low temperature in the underdoped side of the phase diagram of cuprates, once superconductivity is suppressed by a large magnetic field. The low oscillation frequency reveals a Fermi surface made of small pockets, in contrast to the large cylinder characteristic of the overdoped regime. Moreover, the negative sign of the Hall effect at low temperature reveals that these pockets are electron-like rather than hole-like. We propose that the Fermi surface of these Y-based cuprates consists of both electron and hole pockets, probably arising from a reconstruction of the FS [5]. Work in collaboration with N Doiron-Leyraud, D. LeBoeuf and L. Taillefer from the University of Sherbrooke, J. Levallois and B. Vignolle from the LNCMP, A. Bangura and N. Hussey from the University of Bristol and R. Liang, D. Bonn, W. Hardy from the University of British Columbia. [1] N Hussey et al, Nature 425, 814 (2003) [2] M. Norman et al, Nature 392, 157 (1998) [3] N. Doiron-Leyraud et al, Nature 447, 565 (2007) [4] A. Bangura et al, submitted to Phys. Rev. Lett (arXiv: 0707.4461) [5] D. LeBoeuf et al, Nature 450, 533 (2007)
Nonlinear response of the quantum Hall system to a strong electromagnetic radiation
NASA Astrophysics Data System (ADS)
Avetissian, H. K.; Mkrtchian, G. F.
2016-12-01
We study nonlinear response of a quantum Hall system in semiconductor-hetero-structures via third harmonic generation process and nonlinear Faraday effect. We demonstrate that Faraday rotation angle and third harmonic radiation intensity have a characteristic Hall plateaus feature. These nonlinear effects remain robust against the significant broadening of Landau levels. We predict realization of an experiment through the observation of the third harmonic signal and Faraday rotation angle, which are within the experimental feasibility.
Exotic emergent phenomena in the fractional quantum Hall effect
NASA Astrophysics Data System (ADS)
Coimbatore Balram, Ajit
When two-dimensional electron systems are subjected to a perpendicular magnetic field, they exhibit the marvelous phenomenon known as the fractional quantum Hall effect (FQHE). This arises as a result of the formation of composite fermions (CFs), which are bound states of electrons and an even number of vortices. The FQHE of electrons is understood as arising from the integer QHE (IQHE) of CFs. Alongside superconductivity, Bose-Einstein condensation and spin-liquids, the CF quantum fluid provides a model system for understanding strongly correlated systems and their collective behavior. Although it has been more than three decades since the experimental discovery of FQHE, the field continues to produce profound insights and pose interesting problems some of which have been addressed in this thesis. A major unanswered question in the field of FQHE is the mechanism of FQHE for the 1/3 state in the second Landau level (7/3 state). Numerical studies of this state have brought out the following puzzle: exact diagonalization studies suggest that the ground state and excitations of 1/3 state in the second Landau level are different from its counterpart in the lowest Landau level (LLL), while entanglement spectra of the two states point to the fact that they fall in the same universality class. Using methods from CF theory we show that the excitations of the 7/3 FQHE lie in the same universality class as those of the 1/3 state but are strongly modified due to screening by CF excitons, thereby settling the above discrepancy. Armed with the exciton calculation, we illustrate that by imposing certain exclusion rules for CF excitons one can build the full spectrum of FQHE in the lowest Landau level. Equipped with the techniques to calculate the spectra of FQHE systems, we carry out an extensive study of FQHE of multi-component CFs (systems possessing degrees of freedom for eg: valley and spin degeneracy), which is applicable to FQHE in systems such as graphene, AlAs and Ga
Quasiparticle Tunneling in the Fractional Quantum Hall effect at filling fraction ν=5/2
NASA Astrophysics Data System (ADS)
Radu, Iuliana P.
