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.
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. PMID:27199424
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. PMID:27533362
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.
Insulating States in the Integer Quantum Hall Regime
NASA Astrophysics Data System (ADS)
Knighton, Talbot; Serafin, Alessandro; Wu, Zhe; Tarquini, Vinicio; Xia, J. F.; Sullivan, Neil; Pfeiffer, Loren; West, Ken; Huang, Jian
Quantum Hall measurements are performed at temperatures 20-300 mK in high quality p-type GaAs quantum well systems having mobility μ = 4 ×106 cm2/V .s for density 5 ×1010 cm-2. We report a series of insulating phases appearing at or near integer filling factors ν >= 1 . The DC resistance demonstrates a maximum of 25M Ω, much larger than the quantum resistance h /e2 , with threshold transport behavior at low currents around 10 pA at low temperatures. The threshold diminishes upon heating up to 200 mK, consistent with a finite temperature melting of bubble phases or Wigner crystal. Additionally, these peaks have a complex electrical impedance for AC signals, with large phase shifts down to 1Hz. In this regime, the ac impedance of the two chiral edges show distinct correlated characteristics. NSF DMR-1410302.
Robust electron pairing in the integer quantum hall effect regime.
Choi, H K; Sivan, I; Rosenblatt, A; Heiblum, M; Umansky, V; Mahalu, D
2015-01-01
Electron pairing is a rare phenomenon appearing only in a few unique physical systems; for example, superconductors and Kondo-correlated quantum dots. Here, we report on an unexpected electron pairing in the integer quantum Hall effect regime. The pairing takes place within an interfering edge channel in an electronic Fabry-Perot interferometer at a wide range of bulk filling factors, between 2 and 5. We report on three main observations: high-visibility Aharonov-Bohm conductance oscillations with magnetic flux periodicity equal to half the magnetic flux quantum; an interfering quasiparticle charge equal to twice the elementary electron charge as revealed by quantum shot noise measurements, and full dephasing of the pairs' interference by induced dephasing of the adjacent inner edge channel-a manifestation of inter-channel entanglement. Although this pairing phenomenon clearly results from inter-channel interaction, the exact mechanism that leads to electron-electron attraction within a single edge channel is not clear. We believe that substantial efforts are needed in order to clarify these intriguing and unexpected findings. PMID:26096516
Inhomogeneous transport and derivative relations in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Simon, Steven H.
1998-12-01
Several derivative relations have been observed in the quantum Hall regime including a relation between elements of the macroscopic resistivity tensor Rxx= αB(d Rxy/d B), a relation between elements of the macroscopic thermopower tensor Syx= αB(d Sxx/d B), as well as a similar relation observed in acoustoelectric experiments (here B is the magnetic field and α is a constant). It has been proposed in a number of recent works by the author and collaborators that these relations can be explained with a model of classical transport in an inhomogeneous medium. We review these works and briefly discuss to what extent the models which predict these derivative relations are appropriate for describing the experimental systems.
Optically Pumped Nuclear Magnetic Resonance in the Quantum Hall Regimes
NASA Astrophysics Data System (ADS)
Barrett, S. E.; Tycko, R.; Dabbagh, G.; Pfeiffer, L. N.; West, K. W.
1996-03-01
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 shiftfootnote S. E. Barrett et al., Phys. Rev. Lett. 74, 5112 (1995) and spin-lattice relaxation timefootnote R. Tycko et al., Science 268, 1460 (1995) have been carried out in the Quantum Hall regimes. It is clear from these measurements that probing the electronic spin degree of freedom can lead to new insights about the effect of interactions on the many-body ground state and low-lying excited states of these systems. For example, the Knight shift measurements provided the first experimental support for the recent 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, 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.
Gate-Defined Graphene Quantum Point Contact in the Quantum Hall Regime
NASA Astrophysics Data System (ADS)
Nakaharai, S.; Williams, J. R.; Marcus, C. M.
2011-07-01
We investigate transport in a gate-defined graphene quantum point contact in the quantum Hall regime. Edge states confined to the interface of p and n regions in the graphene sheet are controllably brought together from opposite sides of the sample and allowed to mix in this split-gate geometry. Among the expected quantum Hall features, an unexpected additional plateau at 0.5h/e2 is observed. We propose that chaotic mixing of edge channels gives rise to the extra plateau.
Observation of neutral modes in the fractional quantum Hall regime.
Bid, Aveek; Ofek, N; Inoue, H; Heiblum, M; Kane, C L; Umansky, V; Mahalu, D
2010-07-29
The quantum Hall effect takes place in a two-dimensional electron gas under a strong magnetic field and involves current flow along the edges of the sample. For some particle-hole conjugate states of the fractional regime (for example, with fillings between 1/2 and 1 of the lowest Landau level), early predictions suggested the presence of counter-propagating edge currents in addition to the expected ones. When this did not agree with the measured conductance, it was suggested that disorder and interactions will lead to counter-propagating modes that carry only energy--the so called neutral modes. In addition, a neutral upstream mode (the Majorana mode) was expected for selected wavefunctions proposed for the even-denominator filling 5/2. Here we report the direct observation of counter-propagating neutral modes for fillings of 2/3, 3/5 and 5/2. The basis of our approach is that, if such modes impinge on a narrow constriction, the neutral quasiparticles will be partly reflected and fragmented into charge carriers, which can be detected through shot noise measurements. We find that the resultant shot noise is proportional to the injected current. Moreover, when we simultaneously inject a charge mode, the presence of the neutral mode was found to significantly affect the Fano factor and the temperature of the backscattered charge mode. In particular, such observations for filling 5/2 may single out the non-Abelian wavefunctions for the state. PMID:20671702
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.
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.
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
Nonequilibrated Counterpropagating Edge Modes in the Fractional Quantum Hall Regime
NASA Astrophysics Data System (ADS)
Grivnin, Anna; Inoue, Hiroyuki; Ronen, Yuval; Baum, Yuval; Heiblum, Moty; Umansky, Vladimir; Mahalu, Diana
2014-12-01
It is well established that density reconstruction at the edge of a two-dimensional electron gas takes place for hole-conjugate states in the fractional quantum Hall effect (such as v =2 /3 , 3 /5 , etc.). Such reconstruction leads, after equilibration between counterpropagating edge channels, to a downstream chiral current edge mode accompanied by upstream chiral neutral modes (carrying energy without net charge). Short equilibration length prevented thus far observation of the counterpropagating current channels—the hallmark of density reconstruction. Here, we provide evidence for such nonequilibrated counterpropagating current channels, in short regions (l =4 μ m and l =0.4 μ m ) of fractional filling v =2 /3 and, unexpectedly, v =1 /3 , sandwiched between two regions of integer filling v =1 . Rather than a two-terminal fractional conductance, the conductance exhibited a significant ascension towards unity quantum conductance (GQ=e2/h ) at or near the fractional plateaus. We attribute this conductance rise to the presence of a nonequilibrated channel in the fractional short regions.
Avalanche electron bunching in a Corbino disk in the quantum Hall effect breakdown regime
NASA Astrophysics Data System (ADS)
Chida, Kensaku; Hata, Tokuro; Arakawa, Tomonori; Matsuo, Sadashige; Nishihara, Yoshitaka; Tanaka, Takahiro; Ono, Teruo; Kobayashi, Kensuke
2014-06-01
We have measured the current noise in a device with Corbino geometry to investigate the dynamics of electrons in the breakdown regime of the integer quantum Hall effect (QHE). In the breakdown regime, the Fano factor of the current noise exceeds 103, which indicates the presence of electron bunching. As super-Poissonian current noise is observed only in the breakdown regime, the bunching effect is related to the QHE breakdown. These observations support a QHE breakdown mechanism that involves an electron avalanche.
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.
Imaging of Condensed Quantum States in the Quantum Hall Effect Regime
NASA Astrophysics Data System (ADS)
Oswald, Josef; Römer, Rudolf A.
It has been proposed already some time ago that Wigner crystallization in the tails of the Landau levels may play an important role in the quantum Hall regime. Here we use numerical simulations for modelling condensed quantum states and propose real space imaging of such highly correlated electron states by scanning gate microscopy (SGM). The ingredients for our modelling are a many particle model that combines a self-consistent Hartree-Fock calculation for the steady state with a non-equilibrium network model for the electron transport. If there exist condensed many particle quantum states in our electronic model system, our simulations demonstrate that the response pattern of the total sample current as a function of the SGM tip position delivers detailed information about the geometry of the underlying quantum state. For the case of a ring shaped dot potential in the few electron limit it is possible to find regimes with a rigid (condensed) charge distribution in the ring, where the SGM pattern corresponds to the probability density of the quantum states. The existence of the SGM image can be interpreted as the manifestation of an electron solid, since the pattern generation of the charge distribution requires certain stability against the moving tip potential.
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.
Hysteresis in the Quantum Hall Regimes in Electron Double-Quantum Structures
NASA Astrophysics Data System (ADS)
Pan, W.; Reno, J. L.; Simmons, J. A.
We present in this paper the experimental results of transport hysteresis in an extremely imbalanced electron double-quantum-well (DQW) structure. The ratio of the top layer density (ntop) to bottom layer density (nbot) is continuously tuned by applying voltage to a front gate. Under a condition when the top layer is nearly depleted (ntop~3×1010 cm-2) while the bottom layer remains at nbot=1.9×1011 cm-2, the hysteresis is absent in the B sweeps as long as the total Landau level filling ν<1 and the 2D electron systems are in the fractional quantum Hall effect regime. Surprisingly, a large hysteresis is observed during the gate sweeps at the same values of B and ntop. We attribute this unexpected hysteresis to the formation of an insulating state, probably a weakly pinned Wigner solid state, in the top layer.
Hysteresis in the Quantum Hall Regimes in Electron Double-Quantum Structures
NASA Astrophysics Data System (ADS)
Pan, W.; Reno, J. L.; Simmons, J. A.
2005-04-01
We present in this paper the experimental results of transport hysteresis in an extremely imbalanced electron double-quantum-well (DQW) structure. The ratio of the top layer density (ntop) to bottom layer density (nbot) is continuously tuned by applying voltage to a front gate. Under a condition when the top layer is nearly depleted (ntop ~ 3×1010 cm-2) while the bottom layer remains at nbot = 1.9 × 1011 cm-2, the hysteresis is absent in the B sweeps as long as the total Landau level filling ν < 1 and the 2D electron systems are in the fractional quantum Hall effect regime. Surprisingly, a large hysteresis is observed during the gate sweeps at the same values of B and ntop. We attribute this unexpected hysteresis to the formation of an insulating state, probably a weakly pinned Wigner solid state, in the top layer.
Hysteresis in the quantum Hall regimes in electron double quantum well structures
NASA Astrophysics Data System (ADS)
Pan, W.; Reno, J. L.; Simmons, J. A.
2005-04-01
We present here experimental results on magnetotransport coefficients in electron double quantum well (DQW) structures. Consistent with previous studies, transport hysteresis is is observed in the electron DQWs. Furthermore, in our gated DQW samples, by varying the top layer Landau level filling (νtop) while maintaining a relatively constant filling factor in the bottom layer (νbot) , we are able to explain the sign of Rxx(up)-Rxx(down) , where Rxx(up) is the magnetoresistance when the gate voltage Vg is swept up and Rxx(down) when Vg is swept down. Interestingly, at small magnetic fields hysteresis is generally stronger when the top quantum well is in the even integer quantum Hall effect (IQHE) regime (e.g., νtop=2 ) than in the odd IQHE regime (e.g, νtop=1 ). While at higher B fields, the hysteresis at νtop=1 becomes the strongest. The switching occurs around the B field at νbot=3 .
Topological dephasing in the ν =2 /3 fractional quantum Hall regime
NASA Astrophysics Data System (ADS)
Park, Jinhong; Gefen, Yuval; Sim, H.-S.
2015-12-01
We study dephasing in electron transport through a large quantum dot (a Fabry-Perot interferometer) in the fractional quantum Hall regime with filling factor 2 /3 . In the regime of sequential tunneling, dephasing occurs due to electron fractionalization into counterpropagating charge and neutral edge modes on the dot. In particular, when the charge mode moves much faster than the neutral mode, and at temperatures higher than the level spacing of the dot, electron fractionalization combined with the fractional statistics of the charge mode leads to the dephasing selectively suppressing h /e Aharonov-Bohm oscillations but not h /(2 e ) oscillations, resulting in oscillation-period halving.