2009-03-01
In a two-dimensional electron gas (2DEG), in the fractional quantum Hall regime, the quasiparticles are predicted to have fractional charge and statistics, as well as modified Coulomb interactions. The state at filling fraction ν=5/2 is predicted by some theories to have non-abelian statistics, a property that might be exploited for topological quantum computing. However, alternative models with abelian properties have been proposed as well. Weak quasiparticle tunneling between counter-propagating edges is one of the methods that can be used to learn about the properties of the state and potentially distinguish between models describing it. We employ an electrostatically defined quantum point contact (QPC) fabricated on a high mobility GaAs/AlGaAs 2DEG to create a constriction where quasiparticles can tunnel between counter-propagating edges. We study the temperature and dc bias dependence of the tunneling conductance, while preserving the same filling fraction in the constriction and the bulk of the sample. The data show scaling of the bias-dependent tunneling over a range of temperatures, in agreement with the theory of weak quasiparticle tunneling, and we extract values for the effective charge and interaction parameter of the quasiparticles. The ranges of values obtained are consistent with those predicted by certain models describing the 5/2 state, indicating as more probable a non-abelian state. This work was done in collaboration with J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer and K. W. West. This work was supported in part by the Army Research Office (W911NF-05-1-0062), the Nanoscale Science and Engineering Center program of NSF (PHY-0117795), NSF (DMR-0701386), the Center for Materials Science and Engineering program of NSF (DMR-0213282) at MIT, the Microsoft Corporation Project Q, and the Center for Nanoscale Systems at Harvard University.
Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians.
Zaletel, Michael P; Mong, Roger S K; Pollmann, Frank
2013-06-07
We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall Hamiltonian. To find the set of degenerate ground states, we employ the infinite density matrix renormalization group method based on the matrix-product state representation of fractional quantum Hall states on an infinite cylinder. To study localized quasiparticles of a chosen topological charge, we use pairs of degenerate ground states as boundary conditions for the infinite density matrix renormalization group. We then show that the wave function obtained on the infinite cylinder geometry can be adapted to a torus of arbitrary modular parameter, which allows us to explicitly calculate the non-Abelian Berry connection associated with the modular T transformation. As a result, the quantum dimensions, topological spins, quasiparticle charges, chiral central charge, and Hall viscosity of the phase can be obtained using data contained entirely in the entanglement spectrum of an infinite cylinder.
Quantum anomalous Hall effect and tunable topological states in 3d transition metals doped silicene.
Zhang, Xiao-Long; Liu, Lan-Feng; Liu, Wu-Ming
2013-10-09
Silicene is an intriguing 2D topological material which is closely analogous to graphene but with stronger spin orbit coupling effect and natural compatibility with current silicon-based electronics industry. Here we demonstrate that silicene decorated with certain 3d transition metals (Vanadium) can sustain a stable quantum anomalous Hall effect using both analytical model and first-principles Wannier interpolation. We also predict the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition metal doped silicene where the energy band inversion occurs. Our findings provide new scheme for the realization of quantum anomalous Hall effect and platform for electrically controllable topological states which are highly desirable for future nanoelectronics and spintronics application.
Fragility of Nonlocal Edge-Mode Transport in the Quantum Spin Hall State
NASA Astrophysics Data System (ADS)
Mani, Arjun; Benjamin, Colin
2016-07-01
Nonlocal currents and voltages are better at withstanding the deleterious effects of dephasing than local currents and voltages in nanoscale systems. This hypothesis is known to be true in quantum Hall setups. We test this hypothesis in a four-terminal quantum spin Hall setup wherein we compare the local resistance measurement with the nonlocal one. In addition to inelastic-scattering-induced dephasing, we also test the resilience of the resistance measurements in the aforesaid setups to disorder and spin-flip scattering. We find the axiom that nonlocal resistance is less affected by the detrimental effects of disorder and dephasing to be untrue, in general, for the quantum spin Hall case. This has important consequences since it is widely communicated that nonlocal transport through edge channels in topological insulators have potential applications in low-power information processing.
Strong electronic interaction and multiple quantum Hall ferromagnetic phases in trilayer graphene
NASA Astrophysics Data System (ADS)
Datta, Biswajit; Dey, Santanu; Samanta, Abhisek; Agarwal, Hitesh; Borah, Abhinandan; Watanabe, Kenji; Taniguchi, Takashi; Sensarma, Rajdeep; Deshmukh, Mandar M.
2017-02-01
Quantum Hall effect provides a simple way to study the competition between single particle physics and electronic interaction. However, electronic interaction becomes important only in very clean graphene samples and so far the trilayer graphene experiments are understood within non-interacting electron picture. Here, we report evidence of strong electronic interactions and quantum Hall ferromagnetism seen in Bernal-stacked trilayer graphene. Due to high mobility ~500,000 cm2 V-1 s-1 in our device compared to previous studies, we find all symmetry broken states and that Landau-level gaps are enhanced by interactions; an aspect explained by our self-consistent Hartree-Fock calculations. Moreover, we observe hysteresis as a function of filling factor and spikes in the longitudinal resistance which, together, signal the formation of quantum Hall ferromagnetic states at low magnetic field.
Parity effect of bipolar quantum Hall edge transport around graphene antidots.
Matsuo, Sadashige; Nakaharai, Shu; Komatsu, Katsuyoshi; Tsukagoshi, Kazuhito; Moriyama, Takahiro; Ono, Teruo; Kobayashi, Kensuke
2015-06-30
Parity effect, which means that even-odd property of an integer physical parameter results in an essential difference, ubiquitously appears and enables us to grasp its physical essence as the microscopic mechanism is less significant in coarse graining. Here we report a new parity effect of quantum Hall edge transport in graphene antidot devices with pn junctions (PNJs). We found and experimentally verified that the bipolar quantum Hall edge transport is drastically affected by the parity of the number of PNJs. This parity effect is universal in bipolar quantum Hall edge transport of not only graphene but also massless Dirac electron systems. These results offer a promising way to design electron interferometers in graphene.
Strong electronic interaction and multiple quantum Hall ferromagnetic phases in trilayer graphene.
Datta, Biswajit; Dey, Santanu; Samanta, Abhisek; Agarwal, Hitesh; Borah, Abhinandan; Watanabe, Kenji; Taniguchi, Takashi; Sensarma, Rajdeep; Deshmukh, Mandar M
2017-02-20
Quantum Hall effect provides a simple way to study the competition between single particle physics and electronic interaction. However, electronic interaction becomes important only in very clean graphene samples and so far the trilayer graphene experiments are understood within non-interacting electron picture. Here, we report evidence of strong electronic interactions and quantum Hall ferromagnetism seen in Bernal-stacked trilayer graphene. Due to high mobility ∼500,000 cm(2 )V(-1 )s(-1) in our device compared to previous studies, we find all symmetry broken states and that Landau-level gaps are enhanced by interactions; an aspect explained by our self-consistent Hartree-Fock calculations. Moreover, we observe hysteresis as a function of filling factor and spikes in the longitudinal resistance which, together, signal the formation of quantum Hall ferromagnetic states at low magnetic field.
Split-quaternionic Hopf map, quantum Hall effect, and twistor theory
Hasebe, Kazuki
2010-02-15
Introducing a noncompact version of the Hopf map, we demonstrate remarkable close relations between quantum Hall effect and twistor theory. We first construct quantum Hall effect on a hyperboloid based on the noncompact 2nd Hopf map of split-quaternions. We analyze a hyperbolic one-particle mechanics, and explore many-body problem, where a many-body ground state wave function and membrane-like excitations are derived explicitly. In the lowest Landau level, the symmetry is enhanced from SO(3,2) to the SU(2,2) conformal symmetry. We point out that the quantum Hall effect naturally realizes the philosophy of twistor theory. In particular, emergence mechanism of fuzzy space-time is discussed somehow in detail.
Strong electronic interaction and multiple quantum Hall ferromagnetic phases in trilayer graphene
Datta, Biswajit; Dey, Santanu; Samanta, Abhisek; Agarwal, Hitesh; Borah, Abhinandan; Watanabe, Kenji; Taniguchi, Takashi; Sensarma, Rajdeep; Deshmukh, Mandar M.