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.
Signatures of single quantum dots in graphene nanoribbons within the quantum Hall regime.
Tóvári, Endre; Makk, Péter; Rickhaus, Peter; Schönenberger, Christian; Csonka, Szabolcs
2016-06-01
We report on the observation of periodic conductance oscillations near quantum Hall plateaus in suspended graphene nanoribbons. They are attributed to single quantum dots that are formed in the narrowest part of the ribbon, in the valleys and hills of a disorder potential. In a wide flake with two gates, a double-dot system's signature has been observed. Electrostatic confinement is enabled in single-layer graphene due to the gaps that are formed between the Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states. PMID:27198562
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.
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. PMID:26761118
Signatures of single quantum dots in graphene nanoribbons within the quantum Hall regime
NASA Astrophysics Data System (ADS)
Tóvári, Endre; Makk, Péter; Rickhaus, Peter; Schönenberger, Christian; Csonka, Szabolcs
2016-06-01
We report on the observation of periodic conductance oscillations near quantum Hall plateaus in suspended graphene nanoribbons. They are attributed to single quantum dots that are formed in the narrowest part of the ribbon, in the valleys and hills of a disorder potential. In a wide flake with two gates, a double-dot system's signature has been observed. Electrostatic confinement is enabled in single-layer graphene due to the gaps that are formed between the Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states.We report on the observation of periodic conductance oscillations near quantum Hall plateaus in suspended graphene nanoribbons. They are attributed to single quantum dots that are formed in the narrowest part of the ribbon, in the valleys and hills of a disorder potential. In a wide flake with two gates, a double-dot system's signature has been observed. Electrostatic confinement is enabled in single-layer graphene due to the gaps that are formed between the Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states. Electronic supplementary information (ESI) available. See DOI: 10.1039/C6NR00187D
Optically pumped nuclear magnetic resonance in the quantum Hall regimes
NASA Astrophysics Data System (ADS)
Barrett, S. E.; Dabbagh, G.; Pfeiffer, L. N.; West, K. W.; Tycko, R.
1996-11-01
We review our recent measurements of the Knight shift 0268-1242/11/11S/005/img1 and spin-lattice relaxation time 0268-1242/11/11S/005/img2 of the 0268-1242/11/11S/005/img3 nuclei located in n-doped GaAs quantum wells using optically pumped NMR, for Landau level filling 0268-1242/11/11S/005/img4 and temperature 0268-1242/11/11S/005/img5. 0268-1242/11/11S/005/img6 (0268-1242/11/11S/005/img7 the electron spin polarization 0268-1242/11/11S/005/img8) drops precipitously on either side of 0268-1242/11/11S/005/img9, which is evidence that the charged excitations of the 0268-1242/11/11S/005/img9 ground state are finite-size skyrmions. For 0268-1242/11/11S/005/img11, the data are consistent with a many-body ground state which is not fully spin polarized, with a very small spin excitation gap that increases as 0268-1242/11/11S/005/img12.
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.
Visualizing edge states with an atomic Bose gas in the quantum Hall regime.
Stuhl, B K; Lu, H-I; Aycock, L M; Genkina, D; Spielman, I B
2015-09-25
Bringing ultracold atomic gases into the quantum Hall regime is challenging. We engineered an effective magnetic field in a two-dimensional lattice with an elongated-strip geometry, consisting of the sites of an optical lattice in the long direction and of three internal atomic spin states in the short direction. We imaged the localized states of atomic Bose-Einstein condensates in this strip; via excitation dynamics, we further observed both the skipping orbits of excited atoms traveling down the system's edges, analogous to edge magnetoplasmons in two-dimensional electron systems, and a dynamical Hall effect for bulk excitations. Our technique involves minimal heating, which will be important for spectroscopic measurements of the Hofstadter butterfly and realizations of Laughlin's charge pump. PMID:26404830
Coherent tunnelling across a quantum point contact in the quantum Hall regime.
Martins, F; Faniel, S; Rosenow, B; Sellier, H; Huant, S; Pala, M G; Desplanque, L; Wallart, X; Bayot, V; Hackens, B
2013-01-01
The unique properties of quantum hall devices arise from the ideal one-dimensional edge states that form in a two-dimensional electron system at high magnetic field. Tunnelling between edge states across a quantum point contact (QPC) has already revealed rich physics, like fractionally charged excitations, or chiral Luttinger liquid. Thanks to scanning gate microscopy, we show that a single QPC can turn into an interferometer for specific potential landscapes. Spectroscopy, magnetic field and temperature dependences of electron transport reveal a quantitatively consistent interferometric behavior of the studied QPC. To explain this unexpected behavior, we put forward a new model which relies on the presence of a quantum Hall island at the centre of the constriction as well as on different tunnelling paths surrounding the island, thereby creating a new type of interferometer. This work sets the ground for new device concepts based on coherent tunnelling. PMID:23475303
Coherent tunnelling across a quantum point contact in the quantum Hall regime
Martins, F.; Faniel, S.; Rosenow, B.; Sellier, H.; Huant, S.; Pala, M. G.; Desplanque, L.; Wallart, X.; Bayot, V.; Hackens, B.
2013-01-01
The unique properties of quantum hall devices arise from the ideal one-dimensional edge states that form in a two-dimensional electron system at high magnetic field. Tunnelling between edge states across a quantum point contact (QPC) has already revealed rich physics, like fractionally charged excitations, or chiral Luttinger liquid. Thanks to scanning gate microscopy, we show that a single QPC can turn into an interferometer for specific potential landscapes. Spectroscopy, magnetic field and temperature dependences of electron transport reveal a quantitatively consistent interferometric behavior of the studied QPC. To explain this unexpected behavior, we put forward a new model which relies on the presence of a quantum Hall island at the centre of the constriction as well as on different tunnelling paths surrounding the island, thereby creating a new type of interferometer. This work sets the ground for new device concepts based on coherent tunnelling. PMID:23475303
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.
Edge-state transport in graphene p -n junctions in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Klimov, Nikolai N.; Le, Son T.; Yan, J.; Agnihotri, Pratik; Comfort, Everett; Lee, Ji Ung; Newell, David B.; Richter, Curt A.
2015-12-01
We experimentally investigate charge carrier transport in a graphene p -n junction device by using independent p -type and n -type electrostatic gating which allow full characterization of the junction interface in the quantum Hall regime covering a wide range of filling factors [-10 ≤(ν1,ν2) ≤10 ] . Recent charge transport measurements across a graphene p -n junction in this quantized regime presume that equilibration of all of the Landauer-Büttiker edge states occurs across the p -n junction interface. Here we show that, in our devices, only the edge state associated with the lowest Landau level fully equilibrate across the p -n junction, while none of the other edge states equilibrate to transmit current across the junction.
Effect of strain on stripe phases in the quantum Hall regime.
Koduvayur, Sunanda P; Lyanda-Geller, Yuli; Khlebnikov, Sergei; Csathy, Gabor; Manfra, Michael J; Pfeiffer, Loren N; West, Kenneth W; Rokhinson, Leonid P
2011-01-01
Preferential orientation of the stripe phases in the quantum Hall (QH) regime has remained a puzzle since its discovery. We show experimentally and theoretically that the direction of high and low resistance of the two-dimensional (2D) hole gas in the QH regime can be controlled by an external strain. Depending on the sign of the in-plane shear strain, the Hartree-Fock energy of holes or electrons is minimized when the charge density wave (CDW) is oriented along the [110] or [110] directions. We suggest that shear strains due to internal electric fields in the growth direction are responsible for the observed orientation of CDW in pristine electron and hole samples. PMID:21231765
Formation of a helical channel in a 2D system in a quantum Hall regime
NASA Astrophysics Data System (ADS)
Kazakov, Aleksandr; Kolkovsky, V.; Adamus, Z.; Karczewski, G.; Wojtowicz, T.; Rokhinson, Leonid
A two-dimensional system with reconfigurable network of one-dimensional p-wave superconducting channels is a perfect platform to perform braiding of non-Abelian excitations. Such channels can be realized in CdTe:Mn quantum wells in a quantum Hall effect regime, where counterpropagaring edge states with opposite spin polarization can be formed by electrostatic gating. These edges form helical channels similar to the edges of 2D topological insulators and, coupled to a superconductor, should support non-Abelian excitations. While long channels are localized at low temperatures, we found that resistance in short (<6 μm) helical channels remains finite at low temperatures. Transport data and resistance scaling with channel length will be presented. Work supported by ONR, National Science Centre (Poland) and Foundation for Polish Science.
Anomalous Interlayer Transport of Quantum Hall Bilayers in the Strongly Josephson-Coupled Regime
NASA Astrophysics Data System (ADS)
Zhang, Ding; Dietsche, Werner; von Klitzing, Klaus
2016-05-01
We investigate Josephson coupling in a closely spaced quantum Hall bilayer. Reduction of the interlayer barrier from the widely used values of 10-12 nm to the present one of 8 nm leads to qualitatively different interlayer transport properties. The breakdown of interlayer coherence can be spatially confined in regions that are smaller than the device size. Such a spatial inhomogeneity depends crucially on the Josephson-coupling strength and can be removed by adding an in-plane magnetic field of about 0.5 T. At higher in-plane fields, the interlayer tunneling I -V curve develops unexpected overshoot features. These results challenge current theoretical understanding and suggest that our bilayer system has entered a previously unexplored regime.
Bound states induced giant oscillations of the conductance in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Kadigrobov, A. M.; Fistul, M. V.
2016-06-01
We theoretically studied the quasiparticle transport in a 2D electron gas biased in the quantum Hall regime and in the presence of a lateral potential barrier. The lateral junction hosts the specific magnetic field dependent quasiparticle states highly localized in the transverse direction. The quantum tunnelling across the barrier provides a complex bands structure of a one-dimensional energy spectrum of these bound states, {εn}≤ft( {{p}y}\\right) , where p y is the electron momentum in the longitudinal direction y. Such a spectrum manifests itself by a large number of peaks and drops in the dependence of the magnetic edge states transmission coefficient D(E ) on the electron energy E. E.g. the high value of D occurs as soon as the electron energy E reaches gaps in the spectrum. These peaks and drops of D(E) result in giant oscillations of the transverse conductance G x with the magnetic field and/or the transport voltage. Our theoretical analysis, based on the coherent macroscopic quantum superposition of the bound states and the magnetic edge states propagating along the system boundaries, is in a good accord with the experimental observations found in Kang et al (2000 Lett. Nat. 403 59)
Bound states induced giant oscillations of the conductance in the quantum Hall regime.
Kadigrobov, A M; Fistul, M V
2016-06-29
We theoretically studied the quasiparticle transport in a 2D electron gas biased in the quantum Hall regime and in the presence of a lateral potential barrier. The lateral junction hosts the specific magnetic field dependent quasiparticle states highly localized in the transverse direction. The quantum tunnelling across the barrier provides a complex bands structure of a one-dimensional energy spectrum of these bound states, [Formula: see text], where p y is the electron momentum in the longitudinal direction y. Such a spectrum manifests itself by a large number of peaks and drops in the dependence of the magnetic edge states transmission coefficient D(E ) on the electron energy E. E.g. the high value of D occurs as soon as the electron energy E reaches gaps in the spectrum. These peaks and drops of D(E) result in giant oscillations of the transverse conductance G x with the magnetic field and/or the transport voltage. Our theoretical analysis, based on the coherent macroscopic quantum superposition of the bound states and the magnetic edge states propagating along the system boundaries, is in a good accord with the experimental observations found in Kang et al (2000 Lett. Nat. 403 59). PMID:27166511
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.
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)
Akiba, Keiichirou; Nagase, Katsumi; Hirayama, Yoshiro
2016-08-01
We observe nuclear magnetic resonance (NMR) in the fractional quantum Hall regime at the Landau-level filling factor of ν =2 /3 from simultaneous measurement of longitudinal resistance and photoluminescence (PL). The dynamic nuclear-spin polarization is induced by applying a huge electronic current at the spin phase transition point of ν =2 /3 . The NMR spectra obtained from changes in resistance and PL intensity are qualitatively the same; that is, the Knight-shift (spin-polarized region) and zero-shift (spin-unpolarized region) resonances are observed in both. The observed change in PL intensity is interpreted as a consequence of the trion scattering induced by polarized nuclear spins. We conclude that both detection methods probe almost the same local phenomena.