2017-01-01
Quantum Hall effect provides a simple way to study the competition between single particle physics and electronic interaction. However, electronic interaction becomes important only in very clean graphene samples and so far the trilayer graphene experiments are understood within non-interacting electron picture. Here, we report evidence of strong electronic interactions and quantum Hall ferromagnetism seen in Bernal-stacked trilayer graphene. Due to high mobility ∼500,000 cm2 V−1 s−1 in our device compared to previous studies, we find all symmetry broken states and that Landau-level gaps are enhanced by interactions; an aspect explained by our self-consistent Hartree–Fock calculations. Moreover, we observe hysteresis as a function of filling factor and spikes in the longitudinal resistance which, together, signal the formation of quantum Hall ferromagnetic states at low magnetic field. PMID:28216666
Quantum Anomalous Hall Effect and Tunable Topological States in 3d Transition Metals Doped Silicene
Zhang, Xiao-Long; Liu, Lan-Feng; Liu, Wu-Ming
2013-01-01
Silicene is an intriguing 2D topological material which is closely analogous to graphene but with stronger spin orbit coupling effect and natural compatibility with current silicon-based electronics industry. Here we demonstrate that silicene decorated with certain 3d transition metals (Vanadium) can sustain a stable quantum anomalous Hall effect using both analytical model and first-principles Wannier interpolation. We also predict the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition metal doped silicene where the energy band inversion occurs. Our findings provide new scheme for the realization of quantum anomalous Hall effect and platform for electrically controllable topological states which are highly desirable for future nanoelectronics and spintronics application. PMID:24105063
Shi, Yanmeng; Lee, Yongjin; Che, Shi; Pi, Ziqi; Espiritu, Timothy; Stepanov, Petr; Smirnov, Dmitry; Lau, Chun Ning; Zhang, Fan
2016-02-05
Owing to the spin, valley, and orbital symmetries, the lowest Landau level in bilayer graphene exhibits multicomponent quantum Hall ferromagnetism. Using transport spectroscopy, we investigate the energy gaps of integer and fractional quantum Hall (QH) states in bilayer graphene with controlled layer polarization. The state at filling factor ν=1 has two distinct phases: a layer polarized state that has a larger energy gap and is stabilized by high electric field, and a hitherto unobserved interlayer coherent state with a smaller gap that is stabilized by large magnetic field. In contrast, the ν=2/3 quantum Hall state and a feature at ν=1/2 are only resolved at finite electric field and large magnetic field. These results underscore the importance of controlling layer polarization in understanding the competing symmetries in the unusual QH system of BLG.
Parity effect of bipolar quantum Hall edge transport around graphene antidots
Matsuo, Sadashige; Nakaharai, Shu; Komatsu, Katsuyoshi; Tsukagoshi, Kazuhito; Moriyama, Takahiro; Ono, Teruo; Kobayashi, Kensuke
2015-01-01
Parity effect, which means that even-odd property of an integer physical parameter results in an essential difference, ubiquitously appears and enables us to grasp its physical essence as the microscopic mechanism is less significant in coarse graining. Here we report a new parity effect of quantum Hall edge transport in graphene antidot devices with pn junctions (PNJs). We found and experimentally verified that the bipolar quantum Hall edge transport is drastically affected by the parity of the number of PNJs. This parity effect is universal in bipolar quantum Hall edge transport of not only graphene but also massless Dirac electron systems. These results offer a promising way to design electron interferometers in graphene. PMID:26122468
Energy Gaps and Layer Polarization of Integer and Fractional Quantum Hall States in Bilayer Graphene
NASA Astrophysics Data System (ADS)
Shi, Yanmeng; Lee, Yongjin; Che, Shi; Pi, Ziqi; Espiritu, Timothy; Stepanov, Petr; Smirnov, Dmitry; Lau, Chun Ning; Zhang, Fan
2016-02-01
Owing to the spin, valley, and orbital symmetries, the lowest Landau level in bilayer graphene exhibits multicomponent quantum Hall ferromagnetism. Using transport spectroscopy, we investigate the energy gaps of integer and fractional quantum Hall (QH) states in bilayer graphene with controlled layer polarization. The state at filling factor ν =1 has two distinct phases: a layer polarized state that has a larger energy gap and is stabilized by high electric field, and a hitherto unobserved interlayer coherent state with a smaller gap that is stabilized by large magnetic field. In contrast, the ν =2 /3 quantum Hall state and a feature at ν =1 /2 are only resolved at finite electric field and large magnetic field. These results underscore the importance of controlling layer polarization in understanding the competing symmetries in the unusual QH system of BLG.