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
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
NMR measurement of the spin magnetization and spin dynamics in the quantum Hall regimes
NASA Astrophysics Data System (ADS)
Barrett, S. E.; Dabbagh, G.; Pfeiffer, L. N.; West, K. W.; Tycko, R.
1996-07-01
We review our recent measurements of the Knight shift ( Ks( v, T)) and spin-lattice relaxation time ( T1( v,T) of the 71Ga nuclei located in n-doped GaAs quantum wells using optically pumped NMR, for Landau-level filling 0.66 < v < 1.76 and temperature 1.55K< T
Spontaneous Quantum Hall Liquids
NASA Astrophysics Data System (ADS)
Zhang, Fan
2012-02-01
Driven by electron-electron interactions, bilayer graphene and its thicker cousins, chirally (ABC) stacked multilayers, exhibit a variety of distinct broken symmetry states in which each spin-valley flavor spontaneously transfers charge between layers, because of their flat touching bands and large pseudospin chiralities. These gapped states are accompanied by large momentum space Berry curvatures and different types of topological orders. These competing ground states are distinguished by their flavor Hall conductivities, orbital magnetizations, edge state properties, and response to external fields. These spontaneous quantum Hall (SQH) states at zero field smoothly evolve into quantum Hall ferromagnet states at finite field. Various phase transitions occur by tuning carrier densities, temperature, and external fields. Recently, SQH states have started to be observed and explored in transport and Hall experiments on suspended devices with dual gates.
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
Knighton, Talbot Tarquini, Vinicio; Wu, Zhe; Huang, Jian; Pfeiffer, Loren; West, Ken
2014-05-12
Quantum Hall measurements are performed for a two-dimensional hole system (2DHS) confined to a 20 nm quantum well in 〈100〉 GaAs. Quantum oscillations reveal a density of 4 - 5×10{sup 10} cm{sup −2} with mobility μ = 1 × 10{sup 6} cm{sup 2}/V s. For temperatures less than ∼350 mK, anomalous insulating peaks are observed between integer fillings 1-2, 2-3, and 3-4. A large out-of-phase signal appears at these peaks, which indicates a substantial inductance inherent to the charge carriers.
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.
Anomalous Hall effect in localization regime
NASA Astrophysics Data System (ADS)
Wu, Lin; Zhu, Kai; Yue, Di; Tian, Yuan; Jin, Xiaofeng
2016-06-01
The anomalous Hall effect in the ultrathin film regime is investigated in Fe(001)(1-3 nm) films epitaxial on MgO(001). The logarithmic localization correction to longitudinal resistivity and anomalous Hall resistivity are observed at low temperature. We identify that the coefficient of skew scattering has a reduction from metallic to localized regime, while the contribution of side jump has inconspicuous change except for a small drop below 10 K. Furthermore, we discover that the intrinsic anomalous Hall conductivity decreases with the reduction of thickness below 2 nm. Our results provide unambiguous experimental evidence to clarify the problem of localization correction to the anomalous Hall effect.
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)
Park, Jeongmin; Kang, Haeyong; Kim, Joonggyu; Kim, Jeong-Gyun; Yun, Yoojoo; Park, Nahee; Truong, Kieu; Lee, Yourack; Chung, Dongsub; Kim, Donggyn; Yun, Hoyeol; Lee, Sangwook; Lee, Young Hee; Suh, Dongseok
2015-03-01
We have fabricated a dual-gate graphene field-effect-transistor (FET) for the study of integer Quantum Hall Effect in terms of its edge-state transport. The graphene was encapsulated by hexagonal boron-nitride (h-BN) flakes without any interlayer residues using the `stamping-transfer' method, which is critical for the observation of graphene's intrinsic transport properties. Using the poly propylene carbonate (PPC) and Polydimethylsiloxane (PDMS), initially top h-BN flake is picked up and then graphene flake is picked up by van der Waals' force between graphene and top h-BN. These two layers are dropped down on the bottom h-BN flake to complete the encapsulated formation. To make the source/drain (S/D) and top-gate electrodes, whole area of graphene is not covered by top h-BN flake. The open areas of graphene, located at both ends, are covered by S/D metal electrodes, which made whole graphene channel region sandwiched by top and bottom hBN. We compared this method with the old one which put the two-dimensional flakes one by one using `dry-transfer'' method, and found out a significant difference in the device quality especially at low temperatures and high magnetic fields in the quantum Hall regime.
NASA Astrophysics Data System (ADS)
Akiba, K.; Kanasugi, S.; Yuge, T.; Nagase, K.; Hirayama, Y.
2015-07-01
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 BN by means of the sensitive resistive detection. We find the dependence of BN on the filling factor nonmonotonic. The comprehensive measurements of BN 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 BN is understood by the effect of electron spin polarization through excitons and trions.
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. PMID:26207494
NASA Astrophysics Data System (ADS)
Komatsu, Katsuyoshi; Li, Chuan; Autier-Laurent, S.; Bouchiat, H.; Guéron, S.
2012-09-01
We investigate the superconducting proximity effect through graphene in the long diffusive junction limit, at low and high magnetic field. The interface quality and sample phase coherence lead to a zero-resistance state at low temperature, zero magnetic field, and high doping. We find a striking suppression of the critical current near graphene's charge neutrality point, which we attribute to specular reflection of Andreev pairs at the interface of charge puddles. This type of reflection, specific to the Dirac band structure, had up to now remained elusive. At high magnetic field, the use of superconducting electrodes with high critical field enables the investigation of the proximity effect in the quantum Hall regime. Although the supercurrent is not directly detectable in our two-wire configuration, interference effects are visible which may be attributed to the injection of Cooper pairs into edge states.
Automated quantum Hall resistance standard
Schumacher, B.
1994-12-31
For precision quantized Hall resistance measurements quantum Hall effect samples have to be checked according to the CCE-guidelines. To perform these checks an automated measuring system is described, which is able to examine and characterize various samples. With these measurements a calibration of a precision 10 k{Omega} resistance standard is obtained with an uncertainty of better than 5 x 10{sup -8} (1 {sigma}) using a long-scale digital multimeter.
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.
Imaging quantum Hall Coulomb islands inside a quantum ring
NASA Astrophysics Data System (ADS)
Martins, Frederico; Hackens, Benoit; Faniel, Sebastien; Bayot, Vincent; Pala, Marco; Sellier, Hermann; Huant, Serge; Desplanque, Ludovic; Wallart, Xavier
2011-03-01
In the quantum Hall regime near integer filling factors, electrons are transmitted through edge states confined at the borders of the device. In mesoscopic samples, however, edge states may be sufficiently close to allow electrons to tunnel, or to be transmitted through localized states (``Coulomb islands''). Here, we use the biased tip of a low temperature scanning gate microscope to alter tunneling through quantum Hall Coulomb islands localized inside a quantum ring patterned in an InGaAs/InAlAs heterostructure. Simultaneously, we map the quantum ring resistance and observe different sets of concentric resistance fringes, due to charging/discharging of each Coulomb island. Tuning the magnetic field and the tip voltage, we reveal the rich and complex behaviour of these fringes.
Fractional Quantum Hall States in a Ge Quantum Well
NASA Astrophysics Data System (ADS)
Mironov, O. A.; d'Ambrumenil, N.; Dobbie, A.; Leadley, D. R.; Suslov, A. V.; Green, E.
2016-04-01
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.
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. PMID:27176531
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.
The quantum Hall impedance standard
NASA Astrophysics Data System (ADS)
Schurr, J.; Kučera, J.; Pierz, K.; Kibble, B. P.
2011-02-01
Alternating current measurements of double-shielded quantum Hall devices have revealed a fascinating property of which only a quantum effect is capable: it can detect its own frequency dependence and convert it to a current dependence which can be used to eliminate both of them. According to an experimentally verified model, the residual frequency dependence is smaller than the measuring uncertainty of 1.3 × 10-9 kHz-1. In this way, a highly precise quantum standard of impedance can be established, without having to correct for any calculated frequency dependence and without the need for any artefact with a calculated frequency dependence. Nothing else like that is known to us and we hope that our results encourage other national metrology institutes to also apply it to impedance metrology and further explore its beautiful properties.
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.).
A holographic quantum Hall ferromagnet
NASA Astrophysics Data System (ADS)
Kristjansen, C.; Pourhasan, R.; Semenoff, G. W.
2014-02-01
A detailed numerical study of a recent proposal for exotic states of the D3-probe D5 brane system with charge density and an external magnetic field is presented. The state has a large number of coincident D5 branes blowing up to a D7 brane in the presence of the worldvolume electric and magnetic fields which are necessary to construct the holographic state. Numerical solutions have shown that these states can compete with the the previously known chiral symmetry breaking and maximally symmetric phases of the D3-D5 system. Moreover, at integer filling fractions, they are incompressible with integer quantized Hall conductivities. In the dual superconformal defect field theory, these solutions correspond to states which break the chiral and global flavor symmetries spontaneously. The region of the temperature-density plane where the D7 brane has lower energy than the other known D5 brane solutions is identified. A hypothesis for the structure of states with filling fraction and Hall conductivity greater than one is made and tested by numerical computation. A parallel with the quantum Hall ferromagnetism or magnetic catalysis phenomenon which is observed in graphene is drawn. As well as demonstrating that the phenomenon can exist in a strongly coupled system, this work makes a number of predictions of symmetry breaking patterns and phase transitions for such systems.
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.
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. PMID:21981487
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.).
Typology for quantum Hall liquids
NASA Astrophysics Data System (ADS)
Parameswaran, S. A.; Kivelson, S. A.; Rezayi, E. H.; Simon, S. H.; Sondhi, S. L.; Spivak, B. Z.
2012-06-01
There is a close analogy between the response of a quantum Hall liquid (QHL) to a small change in the electron density and the response of a superconductor to an externally applied magnetic flux—an analogy which is made concrete in the Chern-Simons Landau-Ginzburg (CSLG) formulation of the problem. As the types of superconductors are distinguished by this response, so too for QHLs: A typology can be introduced which is, however, richer than that in superconductors owing to the lack of any time-reversal symmetry relating positive and negative fluxes. At the boundary between type I and type II behavior, the CSLG action has a “Bogomol'nyi point,” where the quasiholes (vortices) are noninteracting—at the microscopic level, this corresponds to the behavior of systems governed by a set of model Hamiltonians which have been constructed to render exact a large class of QHL wave functions. All types of QHLs are capable of giving rise to quantized Hall plateaux.
The Stringy Quantum Hall Fluid
Brodie, John H
2001-08-20
Using branes in massive Type IIA string theory, and a novel decoupling limit, we provide an explicit correspondence between non-commutative Chern-Simons theory and the fractional quantum Hall fluid. The role of the electrons is played by D-particles, the background magnetic field corresponds to a RR 2-form flux, and the two-dimensional fluid is described by non-commutative D2-branes. The filling fraction is given by the ratio of the number of D2-branes and the number of D8-branes, and therefore by the ratio rank/level of the Chern-Simons gauge theory. Quasiparticles and quasiholes are realized as endpoints of fundamental strings on the D2-branes, and are found to possess fractional D-particle charges and fractional statistics.
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.
Flux sensitivity of quantum spin Hall rings
NASA Astrophysics Data System (ADS)
Crépin, F.; Trauzettel, B.
2016-01-01
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.
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.
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.
Quantum theory of bilayer quantum Hall smectics
NASA Astrophysics Data System (ADS)
Papa, Emiliano; Schliemann, John; MacDonald, A. H.; Fisher, Matthew P.