Nuclear-Spin Measurements of Quantum Hall Systems
NASA Astrophysics Data System (ADS)
Hirayama, Yoshiro
Nuclear magnetic resonance (NMR) is widely used in the physical, chemical, and biological sciences. However, conventional NMR techniques based on induction-detection have drawbacks of low-sensitivity and the need of a relatively large sample. It is not suitable to investigate single or double layers (or their nanostructure), which is essential in studying quantum Hall (QH) effects. In this presentation, I discussed a resistively-detected technique to overcome the low-sensitivity limitation of conventional NMR and its application to QH systems. Resistively-detected nuclear-spin-based measurements rely on enhanced interactions between electron and nuclear spins at the degenerate point of different electron-spin states. For example, at the ν = 2/3 degenerate point in a AlGaAs/GaAs system,1-3 nuclear-spin polarization far beyond the thermal equilibrium is generated using current flow (dynamic nuclear-spin polarization). Moreover, nuclear-spin polarization can be detected as enhanced resistance, which is proportional to the magnetization, Mz, of nuclear spins.2 It should be stressed that the special states of ν = 2/3 are needed for dynamic nuclear-spin polarization and Mz detection, but we can apply NMR spectrum and nuclear-spin relaxation (T1 time) measurements for any state we want to estimate. These nuclear-spin-based measurements were successfully applied to characterize QH systems, especially their electron-spin features, using single and double layer systems where characteristics are controlled electrically by the gate biases. For a single layer, we could clarify skyrmion,2 spin-polarization of composite fermion,4 and enhanced spin-orbit interactions in a strongly asymmetric confinement.5 Exciting phases, like a canted antiferromagnetic phase, were studied in a double layer QH system with a total filling factor of 2 (Refs. 6, 7). The low-frequency mode was sensitively detected by monitoring T1, reflecting correlated electron spin features.7 The clear
Properties of minimum spanning trees and fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Jackson, Thomas Sundal
This dissertation consists of work done on two disjoint problems. In the first two chapters I discuss fractal properties of average-case solutions to the random minimal spanning tree (MST) problem: given a graph with costs on the edges, the MST is the spanning tree minimizing the sum of the total cost of the chosen edges. In the random version the costs are quenched random variables. I solve the random MST problem on the Bethe lattice with appropriate boundary conditions and use the results to infer fractal dimensions in the mean-field approximation. I find that connected components of the MST in a window have dimension D=6, which establishes the upper critical dimension dc=6. This contradicts a value dc=8 proposed previously in the literature; I correct the argument that led to this value. I then develop an exact low-density expansion for the random MST on a finite graph and use it to develop an expansion for the MST on critical percolation clusters. I prove this perturbation expansion is renormalizable around dc=6. Using a renormalization-group approach, I calculate the fractal dimension Dp of paths on the latter MST to first order in epsilon=6-d for d≤6, with the result Dp˜2-epsilon/7. In the final chapter, I investigate the correspondence between wavefunctions in the fractional quantum Hall effect obtained as blocks of a conformal field theory (CFT) versus those defined as zero-energy eigenstates of projection Hamiltonians, specifically one which forbids three particles to come together in one of two linearly-independent states of relative angular momentum six and all states of lesser relative angular momentum. I construct zero-energy states from amplitudes of superconformal currents using a result due to Simon. The counting of edge excitations of these states agrees with the character formula for the superconformal Kac vacuum module at generic central charge c, which implies this Hamiltonian is gapless for all c. I attempt to obtain a rational theory by
Fano-Andreev effect in Quantum Dots in Kondo regime
NASA Astrophysics Data System (ADS)
Orellana, Pedro; Calle, Ana Maria; Pacheco, Monica; Apel, Victor
In the present work, we investigate the transport through a T-shaped double quantum dot system coupled to two normal leads and to a superconducting lead. We study the role of the superconducting lead in the quantum interferometric features of the double quantum dot and by means of a slave boson mean field approximation at low temperature regime. We inquire into the influence of intradot interactions in the electronic properties of the system as well. Our results show that Fano resonances due to Andreev bound states are exhibited in the transmission from normal to normal lead as a consequence of quantum interference and proximity effect. This Fano effect produced by Andreev bound states in a side quantum dot was called Fano-Andreev effect, which remains valid even if the electron-electron interaction are taken into account, that is, the Fano-Andreev effect is robust against e-e interactions even in Kondo regime. We acknowledge the financial support from FONDECYT program Grants No. 3140053 and 11400571.
NASA Astrophysics Data System (ADS)
Ludwig, Andreas W. W.