2003-03-01
Mean-field theory predicts that bilayer quantum Hall systems at odd integer total filling factors can have stripe ground states, in which the top Landau level is occupied alternately by electrons in one of the two layers. We report on an analysis of the properties of these states based on a coupled-Luttinger-liquid description that is able to account for quantum fluctuations of charge-density and position along each stripe edge. The soft modes associated with the broken symmetries of the stripe state lead to an unusual coupled-Luttinger-liquid system with strongly enhanced low-temperature heat capacity and strongly suppressed low-energy tunneling density of states. We assess the importance of the intralayer and interlayer backscattering terms in the microscopic Hamiltonian, which are absent in the Luttinger liquid description, by employing a perturbative renormalization group approach which rescales time and length along but not transverse to the stripes. With interlayer backscattering interactions present the Luttinger-liquid states are unstable either to an incompressible striped state that has spontaneous interlayer phase coherence and a sizable charge gap even at relatively large layer separations, or to Wigner crystal states. Our quantitative estimates of the gaps produced by backscattering interactions are summarized in Fig. 11 by a schematic phase diagram intended to represent predicted experimental findings in very high mobility bilayer systems at dilution refrigerator temperatures as a function of layer separation and bilayer density balance. We predict that the bilayer will form incompressible isotropic interlayer phase-coherent states for small layer separations, say d⩽1.5l. At larger interlayer spacings, however, the bilayer will tend to form one of several different anisotropic states depending on the layer charge balance, which we parametrize by the fractional filling factor ν contributed by one of the two layers. For large charge imbalances (
Competition between Kondo Screening and Quantum Hall Edge Reconstruction.
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. PMID:26991192
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.
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.
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.
Thermodynamic properties of a quantum Hall anti-dot interferometer
NASA Astrophysics Data System (ADS)
Levy Schreier, Sarah; Stern, Ady; Rosenow, Bernd; Halperin, Bertrand I.
2016-02-01
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.
Theory of Nematic Fractional Quantum Hall States
NASA Astrophysics Data System (ADS)
You, Yizhi; Cho, Gil Young; Fradkin, Eduardo
2014-10-01
We derive an effective field theory for the isotropic-nematic quantum phase transition of fractional quantum Hall states. We demonstrate that for a system with an isotropic background the low-energy effective theory of the nematic order parameter has z =2 dynamical scaling exponent, due to a Berry phase term of the order parameter, which is related to the nondissipative Hall viscosity. Employing the composite fermion theory with a quadrupolar interaction between electrons, we show that a sufficiently attractive quadrupolar interaction triggers a phase transition from the isotropic fractional quantum Hall fluid into a nematic fractional quantum Hall phase. By investigating the spectrum of collective excitations, we demonstrate that the mass gap of the Girvin-MacDonald-Platzman mode collapses at the isotropic-nematic quantum phase transition. On the other hand, Laughlin quasiparticles and the Kohn collective mode remain gapped at this quantum phase transition, and Kohn's theorem is satisfied. The leading couplings between the nematic order parameter and the gauge fields include a term of the same form as the Wen-Zee term. A disclination of the nematic order parameter carries an unquantized electric charge. We also discuss the relation between nematic degrees of freedom and the geometrical response of the fractional quantum Hall fluid.
From rotating atomic rings to quantum Hall states
Roncaglia, M.; Rizzi, M.; Dalibard, J.
2011-01-01
Considerable efforts are currently devoted to the preparation of ultracold neutral atoms in the strongly correlated quantum Hall regime. However, the necessary angular momentum is very large and in experiments with rotating traps this means spinning frequencies extremely near to the deconfinement limit; consequently, the required control on parameters turns out to be too stringent. Here we propose instead to follow a dynamic path starting from the gas initially confined in a rotating ring. The large moment of inertia of the ring-shaped fluid facilitates the access to large angular momenta, corresponding to giant vortex states. The trapping potential is then adiabatically transformed into a harmonic confinement, which brings the interacting atomic gas in the desired quantum-Hall regime. We provide numerical evidence that for a broad range of initial angular frequencies, the giant-vortex state is adiabatically connected to the bosonic ν = 1/2 Laughlin state. PMID:22355562
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.
The quantum Hall effect in quantum dot systems
NASA Astrophysics Data System (ADS)
Beltukov, Y. M.; Greshnov, A. A.
2014-12-01
It is proposed to use quantum dots in order to increase the temperatures suitable for observation of the integer quantum Hall effect. A simple estimation using Fock-Darwin spectrum of a quantum dot shows that good part of carriers localized in quantum dots generate the intervals of plateaus robust against elevated temperatures. Numerical calculations employing local trigonometric basis and highly efficient kernel polynomial method adopted for computing the Hall conductivity reveal that quantum dots may enhance peak temperature for the effect by an order of magnitude, possibly above 77 K. Requirements to potentials, quality and arrangement of the quantum dots essential for practical realization of such enhancement are indicated. Comparison of our theoretical results with the quantum Hall measurements in InAs quantum dot systems from two experimental groups is also given.
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.
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
2016-01-01
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
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.
Quasihole condensates in quantum Hall liquids
Suorsa, J.; Viefers, S.; Hansson, T. H.
2011-06-15
We develop a formalism to describe quasihole condensates in quantum Hall liquids and thereby extend the conformal field theory approach to the full hierarchy of spin-polarized Abelian states and to several classes of non-Abelian hierarchical states. Most previously proposed spin-polarized quantum Hall wave functions appear as special cases. In this paper we explain the physical motivations for the approach, and exemplify it by explicitly constructing the level-two quasihole condensate state at filling fraction 2/3, and the two level-three states at 5/13 and 5/7 which are built from combinations of quasielectron and quasihole condensates.
Boundary Effective Action for Quantum Hall States.
Gromov, Andrey; Jensen, Kristan; Abanov, Alexander G
2016-03-25
We consider quantum Hall states on a space with boundary, focusing on the aspects of the edge physics which are completely determined by the symmetries of the problem. There are four distinct terms of Chern-Simons type that appear in the low-energy effective action of the state. Two of these protect gapless edge modes. They describe Hall conductance and, with some provisions, thermal Hall conductance. The remaining two, including the Wen-Zee term, which contributes to the Hall viscosity, do not protect gapless edge modes but are instead related to the local boundary response fixed by symmetries. We highlight some basic features of this response. It follows that the coefficient of the Wen-Zee term can change across an interface without closing a gap or breaking a symmetry. PMID:27058090
Boundary Effective Action for Quantum Hall States
NASA Astrophysics Data System (ADS)
Gromov, Andrey; Jensen, Kristan; Abanov, Alexander G.
2016-03-01
We consider quantum Hall states on a space with boundary, focusing on the aspects of the edge physics which are completely determined by the symmetries of the problem. There are four distinct terms of Chern-Simons type that appear in the low-energy effective action of the state. Two of these protect gapless edge modes. They describe Hall conductance and, with some provisions, thermal Hall conductance. The remaining two, including the Wen-Zee term, which contributes to the Hall viscosity, do not protect gapless edge modes but are instead related to the local boundary response fixed by symmetries. We highlight some basic features of this response. It follows that the coefficient of the Wen-Zee term can change across an interface without closing a gap or breaking a symmetry.
Nematic and Valley Ordering in Anisotropic Quantum Hall Systems
NASA Astrophysics Data System (ADS)
Parameswaran, S. A.; Abanin, D. A.; Kivelson, S. A.; Sondhi, S. L.
2010-03-01
We consider a multi-valley two dimensional electron system in the quantum Hall effect (QHE) regime. We focus on QHE states that arise due to spontaneous breaking of the valley symmetry by the Coulomb interactions. We show that the anisotropy of the Fermi surface in each valley, which is generally present in such systems, favors states where all the electrons reside in one of the valleys. In a clean system, the valley ordering occurs via a finite temperature Ising-like phase transition, which, owing to the Fermi surface anisotropy, is accompanied by the onset of nematic order. In a disordered system, domains of opposite polarization are formed, and therefore long-range valley order is destroyed, however, the resulting state is still compressible. We discuss the transport properties in ordered and disordered regimes, and point out the possible relation of our results to recent experiments in AlAs [1]. [1] Y. P. Shkolnikov, S. Misra, N. C. Bishop, E. P. De Poortere, and M. Shayegan, Observation of Quantum Hall ``Valley Skyrmions", Phys. Rev. Lett. 95, 068809 (2005)[2] D.A. Abanin, S.A. Parameswaran, S.A. Kivelson and S.L. Sondhi, Nematic and Valley Ordering in Anisotropic Quantum Hall Systems, to be published.
Geometric Adiabatic Transport in Quantum Hall States
NASA Astrophysics Data System (ADS)
Klevtsov, S.; Wiegmann, P.
2015-08-01
We argue that in addition to the Hall conductance and the nondissipative component of the viscous tensor, there exists a third independent transport coefficient, which is precisely quantized. It takes constant values along quantum Hall plateaus. We show that the new coefficient is the Chern number of a vector bundle over moduli space of surfaces of genus 2 or higher and therefore cannot change continuously along the plateau. As such, it does not transpire on a sphere or a torus. In the linear response theory, this coefficient determines intensive forces exerted on electronic fluid by adiabatic deformations of geometry and represents the effect of the gravitational anomaly. We also present the method of computing the transport coefficients for quantum Hall states.
Geometric Adiabatic Transport in Quantum Hall States.
Klevtsov, S; Wiegmann, P
2015-08-21
We argue that in addition to the Hall conductance and the nondissipative component of the viscous tensor, there exists a third independent transport coefficient, which is precisely quantized. It takes constant values along quantum Hall plateaus. We show that the new coefficient is the Chern number of a vector bundle over moduli space of surfaces of genus 2 or higher and therefore cannot change continuously along the plateau. As such, it does not transpire on a sphere or a torus. In the linear response theory, this coefficient determines intensive forces exerted on electronic fluid by adiabatic deformations of geometry and represents the effect of the gravitational anomaly. We also present the method of computing the transport coefficients for quantum Hall states. PMID:26340197
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.
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; et al
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.
2015-01-01
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. PMID:26442609
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.
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.
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.
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. PMID:16147506
Collective field theory for quantum Hall states
NASA Astrophysics Data System (ADS)
Laskin, M.; Can, T.; Wiegmann, P.
2015-12-01
We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian field theory arise from the covariant ultraviolet regularization of the theory, which produces the gravitational anomaly. These corrections are described by a theory closely related to the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.
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.
Current contacts and the breakdown of the quantum Hall effect
NASA Astrophysics Data System (ADS)
van Son, P. C.; Kruithof, G. H.; Klapwijk, T. M.
1990-12-01
The nonlinearities in the I-V characteristics have been studied of high-mobility Si metal oxide semiconductor field-effect transistors in the quantum Hall regime. The breakdown curves were measured with different sets of voltage contacts and for different directions of magnetic field and current. Comparison of these curves shows that the breakdown of the quantum Hall effect (QHE) in these samples is an intrinsic effect that starts at the current contact where the electrons are injected into the two-dimensional electron gas (2DEG). This fundamental asymmetry and the crucial role of the current contact are explained using the Büttiker-Landauer approach to the QHE and its recent extension to the nonlinear regime. The electron-injection process contains two mechanisms that lead to breakdown voltages in the 2DEG. We have identified both experimentally by comparing the critical currents of different configurations of current and voltage contacts. In one of the mechanisms, the nonequilibrium distribution of electrons that is injected into the 2DEG extends to the voltage contacts. This means that the equilibration length of the 2D electrons is at least of the order of 100 μm. For currents far beyond breakdown and for voltage contacts that are further from the electron-injection contact, the breakdown characteristics are harder to understand. The variation of the electron density of the 2DEG due to the large Hall voltage has to be taken into account as well as the equilibration induced by additional voltage contacts.
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.
The fractional quantum hall effect (experiment)
NASA Astrophysics Data System (ADS)
Stormer, H. L.
1984-11-01
Quantization of the Hall resistance ϱ XY in two-dimensional electron systems and simultaneously vanishing resistivity ϱ XX have been observed at fractional filling ν of Landau levels, ν being close to various rational fractions of p/q with exclusively odd denominator. Where resolved, the Hall resistance is quantized to ϱ XY=h/νe 2 to high accuracy. While the normal quantized Hall effect at integer values of ν=i, (i=1,2,3...) reflects the Landau and spin gaps in the single particle density of states of electrons in a magnetic field, this new phenomena is believed to indicate the condensation of the carriers into a novel, highly-correlated electronic state best described as an electron quantum liquid.
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.
Fractional quantum Hall states of Rydberg polaritons
NASA Astrophysics Data System (ADS)
Maghrebi, Mohammad F.; Yao, Norman Y.; Hafezi, Mohammad; Pohl, Thomas; Firstenberg, Ofer; Gorshkov, Alexey V.