1996-03-01
We review recent exact results (Work done in collaboration with Paul Fendley and Hubert Saleur, Physics Dept., University of Southern California, Los Angeles, CA 90089-0484.) for transport properties through a local impurity in a Luttinger liquid. These represent ``spectroscopic probes'' of the Luttinger non-Fermi-liquid state. Edge modes occuring in the fractional quantum Hall effect provide realizations of Luttinger liquids, insensitive to disorder. The linear-response conductance through a point contact in the ν =1/3 quantum Hall state has been predicted to be a universal function of temperature and point-contact interaction strength, independent of sample-specific details of the device. Our exact result for this scaling function is in quantitative agreement with experimental measurements (F.P. Milliken, C.P. Umbach and R.A. Webb, preprint.). The theoretical advance made in this work(P. Fendley, A.W.W. Ludwig and H. Saleur, Phys. Rev. Lett. 74) (1995) 3005; 75 (1995) 2196; Phys. Rev. B 52 (1995) 8934. is the computation of exact transport properties from the Bethe ansatz; in the past, the Bethe ansatz was useful mainly for thermodynamic quantities. We utilize an exact kinetic transport equation in a particular quasiparticle basis of the Luttinger liquid dictated by the integrability of the point-contact interaction. Since this equation is also valid out of equilibrium, we obtain also non-equilibrium quantum transport properties in this fully interacting system. In particular, we also present universal exact results for the I(V) characteristics and the DC shot noise of the point contact. The differential conductance develops a peak beyond a critical value e V/kB T >7.18868 of driving.
Evolution of Plasmonic Metamolecule Modes in the Quantum Tunneling Regime.
Scholl, Jonathan A; Garcia-Etxarri, Aitzol; Aguirregabiria, Garikoitz; Esteban, Ruben; Narayan, Tarun C; Koh, Ai Leen; Aizpurua, Javier; Dionne, Jennifer A
2016-01-26
Plasmonic multinanoparticle systems exhibit collective electric and magnetic resonances that are fundamental for the development of state-of-the-art optical nanoantennas, metamaterials, and surface-enhanced spectroscopy substrates. While electric dipolar modes have been investigated in both the classical and quantum realm, little attention has been given to magnetic and other "dark" modes at the smallest dimensions. Here, we study the collective electric, magnetic, and dark modes of colloidally synthesized silver nanosphere trimers with varying interparticle separation using scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy (EELS). This technique enables direct visualization and spatially selective excitation of individual trimers, as well as manipulation of the interparticle distance into the subnanometer regime with the electron beam. Our experiments reveal that bonding electric and magnetic modes are significantly impacted by quantum effects, exhibiting a relative blueshift and reduced EELS amplitude compared to classical predictions. In contrast, the trimer's electric dark mode is not affected by quantum tunneling for even Ångström-scale interparticle separations. We employ a quantum-corrected model to simulate the effect of electron tunneling in the trimer which shows excellent agreement with experimental results. This understanding of classical and quantum-influenced hybridized modes may impact the development of future quantum plasmonic materials and devices, including Fano-like molecular sensors and quantum metamaterials.
Endoreversible quantum heat engines in the linear response regime
NASA Astrophysics Data System (ADS)
Wang, Honghui; He, Jizhou; Wang, Jianhui
2017-07-01
We analyze general models of quantum heat engines operating a cycle of two adiabatic and two isothermal processes. We use the quantum master equation for a system to describe heat transfer current during a thermodynamic process in contact with a heat reservoir, with no use of phenomenological thermal conduction. We apply the endoreversibility description to such engine models working in the linear response regime and derive expressions of the efficiency and the power. By analyzing the entropy production rate along a single cycle, we identify the thermodynamic flux and force that a linear relation connects. From maximizing the power output, we find that such heat engines satisfy the tight-coupling condition and the efficiency at maximum power agrees with the Curzon-Ahlborn efficiency known as the upper bound in the linear response regime.
Disorder-assisted quantum transport in suboptimal decoherence regimes
Novo, Leonardo; Mohseni, Masoud; Omar, Yasser
2016-01-01
We investigate quantum transport in binary tree structures and in hypercubes for the disordered Frenkel-exciton Hamiltonian under pure dephasing noise. We compute the energy transport efficiency as a function of disorder and dephasing rates. We demonstrate that dephasing improves transport efficiency not only in the disordered case, but also in the ordered one. The maximal transport efficiency is obtained when the dephasing timescale matches the hopping timescale, which represent new examples of the Goldilocks principle at the quantum scale. Remarkably, we find that in weak dephasing regimes, away from optimal levels of environmental fluctuations, the average effect of increasing disorder is to improve the transport efficiency until an optimal value for disorder is reached. Our results suggest that rational design of the site energies statistical distributions could lead to better performances in transport systems at nanoscale when their natural environments are far from the optimal dephasing regime. PMID:26726133