2015-03-01
We propose a scheme for realizing fractional quantum Hall states of light. In our scheme, photons of two polarizations are coupled to different atomic Rydberg states to form two flavors of Rydberg polaritons that behave as an effective spin. An array of optical cavity modes overlapping with the atomic cloud enables the realization of an effective spin-1 /2 lattice. We show that the dipolar interaction between such polaritons, inherited from the Rydberg states, can be exploited to create a flat, topological band for a single spin-flip excitation. At half filling, this gives rise to a photonic (or polaritonic) fractional Chern insulator—a lattice-based, fractional quantum Hall state of light.
Multipole expansion in the quantum hall effect
NASA Astrophysics Data System (ADS)
Cappelli, Andrea; Randellini, Enrico
2016-03-01
The effective action for low-energy excitations of Laughlin's states is obtained by systematic expansion in inverse powers of the magnetic field. It is based on the W- infinity symmetry of quantum incompressible fluids and the associated higher-spin fields. Besides reproducing the Wen and Wen-Zee actions and the Hall viscosity, this approach further indicates that the low-energy excitations are extended objects with dipolar and multipolar moments.
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.
Optical determination of the spin polarization of a quantum Hall ferromagnet
NASA Astrophysics Data System (ADS)
Manfra, M. J.; Goldberg, B. B.; Pfeiffer, L.; West, K.
Recent experimental and theoretical investigations have resulted in a shift in our understanding of the ν=1 quantum Hall state. There now exists a wealth of evidence that the excitation gap and the resulting quasi-particle spectrum at ν=1 are due predominately to the ferromagnetic many-body exchange interaction. A great variety of experimentally observed correlations at ν=1 cannot be incorporated into a perturbative expansion around the single-particle model, a scheme long thought to describe the integral quantum Hall effect (IQHE) at filling factor 1. Theorists now refer to the ν=1 state as the quantum Hall ferromagnet. In this paper, we review recent theoretical and experimental progress and detail our own optical investigations of the ν=1 quantum Hall regime.
Optical determination of the spin polarization of a quantum Hall ferromagnet
NASA Astrophysics Data System (ADS)
Manfra, M. J.; Goldberg, B. B.; Pfeiffer, L.; West, K.
1998-01-01
Recent experimental and theoretical investigations have resulted in a shift in our understanding of the ν=1 quantum Hall state. There now exists a wealth of evidence that the excitation gap and the resulting quasi-particle spectrum at ν=1 are due predominately to the ferromagnetic many-body exchange interaction. A great variety of experimentally observed correlations at ν=1 cannot be incorporated into a perturbative expansion around the single-particle model, a scheme long thought to describe the integral quantum Hall effect (IQHE) at filling factor 1. Theorists now refer to the ν=1 state as the quantum Hall ferromagnet. In this paper, we review recent theoretical and experimental progress and detail our own optical investigations of the ν=1 quantum Hall regime.
Geometric Aspects of Quantum Hall States
NASA Astrophysics Data System (ADS)
Gromov, Andrey
Explanation of the quantization of the Hall conductance at low temperatures in strong magnetic field is one of the greatest accomplishments of theoretical physics of the end of the 20th century. Since the publication of the Laughlin's charge pumping argument condensed matter theorists have come a long way to topological insulators, classification of noninteracting (and sometimes interacting) topological phases of matter, non-abelian statistics, Majorana zero modes in topological superconductors and topological quantum computation---the framework for "error-free'' quantum computation. While topology was very important in these developments, geometry has largely been neglected. We explore the role of space-time symmetries in topological phases of matter. Such symmetries are responsible for the conservation of energy, momentum and angular momentum. We will show that if these symmetries are maintained (at least on average) then in addition to Hall conductance there are other, in principle, measurable transport coefficients that are quantized and sensitive to topological phase transition. Among these coefficients are non-dissipative viscosity of quantum fluids, known as Hall viscosity; thermal Hall conductance, and a recently discovered coefficient---orbital spin variance. All of these coefficients can be computed as linear responses to variations of geometry of a physical sample. We will show how to compute these coefficients for a variety of abelian and non-abelian quantum Hall states using various analytical tools: from RPA-type perturbation theory to non-abelian Chern-Simons-Witten effective topological quantum field theory. We will explain how non-Riemannian geometry known as Newton-Cartan (NC) geometry arises in the computation of momentum and energy transport in non-relativistic gapped systems. We use this geometry to derive a number of thermodynamic relations and stress the non-relativistic nature of condensed matter systems. NC geometry is also useful in the
Comment on "Galilean invariance at quantum Hall edge"
NASA Astrophysics Data System (ADS)
Höller, J.; Read, N.
2016-05-01
In a recent paper by S. Moroz, C. Hoyos, and L. Radzihovsky [Phys. Rev. B 91, 195409 (2015), 10.1103/PhysRevB.91.195409], it is claimed that the conductivity at low frequency ω and small wave vector q along the edge of a quantum Hall system (that possesses Galilean invariance along the edge) contains a universal contribution of order q2 that is determined by the orbital spin per particle in the bulk of the system, or alternatively by the shift of the ground state. (These quantities are known to be related to the Hall viscosity of the bulk.) In this Comment we calculate the real part of the conductivity, integrated over ω , in this regime for the edge of a system of noninteracting electrons filling either the lowest, or the lowest ν (ν =1 ,2 ,... ), Landau level(s), and show that the q2 term is nonuniversal and depends on details of the confining potential at the edge. In the special case of a linear potential, a form similar to the prediction is obtained; it is possible that this corrected form of the prediction may also hold for fractional quantum Hall states in systems with special forms of interactions between electrons.
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.
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. PMID:25786352
Geometry of fractional quantum Hall fluids
NASA Astrophysics Data System (ADS)
Cho, Gil Young; You, Yizhi; Fradkin, Eduardo
2014-09-01
We use the field theory description of the fractional quantum Hall states to derive the universal response of these topological fluids to shear deformations and curvature of their background geometry, i.e., the Hall viscosity, and the Wen-Zee term. To account for the coupling to the background geometry, we show that the concept of flux attachment needs to be modified and use it to derive the geometric responses from Chern-Simons theories. We show that the resulting composite particles minimally couple to the spin connection of the geometry. We derive a consistent theory of geometric responses from the Chern-Simons effective field theories and from parton constructions, and apply it to both Abelian and non-Abelian states.
Paired Quantum Hall States at Weak Coupling: Phenomenology
NASA Astrophysics Data System (ADS)
Parameswaran, S. A.; Kivelson, S. A.; Sondhi, S. L.; Spivak, B. Z.
2012-02-01
Paired quantum Hall states such as the Pfaffian exhibit a weak-coupling regime much like that of BCS superconductivity. In this regime their lowest energy excitations are neutral fermions -- Bogoliubov quasiparticles constructed from the composite fermions -- and not the charged vortices which generally govern the behavior of quantum Hall states. We discuss a rich set of phenomena which follow from this observation. At finite temperatures of order the pairing scale these include (i) an almost sharp phase transition (ii) a new finite-temperature length scale for the penetration of longitudinal electric fields, and (iii) the existence of a new collective excitation in paired QH states which is a cousin to the well known Artemenko-Volkov-Carlson-Goldman-Schmid-Schon mode in conventional superconductors. At lower temperatures, we find (i) a proximity effect between the paired states and their ancestor metals, which in turn mediates (ii) `Josephson' couplings between paired QH droplets separated by metallic regions and leads to (iii) a distinctive response of such states to disorder; and finally, we also comment on (iv) an analog of Andreev reflection in these systems.
Geometry of Fractional Quantum Hall Fluids
NASA Astrophysics Data System (ADS)
Cho, Gil Young
2015-03-01
Fractional quantum Hall (FQH) fluids of two-dimensional electron gases (2DEG) in large magnetic fields are fascinating topological states of matter. As such they are characterized by universal properties such as their fractional quantum Hall conductivity, fractionally charged anyonic excitations and a degeneracy of topological origin on surfaces with the topology of a torus. Quite surprisingly these topological fluids also couple to the geometry on which the 2DEG resides and have universal responses to adiabatic changes in the geometry. These responses are given by a Wen-Zee term (which describes the coupling of the currents to the spin connection of the geometry) and a gravitational Chern-Simons term which reflects the universal energy and momentum transport along the edges of the FQH state. We use a field theory of the FQH states to derive these universal responses. To account for the coupling to the background geometry, we show that the concept of flux attachment needs to be modified and use it to derive the geometric responses from Chern-Simons theories. We show that the resulting composite particles minimally couple to the spin connection of the geometry. Taking account of the framing anomaly of the quantum Chern-Simons theories, we derive a consistent theory of geometric responses from the Chern-Simons effective field theories and from parton constructions, and apply it to both abelian and non-abelian states. This work was supported in part by the NSF Grant DMR-1408713.
Pseudospin anisotropy of trilayer semiconductor quantum Hall ferromagnets
NASA Astrophysics Data System (ADS)
Miravet, D.; Proetto, C. R.
2016-08-01
When two Landau levels are brought to a close coincidence between them and with the chemical potential in the integer quantum Hall regime, the two Landau levels can just cross or collapse while the external or pseudospin field that induces the alignment changes. In this work, all possible crossings are analyzed theoretically for the particular case of semiconductor trilayer systems, using a variational Hartree-Fock approximation. The model includes tunneling between neighboring layers, bias, intralayer, and interlayer Coulomb interaction among the electrons. We have found that the general pseudospin anisotropy classification scheme used in bilayers applies also to the trilayer situation, with the simple crossing corresponding to an easy-axis ferromagnetic anisotropy analogy, and the collapse case corresponding to an easy-plane ferromagnetic analogy. An isotropic case is also possible, with the levels just crossing or collapsing depending on the filling factor and the quantum numbers of the two nearby levels. While our results are valid for any integer filling factor ν (=1 ,2 ,3 ,... ), we have analyzed in detail the crossings at ν =3 and 4, and we have given clear predictions that will help in their experimental search. In particular, the present calculations suggest that by increasing the bias, the trilayer system at these two filling factors can be driven from an easy-plane anisotropy regime to an easy-axis regime, and then can be driven back to the easy-plane regime. This kind of reentrant behavior is a unique feature of the trilayers, compared with the bilayers.
Quantum Hall Super uids in Topological Insulator Thin Films
NASA Astrophysics Data System (ADS)
Tilahun, Dagim; Lee, Byounghak; Hankiewicz, Ewelina; MacDonald, Allan
2012-02-01
Three-dimensional topological insulators have protected Dirac-cone surface states. In this work we argue that gapped excitonic superfluids with spontaneous coherence between top and bottom surfaces can occur in the 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.
Quantum Hall Superfluids in Topological Insulator Thin Films
NASA Astrophysics Data System (ADS)
Tilahun, Dagim; Lee, Byounghak; Hankiewicz, E. M.; MacDonald, A. H.
2011-12-01
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.
Quantum Hall superfluids in topological insulator thin films.
Tilahun, Dagim; Lee, Byounghak; Hankiewicz, E M; MacDonald, A H
2011-12-01
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. PMID:22243013
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.
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.
Hall magnetohydrodynamic reconnection in the plasmoid unstable regime
NASA Astrophysics Data System (ADS)
Baalrud, S. D.; Bhattacharjee, A.; Huang, Y.-M.; Germaschewski, K.
2011-09-01
A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth dη≡SL-1/2√LνA/γ , where SL is the Lundquist number, L, the length of the current sheet, νA, the Alfvén speed, and γ, the growth rate. Modifications to a recent resistive MHD analysis [N. F. Loureiro et al., Phys. Plasmas 14, 100703 (2007)] arise when collisions are sufficiently weak that dη is shorter than the ion skin depth di ≡ c/ωpi. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as (di/L)6/13SL7/13νA/L and the number of plasmoids as (di/L)1/13SL11/26, compared to SL1/4νA/L and S3/8, respectively, in resistive MHD.
Quantum spin Hall effect of light
NASA Astrophysics Data System (ADS)
Bliokh, Konstantin Y.; Smirnova, Daria; Nori, Franco
2015-06-01
Maxwell’s equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect—surface modes with strong spin-momentum locking. These modes are evanescent waves that form, for example, surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments that have demonstrated the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell’s theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces.
OPTICS. Quantum spin Hall effect of light.
Bliokh, Konstantin Y; Smirnova, Daria; Nori, Franco
2015-06-26
Maxwell's equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect—surface modes with strong spin-momentum locking. These modes are evanescent waves that form, for example, surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments that have demonstrated the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell's theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces. PMID:26113717
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.
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 Hall effects in a non-Abelian honeycomb lattice
NASA Astrophysics Data System (ADS)
Li, Ling; Hao, Ningning; Liu, Guocai; Bai, Zhiming; Li, Zai-Dong; Chen, Shu; Liu, W. M.
2015-12-01
We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a multi-Dirac-point system. We find that the quantum Hall effects present different features with the change in relative strengths of several perturbations. Namely, the quantum spin Hall effect can be induced by gauge-field-dressed next-nearest-neighbor hopping, which, together with a Zeeman field, can induce the quantum anomalous Hall effect characterized by different Chern numbers. Furthermore, we find that the edge states of the multi-Dirac-point system represent very different features for different boundary geometries, in contrast with the generic two-Dirac-point system. Our study extends the borders of the field of quantum Hall effects in a honeycomb optical lattice with multivalley degrees of freedom.
Formulation of the relativistic quantum Hall effect and parity anomaly
NASA Astrophysics Data System (ADS)
Yonaga, Kouki; Hasebe, Kazuki; Shibata, Naokazu
2016-06-01
We present a relativistic formulation of the quantum Hall effect on Haldane sphere. An explicit form of the pseudopotential is derived for the relativistic quantum Hall effect with/without mass term. We clarify particular features of the relativistic quantum Hall states with the use of the exact diagonalization study of the pseudopotential Hamiltonian. Physical effects of the mass term to the relativistic quantum Hall states are investigated in detail. The mass term acts as an interpolating parameter between the relativistic and nonrelativistic quantum Hall effects. It is pointed out that the mass term unevenly affects the many-body physics of the positive and negative Landau levels as a manifestation of the "parity anomaly." In particular, we explicitly demonstrate the instability of the Laughlin state of the positive first relativistic Landau level with the reduction of the charge gap.
Comparing conductance quantization in quantum wires and quantum Hall systems
NASA Astrophysics Data System (ADS)
Alekseev, Anton Yu.; Cheianov, Vadim V.; Fröhlich, Jürg
1996-12-01
We suggest a means to calculate the dc conductance of a one-dimensional electron system described by the Luttinger model. Our approach is based on the ideas of Landauer and Büttiker on transport in ballistic channels and on the methods of current algebra. We analyze in detail the way in which the system can be coupled to external reservoirs. This determines whether the conductance is renormalized or not. We provide a parallel treatment of a quantum wire and a fractional quantum Hall system on a cylinder with two widely separated edges. Although both systems are described by the same effective theory, the physical electrons are identified with different types of excitations, and hence the coupling to external reservoirs is different. As a consequence, the conductance in the wire is quantized in integer units of e2/h per spin orientation whereas the Hall conductance allows for fractional quantization.
Fractional quantum Hall effect in a tilted magnetic field
NASA Astrophysics Data System (ADS)
Papić, Z.
2013-06-01
We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional (1)/(3) and (1)/(2) filling of the second electronic subband are studied using finite-size exact diagonalization. In both cases, we obtain the phase diagram consisting of a fractional quantum Hall fluid phase that persists for moderate tilts, and eventually undergoes a direct transition to the stripe phase. It is shown that tilting of the field probes the geometrical degree of freedom of fractional quantum Hall fluids, and can be partly related to the effect of band-mass anisotropy.
Locating an individual quantum hall island inside a quantum ring
NASA Astrophysics Data System (ADS)
Martins, F.; Faniel, S.; Pala, M. G.; Sellier, H.; Huant, S.; Desplanque, L.; Wallart, X.; Bayot, V.; Hackens, B.
2013-12-01
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.
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.
Unconventional Sequence of Fractional Quantum Hall States in Graphene
NASA Astrophysics Data System (ADS)
Feldman, Benjamin
2013-03-01
Electronic compressibility is a powerful tool for the study of correlated electron phases in two-dimensional electron systems. Using a scanning single-electron transistor, we have measured the local electronic compressibility of suspended graphene in the quantum Hall regime. The local nature of the measurement technique allows us to probe exceptionally clean regions of graphene, revealing delicate many-body effects that are obscured by disorder in global transport studies. In this talk, I will review recent measurements of the fractional quantum Hall effect (FQHE) in graphene. We observe a multitude of FQH states that follow the standard composite fermion sequence between ν = 0 and 1, but only occur at even-numerator fractions between ν = 1 and 2, suggesting that an underlying symmetry remains. Moreover, we observe a series of phase transitions in the FQH states between ν = 0 and 1 that are marked by a decreased energy gap and a narrow region of negative compressibility that cuts across the FQH state. We use a simple model based on crossing composite fermion Landau levels with different internal degrees of freedom to reproduce much of the experimental behavior. Our results provide insight into the interplay between electron-electron interactions and the spin and valley symmetries of graphene.
Effect of incoherent scattering on three-terminal quantum Hall thermoelectrics
NASA Astrophysics Data System (ADS)
Sánchez, Rafael; Sothmann, Björn; Jordan, Andrew N.
2016-01-01
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.
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.
Interferometer-Based Studies of Quantum Hall Phenomena
NASA Astrophysics Data System (ADS)
McClure, Douglas Templeton, III
The fractional quantum Hall (FQH) effect harbors a wealth of unique phenomena, many of which remain mysterious. Of particular interest is the predicted existence of quasi-particles with unusual topological properties, especially in light of recent proposals to observe these properties using electronic interferometers. An introduction to quantum Hall physics and electronic interferometry is given in Chapter 1 of this thesis. The remaining chapters, summarized below, describe a set of experiments in which FQH systems are studied using electronic Fabry-Perot interferometry and related techniques. Since prior studies of electronic Fabry-Perot interferometers revealed unexpected behavior even in the integer quantum Hall (IQH) regime, we began our measurements there. Our initial experiment, presented in Chapter 2, disentangles signatures of Coulomb interaction effects from those of Aharonov-Bohm (AB) interference and provides the first measurement of pure AB interference in these devices. In our next experiment, presented in Chapter 3, we measure AB interference oscillations as a function of an applied dc bias, use their period to study the velocity of the interfering electrons, and study how the oscillations decay as a function of bias and magnetic field. Moving to the FQH regime, applying a similar-sized bias to a quantum point contact leads to long-lasting changes in the strengths and positions of FQH plateaus. The involvement of lattice nuclear spins in this effect, suggested by the long persistence times, is confirmed using NMR-type measurements. Although the exact physical process responsible for the effect remains unclear, its filling-factor dependence provides a striking illustration of composite fermion physics. These measurements are described in Chapter 4. In certain devices, interference oscillations associated with several FQH states are observed. Interpretation of their magnetic-field and gate-voltage periods provides a measurement of quasi-particle charge
Unconventional quantum Hall effect in Floquet topological insulators
NASA Astrophysics Data System (ADS)
Tahir, M.; Vasilopoulos, P.; Schwingenschlögl, U.
2016-09-01
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 {σyx}=0 at zero Fermi energy, to a Hall insulator state with {σyx}={{e}2}/2h . These findings open new possibilities for experimentally realizing nontrivial quantum states and unusual quantum Hall plateaus at (+/- 1/2,+/- 3/2,+/- 5/2,...){{e}2}/h .
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]. PMID:27460419
Gor'kov, L P; Teitel'baum, G B
2014-01-29
We address recent experiments shedding light on the energy spectrum of under and optimally doped cuprates at temperatures above the superconducting transition. Angle resolved photoemission reveals coherent excitation only near nodal points on parts of the 'bare' Fermi surface known as the Fermi arcs. The question debated in the literature is whether the small normal pocket, seen via quantum oscillations, exists at higher temperatures or forms below a charge order transition in strong magnetic fields. Assuming the former case as a possibility, expressions are derived for the resistivity and the Hall coefficient (in weak and strong magnetic fields) with both types of carriers participating in the transport. There are two regimes. At higher temperatures (at a fixed field) electrons are dragged by the Fermi arcs' holes. The pocket being small, its contribution to conductivity and the Hall coefficient is negligible. At lower temperatures electrons decouple from holes behaving as a Fermi gas in the magnetic field. As the mobility of holes on the arcs decreases in strong fields with a decrease of temperature, below a crossover point the pocket electrons prevail, changing the sign of the Hall coefficient in the low temperature limit. Such behavior finds its confirmation in recent high-field experiments. PMID:24389670
Confinement of Fractional Quantum Hall States
NASA Astrophysics Data System (ADS)
Willett, Robert; Manfra, Michael; West, Ken; Pfeiffer, Loren
2008-03-01
Confinement of small-gapped fractional quantum Hall states facilitates quasiparticle manipulation and is an important step towards quasiparticle interference measurements. Demonstrated here is conduction through top gate defined, narrow channels in high density, ultra-high mobility heterostructures. Transport evidence for the persistence of a correlated state at filling fraction 5/3 is shown in channels of 2μm length but gated to near 0.3μm in width. The methods employed to achieve this confinement hold promise for interference devices proposed for studying potential non-Abelian statistics at filling fraction 5/2. R.L. Willett, M.J. Manfra, L.N. Pfeiffer, K.W. West, Appl. Phys. Lett. 91, 052105 (2007).
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.
Quantum Numbers of Textured Hall Effect Quasiparticles
Nayak, C.; Wilczek, F.
1996-11-01
We propose a class of variational wave functions with slow variation in spin and charge density and simple vortex structure at infinity, which properly generalize both the Laughlin quasiparticles and baby Skyrmions. We argue, on the basis of these wave functions and a spin-statistics relation in the relevant effective field theory, that the spin of the corresponding quasiparticle has a fractional part related in a universal fashion to the properties of the bulk state. We propose a direct experimental test of this claim. We show that certain spin-singlet quantum Hall states can be understood as arising from primary polarized states by Skyrmion condensation. {copyright} {ital 1996 The American Physical Society.}
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.
Imaging Coulomb islands in a quantum Hall interferometer.
Hackens, B; Martins, F; Faniel, S; Dutu, C A; Sellier, H; Huant, S; Pala, M; Desplanque, L; Wallart, X; Bayot, V
2010-01-01
In the quantum Hall regime, near integer filling factors, electrons should only be transmitted through spatially separated edge states. However, in mesoscopic systems, electronic transmission turns out to be more complex, giving rise to a large spectrum of magnetoresistance oscillations. To explain these observations, recent models put forward the theory that, as edge states come close to each other, electrons can hop between counterpropagating edge channels, or tunnel through Coulomb islands. Here, we use scanning gate microscopy to demonstrate the presence of QH Coulomb islands, and reveal the spatial structure of transport inside a QH interferometer. Locations of electron islands are found by modulating the tunnelling between edge states and confined electron orbits. Tuning the magnetic field, we unveil a continuous evolution of active electron islands. This allows to decrypt the complexity of high-magnetic-field magnetoresistance oscillations, and opens the way to further local-scale manipulations of QH localized states. PMID:20975700
Quantum Hall effect in black phosphorus two-dimensional electron system
NASA Astrophysics Data System (ADS)
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 cm2 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.
NASA Astrophysics Data System (ADS)
Yang, Kun
2016-04-01
We show that an acoustic crystalline wave gives rise to an effect similar to that of a gravitational wave to an electron gas. Applying this idea to a two-dimensional electron gas in the fractional quantum Hall regime, this allows for experimental study of its intra-Landau level dynamical response in the long-wavelength limit. To study such response we generalize Haldane's geometrical description of fractional quantum Hall states to situations where the external metric is time dependent. We show that such time-dependent metric (generated by acoustic wave) couples to collective modes of the system, including a quadrapolar mode at long wavelength, and magnetoroton at finite wavelength. Energies of these modes can be revealed in spectroscopic measurements, controlled by strain-induced Fermi velocity anisotropy. We argue that such geometrical probe provides a potentially highly useful alternative probe of quantum Hall liquids, in addition to the usual electromagnetic response.
Matthews, J.; Cage, M. E.
2005-01-01
We present detailed measurements of the temperature dependence of the Hall and longitudinal resistances on a quantum Hall device [(GaAs(7)] which has been used as a resistance standard at NIST. We find a simple power law relationship between the change in Hall resistance and the longitudinal resistance as the temperature is varied between 1.4 K and 36 K. This power law holds over seven orders of magnitude change in the Hall resistance. We fit the temperature dependence above about 4 K to thermal activation, and extract the energy gap and the effective g-factor. PMID:27308175
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.
Enigmatic 12/5 fractional quantum Hall effect
NASA Astrophysics Data System (ADS)
Pakrouski, Kiryl; Troyer, Matthias; Wu, Yang-Le; Das Sarma, Sankar; Peterson, Michael R.
2016-08-01
We numerically study the fractional quantum Hall effect at filling factors ν =12 /5 and 13/5 (the particle-hole conjugate of 12/5) in high-quality two-dimensional GaAs heterostructures via exact diagonalization including finite well width and Landau-level mixing. We find that Landau-level mixing suppresses the ν =13 /5 fractional quantum Hall effect relative to ν =12 /5 . By contrast, we find both ν =2 /5 and (its particle-hole conjugate) ν =3 /5 fractional quantum Hall effects in the lowest Landau level to be robust under Landau-level mixing and finite well-width corrections. Our results provide a possible explanation for the experimental absence of the 13/5 fractional quantum Hall state as caused by Landau-level mixing effects.
Superconducting quantum spin Hall systems with giant orbital g factors
NASA Astrophysics Data System (ADS)
Reinthaler, R. W.; Tkachov, G.; Hankiewicz, E. M.
2015-10-01
Topological aspects of superconductivity in quantum spin Hall systems (QSHSs) such as thin layers of three-dimensional topological insulators (TIs) or two-dimensional TIs are the focus of current research. Here, we describe a superconducting quantum spin Hall effect (quantum spin Hall system in proximity to an s -wave superconductor and in orbital in-plane magnetic fields), which is protected against elastic backscattering by combined time-reversal and particle-hole symmetry. This effect is characterized by spin-polarized edge states, which can be manipulated in weak magnetic fields due to a giant effective orbital g factor, allowing the generation of spin currents. The phenomenon provides a solution to the outstanding challenge of detecting the spin polarization of the edge states. Here we propose the detection of the edge polarization in a three-terminal junction using unusual transport properties of the superconducting quantum Hall effect: a nonmonotonic excess current and a zero-bias conductance peak splitting.
Guiding-center hall viscosity and intrinsic dipole moment of fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Park, YeJe
The fractional quantum Hall effect (FQHE) is the archetype of the strongly correlated systems and the topologically ordered phases. Unlike the integer quantum Hall effect (IQHE) which can be explained by single-particle physics, FQHE exhibits many emergent properties that are due to the strong correlation among many electrons. In this Thesis, among those emergent properties of FQHE, we focus on the guiding-center metric, the guiding-center Hall viscosity, the guiding-center spin, the intrinsic electric dipole moment and the orbital entanglement spectrum. Specifically, we show that the discontinuity of guiding-center Hall viscosity (a bulk property) at edges of incompressible quantum Hall fluids is associated with the presence of an intrinsic electric dipole moment on the edge. If there is a gradient of drift velocity due to a non-uniform electric field, the discontinuity in the induced stress is exactly balanced by the electric force on the dipole. We show that the total Hall viscosity has two distinct contributions: a "trivial'' contribution associated with the geometry of the Landau orbits, and a non-trivial contribution associated with guiding-center correlations. We describe a relation between the intrinsic dipole moment and "momentum polarization'', which relates the guiding-center Hall viscosity to the "orbital entanglement spectrum(OES)''. We observe that using the computationally-more-onerous "real-space entanglement spectrum (RES)'' in the momentum polarization calculation just adds the trivial Landau-orbit contribution to the guiding-center part. This shows that all the non-trivial information is completely contained in the OES, which also exposes a fundamental topological quantity gamma = c˜ - nu, the difference between the "chiral stress-energy anomaly'' (or signed conformal anomaly) and the chiral charge anomaly. This quantity characterizes correlated fractional quantum Hall fluids, and vanishes in integer quantum Hall fluids which are uncorrelated.
Quantum spin Hall effect in inverted type-II semiconductors.
Liu, Chaoxing; Hughes, Taylor L; Qi, Xiao-Liang; Wang, Kang; Zhang, Shou-Cheng
2008-06-13
The quantum spin Hall (QSH) state is a topologically nontrivial 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 and in this Letter we predict a similar effect arising in Type-II semiconductor quantum wells made from InAs/GaSb/AlSb. The quantum well exhibits an "inverted" phase similar to HgTe/CdTe 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 are essential. Remarkably, the topological quantum phase transition between the conventional insulating state and the quantum spin Hall state can be continuously tuned by the gate voltage, enabling quantitative investigation of this novel phase transition. PMID:18643529
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.
Nuclear magnetometry studies of spin dynamics in quantum Hall systems
NASA Astrophysics Data System (ADS)
Fauzi, M. H.; Watanabe, S.; Hirayama, Y.
2014-12-01
We performed a nuclear magnetometry study on quantum Hall ferromagnet with a bilayer total filling factor of νtot=2 . We found not only a rapid nuclear relaxation but also a sudden change in the nuclear-spin polarization distribution after a one-second interaction with a canted antiferromagnetic phase. We discuss the possibility of observing cooperative phenomena coming from nuclear-spin ensemble triggered by hyperfine interaction in quantum Hall system.
Spin Charge Separation in the Quantum Spin Hall State
Qi, Xiao-Liang; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
The quantum spin Hall state is a topologically non-trivial insulator state protected by the time reversal symmetry. We show that such a state always leads to spin-charge separation in the presence of a {pi} flux. Our result is generally valid for any interacting system. We present a proposal to experimentally observe the phenomenon of spin-charge separation in the recently discovered quantum spin Hall system.
Quantum Hall effect in bilayer system with array of antidots
NASA Astrophysics Data System (ADS)
Pagnossin, I. R.; Gusev, G. M.; Sotomayor, N. M.; Seabra, A. C.; Quivy, A. A.; Lamas, T. E.; Portal, J. C.
2007-04-01
We have studied the Quantum Hall effect in a bilayer system modulated by gate-controlled antidot lattice potential. The Hall resistance shows plateaus which are quantized to anomalous multiplies of h/e2. We suggest that this complex behavior is due to the nature of the edge-states in double quantum well (DQW) structures coupled to an array of antidots: these plateaus may be originated from the coexistence of normal and counter-rotating edge-states in different layers.
Spin-valley quantum Hall phases in graphene
NASA Astrophysics Data System (ADS)
Tian, Hong-Yu
2015-12-01
We theoretically investigate possible quantum Hall phases and corresponding edge states in graphene by taking a strong magnetic field, Zeeman splitting M, and sublattice potential Δ into account but without spin-orbit interaction. It was found that for the undoped graphene either a quantum valley Hall phase or a quantum spin Hall phase emerges in the system, depending on relative magnitudes of M and Δ. When the Fermi energy deviates from the Dirac point, the quantum spin-valley Hall phase appears and its characteristic edge state is contributed only by one spin and one valley species. The metallic boundary states bridging different quantum Hall phases possess a half-integer quantized conductance, like e2/2h or 3e2/2h. The possibility of tuning different quantum Hall states with M and Δ suggests possible graphene-based spintronics and valleytronics applications. Project supported by the National Natural Science Foundation of China (Grant Nos. 11447218, 11274059, 11404278, and 11447216).
The optomechanical instability in the quantum regime
NASA Astrophysics Data System (ADS)
Ludwig, Max; Kubala, Björn; Marquardt, Florian
2008-09-01
We consider a generic optomechanical system, consisting of a driven optical cavity and a movable mirror attached to a cantilever. Systems of this kind (and analogues) have been realized in many recent experiments. It is well known that these systems can exhibit an instability towards a regime where the cantilever settles into self-sustained oscillations. In this paper, we briefly review the classical theory of the optomechanical instability, and then discuss the features arising in the quantum regime. We solve numerically a full quantum master equation for the coupled system, and use it to analyze the photon number, the cantilever's mechanical energy, the phonon probability distribution and the mechanical Wigner density, as a function of experimentally accessible control parameters. When a suitable dimensionless 'quantum parameter' is sent to zero, the results of the quantum mechanical model converge towards the classical predictions. We discuss this quantum-to-classical transition in some detail.
Bosonic Integer Quantum Hall Effect in Optical Flux Lattices
NASA Astrophysics Data System (ADS)
Sterdyniak, A.; Cooper, Nigel R.; Regnault, N.
2015-09-01
In two dimensions strongly interacting bosons in a magnetic field can realize a bosonic integer quantum Hall state, the simplest two-dimensional example of a symmetry-protected topological phase. We propose a realistic implementation of this phase using an optical flux lattice. Through exact diagonalization calculations, we show that the system exhibits a clear bulk gap and the topological signature of the bosonic integer quantum Hall state. In particular, the calculation of the many-body Chern number leads to a quantized Hall conductance in agreement with the analytical predictions. We also study the stability of the phase with respect to some of the experimentally relevant parameters.
The Quantum Spin Hall Effect: Theory and Experiment
NASA Astrophysics Data System (ADS)
König, Markus; Buhmann, Hartmut; Molenkamp, Laurens W.; Hughes, Taylor; Liu, Chao-Xing; Qi, Xiao-Liang; Zhang, Shou-Cheng
2008-03-01
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 (QWs). By varying the thickness of the QW, the band structure changes from a normal to an “inverted” type at a critical thickness dc. 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 QWs. We review both the fabrication of the sample and the experimental setup. For thin QWs with well width dQW<6.3 nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker QWs (dQW>6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2e2/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, dc=6.3 nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.
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.
Quantum Spin Hall phase in multilayer graphene
NASA Astrophysics Data System (ADS)
Garcia, Noel; Lado, Jose Luis; Fernandez-Rossier, Joaquin; Theory of Nanostructures Team
2015-03-01
We address the question of whether multilayer graphene systems are Quantum Spin Hall (QSH) insulators. Since interlayer coupling coples pz orbitals to s orbitals of different layers and Spin-Orbit (SO) couples pz orbitals with px and py of opposite spins, new spins mixing channels appear in the multilayer scenario that were not present in the monolayer. These new spin-mixing channels cast a doubt on the validity of the spin-conserving Kane-Mele model for multilayers and motivates our choice of a four orbital tight-binding model in the Slater-Koster approximation with intrinsic Spin-Orbit interaction. To completely determine if the QSH phase is present we calculate for different number of layers both the Z2 invariant for different stackings (only for inversion symmetric systems), and the density of states at the edge of semi-infinite graphene ribbon with armchair termination. We find that systems with even number of layers are normal insulators while systems with odd number of layers are QSH insulators, regardless of the stacking. We acknowledge financial support by Marie-Curie-ITN 607904-SPINOGRAPH.
Persistent Hall response after a quantum quench in Dirac systems
NASA Astrophysics Data System (ADS)
Wilson, Justin; Song, Justin; Refael, Gil
The geometry and topology of quantum states play a central role in producing novel types of responses, such as the quantum anomalous Hall effect. These have featured prominently in topological materials in equilibrium as well as driven systems in the steady state. Here we unveil how quantum geometry yields radically new types of responses in systems far from equilibrium such as that realized in a quantum quench. To illustrate this, we consider quenches of two-band systems with spin-orbit coupling (e.g. Dirac systems). We find that quenching a time-reversal broken gap gives a Hall-type response that persists even at long times. Intimately tied to the quantum geometry of the underlying Hilbert space, the unconventional persistent Hall response yield clear signatures in quench protocols that can be implemented in cold atoms set-ups.
Quantum Friction in Different Regimes
NASA Astrophysics Data System (ADS)
Klatt, Juliane; Buhmann, Stefan
2015-03-01
Quantum friction is the velocity-dependent force between two polarizable objects in relative motion, resulting from field-fluctuation mediated transfer of energy and momentum between them. Due to its short-ranged nature it has proven difficult to observe experimentally. Theoretical attempts to determine the precise velocity-dependence of the quantum drag experienced by a polarizable atom moving parallel to a surface arrive at contradicting results. Scheel and Barton predict a force linear in relative velocity v - the former using the quantum regression theorem and the latter employing time-dependent perturbation theory. Intravaia, however, predicts a v3 power-law starting from a non-equilibrium fluctuation-dissipation theorem. In order to learn where exactly the above approaches part, we set out to perform all three calculations within one and the same framework: macroscopic QED. In addition, we include contributions to quantum friction from Doppler shift and Röntgen interaction, which play a role for perpendicular motion and retarded distances, respectively, and consider non-stationary states of atom and field. DFG Emmy-Noether Program.
Fractional Quantum Hall Effect of lossy Rydberg Dark-State Polaritons
NASA Astrophysics Data System (ADS)
Grusdt, Fabian; Fleischhauer, Michael; Höning, Michael; Otterbach, Johannes
2012-06-01
Dark-state-polaritons (DSP) are bosonic quasiparticles arising in the interaction of light with 3-level atoms under conditions of electromagnetically induced transparency (EIT). When exposed to a strong artificial magnetic field, they can enter the lowest Landau level regime. With additional long range interactions, as realized e.g. when the 3-level atom contains a Rydberg-excited state, DSPs are natural candidates for a realization of the bosonic fractional quantum Hall effect. Besides their high controllability, they offer the possibility to examine open quantum Hall systems. We show how highly-correlated quantum Hall states of DSPs can be prepared, making use of nonlinear polariton losses. The possibility of realizing these states as stationary states of open systems is investigated. We propose a realistic quantum-optical setup, and show that different fractional quantum Hall states can be prepared, manipulated and observed. Numerical and analytical results for the excitation gaps of the ν=1/2p Laughlin states are presented.
Long-wavelength corrections to Hall conductivity in fractional quantum Hall fluids
NASA Astrophysics Data System (ADS)
Yang, Bo; Haldane, F. D. M.
2013-03-01
Recent work by Hoyos and Son, then Bradlyn et al., has investigated the relation between the long-wavelength (O (q2)) corrections to the Hall conductivity σH (q) and the Hall viscosity of quantum Hall states. These works assume the presence of Galilean and rotational invariance. However, these are not generic symmetries of electrons in condensed matter. We identify translation and (2D) inversion symmetry as the only generic symmetries of an ``ideal'' quantum Hall liquid, as these are needed to guarantee the absence of any dissipationless ground state current density; then σH (q) = σH (- q) characterizes the dissipation less current that flows in response to a spatially-non-uniform electric field. We consider the general problem for fractional quantum Hall (FQH) states without Galilean or rotational invariance, when the guiding-center contribution to the Hall viscosity becomes a non-trivial tensor property related to an emergent geometry of the FQH state, (Bo Yang et,al (PRB 85,165318). Supported by DOE DE-SC0002140 and Agency for Science Technology and Research (A*STAR, Singapore).
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.
The Quantum Hall Liquid to Insulator Transitions
NASA Astrophysics Data System (ADS)
Shahar, Dan
1996-03-01
We have conducted a systematic study of the quantum phase transitions between insulating and quantum Hall effect (QHE) phases of two dimensional electron system (2DES) at high magnetic fields (B<15.5 T) and low temperatures (T>20 mK). More than 100 samples were studied, with mobilities and densities (μ =1.2\\cdot 10^4-5\\cdot 10^6 cm^2/Vsec and n=8\\cdot 10^9-2.26\\cdot 10^11 cm-2, respectively) that effectively cover the whole range of 2DES samples that are currently available. We observed a remarkable similarity among the various transitions which transcends not only the vast differences in the parameters of our samples, but also the differences between the integer and the fractional QHE states. This similarity can be quantitatively expressed in terms of two parameters describing the transitions, the T scaling parameter, 1/ν z =0.45± 0.05 and the the critical resistivity at the transition, ρ_xxc=25.3± 6 kΩ, both of which are independent of sample parameters and transitions, within the errors specified. In the vicinity of the transitions, the I-V_xx traces are strongly non-linear, and exhibit a marked reflection symmetry between the traces in the QHE and those in the insulator, which we take as evidence for the existence of charge-flux duality symmetry near the transitions. These results support the predictions of the bosonic Chern-Simons theory recently developed by Kivelson, Lee and Zhang (KLZ),^1 to describe the interplay between the various phases of 2DES at high B. Finally, our study included ultra-high mobility samples that exhibit reentrant insulating phases near 1/5 and 1/3 fractional QHE state, which are explicitly forbidden in the framework developed by KLZ. Transitions involving these insulating phases show surprising similarities, and intriguing differences, to the allowed transitions. ^*In collaboration with D. C. Tsui, M. Shayegan, J. E. Cunningham, R. N. Bhatt, E. Shimshoni, S. L. Sondhi. [1] S. A. Kivelson, D. H. Lee, and S. C. Zhang, Phys
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.
New Method for Studying Localization effects in Quantum Hall Systems
NASA Astrophysics Data System (ADS)
Bhatt, R. N.; Geraedts, Scott
Disorder is central to the study of the fractional quantum Hall effect. It is responsible for the finite width of the quantum Hall plateaus, and it is of course present in experiment. Numerical studies of the disordered fractional quantum Hall effect are nonetheless very difficult, because the lack of symmetry present in clean systems limits the size of systems that can be studied. We introduce a new method for studying the integer and fractional quantum Hall effect in the presence of disorder that allows larger system sizes to be studied. The method relies on truncating the single particle Hilbert space, which leads to an exponential reduction in the Hilbert space of the many-particle system while preserving the essential topological nature of the state. We apply the model to the study of disorder transitions in the quantum Hall effect, both for the ground state and excited states. This work was supported by the US Department of Energy, Office of Basic Energy Sciences, through Grant DE-SC0002140.
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.
Electron interferometry in integer quantum Hall edge channels
NASA Astrophysics Data System (ADS)
Rech, J.; Wahl, C.; Jonckheere, T.; Martin, T.
2016-05-01
We consider the electronic analog of the Hong-Ou-Mandel interferometer from quantum optics. In this realistic condensed matter device, single electrons are injected and travel along opposite chiral edge states of the integer quantum Hall effect, colliding at a quantum point contact (QPC). We monitor the fate of the colliding excitations by calculating zero-frequency current correlations at the output of the QPC. In the simpler case of filling factor $\
Study of correlations in fractional quantum Hall effect
NASA Astrophysics Data System (ADS)
Shi, Chuntai
Bulk two-dimensional electron systems in a strong perpendicular magnetic field exhibit the fascinating phenomenon of fractional quantum Hall effect. Composite fermion theory was developed in the process of understanding the fractional quantum Hall effect and was proven to work successfully for the FQHE and even beyond. In this dissertation, we explore the effect of the strong correlation between electrons in several cases. All of them belong to the category of 2DES in strong perpendicular magnetic field and they are listed below: (i) A fractional quantum Hall island surrounded by a bulk fractional quantum Hall state with a different filling factor. Specifically, we study the resonant tunneling composite fermions through their quasibound states around the island. A rich set of possible transitions are found and the possible relevance to an interesting experiment is discussed. Also, we discuss the subtlety of separating the effect of fractional braiding statistics from other factors. (ii) Correlated states of a quantum dot, at high magnetic fields, assuming four electrons with two components. Such a dot can be realized by reducing the two lateral dimensions of a 2DES tremendously. Both the liquid states and crystallites (the latter occurring at large angular momenta) of four electrons in terms of composite fermions are considered. Residual interaction between composite fermions is shown to leads to complex spin correlations. (iii) Bilayer quantum Hall effect at total filling nuT = 5. This can accommodate an excitonic superfluid state at small layer separations just like at nuT = 1. At large layer separations, however, nuT = 5 state evolves into uncorrelated nu = 5/2 fractional quantum Hall states in both layers, in contrast to uncorrelated composite Fermi sea in nu T = 1 case. We focus on finding the critical layer separation at which the correlation between electrons on different layers are destroyed. Effects due to the finite width of the layers are also considered.
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. PMID:15447125
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.
Reconstruction of Fractional Quantum Hall Edges: Numerical Studies
NASA Astrophysics Data System (ADS)
Wan, Xin; Yang, Kun; Rezayi, E. H.
2003-03-01
The interplay of electron-electron interaction and confining potential can lead to the reconstruction of fractional quantum Hall edges (Xin Wan, Kun Yang, and E. H. Rezayi, Phys. Rev. Lett. 88, 056802 (2002).). We have performed exact diagonalization studies on microscopic models of fractional quantum Hall liquids, in finite size systems with disc geometry, and found numerical evidence that suggests edge reconstruction occurs under rather general conditions. Due to edge reconstruction, additional nonchiral edge modes can arise for both incompressible and compressible states. We have studied the electron dipole spectral function that is directly related to the microwave conductivity measurement of a two-dimensional electron gas with an array of antidots (P. D. Ye et al., Phys. Rev. B 65, 121305 (2002).). Our results are consistent with the enhanced microwave conductivity observed in experiments at low temperatures, and its suppression at higher temperatures. We also discuss the effects of the edge reconstruction on the fractional quantum Hall edge tunneling experiments.
Scaling of the anomalous Hall effect in lower conductivity regimes
NASA Astrophysics Data System (ADS)
Karel, J.; Bordel, C.; Bouma, D. S.; de Lorimier-Farmer, A.; Lee, H. J.; Hellman, F.
2016-06-01
The scaling of the anomalous Hall effect (AHE) was investigated using amorphous and epitaxial Fe x Si1‑x (0.43 < x < 0.71) magnetic thin films by varying the longitudinal conductivity (σxx) using two different approaches: modifying the carrier mean free path (l) with chemical or structural disorder while holding the carrier concentration (nh) constant or varying n h and keeping l constant. The anomalous Hall conductivity (σxy) , when suitably normalized by magnetization and n h , is shown to be independent of σxx for all samples. This observation suggests a primary dependence on an intrinsic mechanism, unsurprising for the epitaxial high conductivity films where the Berry phase curvature mechanism is expected, but remarkable for the amorphous samples. That the amorphous samples show this scaling indicates a local atomic level description of a Berry phase, resulting in an intrinsic AHE in a system that lacks lattice periodicity.
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.
Universal nonequilibrium states at the fractional quantum Hall edge
NASA Astrophysics Data System (ADS)
Levkivskyi, Ivan P.
2016-04-01
Integrability of electron dynamics in one dimension is manifested by the nonequilibrium stationary states. They emerge near a point contact coupling two quantum Hall edges with different chemical potentials. I use the nonequilibrium bosonization technique to show that the effective temperature of such states at the fractional quantum Hall edges has a universal linear dependence on the current through the contact. In contrast, the temperature at eventual equilibrium scales as the square root of the power dissipating at the point contact. I propose to use this distinction to detect these intriguing nonequilibrium states.
Decoherence induced by magnetic impurities in a quantum hall system
Kagalovsky, V.; Chudnovskiy, A. L.
2013-04-15
Scattering by magnetic impurities is known to destroy coherence of electron motion in metals and semiconductors. We investigate the decoherence introduced in a single act of electron scattering by a magnetic impurity in a quantum Hall system. For this, we introduce a fictitious nonunitary scattering matrix for electrons that reproduces the exactly calculated scattering probabilities. The strength of decoherence is identified by the deviation of eigenvalues of the product from unity. Using the fictitious scattering matrix, we estimate the width of the metallic region at the quantum Hall effect inter-plateau transition and its dependence on the exchange coupling strength and the degree of polarization of magnetic impurities.
Scrutinizing Hall Effect in Mn1 -xFex Si : Fermi Surface Evolution and Hidden Quantum Criticality
NASA Astrophysics Data System (ADS)
Glushkov, V. V.; Lobanova, I. I.; Ivanov, V. Yu.; Voronov, V. V.; Dyadkin, V. A.; Chubova, N. M.; Grigoriev, S. V.; Demishev, S. V.
2015-12-01
Separating between the ordinary Hall effect and anomalous Hall effect in the paramagnetic phase of Mn1 -xFex 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 Mn1 -xFex Si . The change of electron and hole concentrations is considered as a "driving force" for tuning the QC regime in Mn1 -xFex Si via modifying the Ruderman-Kittel-Kasuya-Yosida exchange interaction within the Heisenberg model of magnetism.
On the Quantum Spin Hall Gap of Monolayer 1T'-WTe2.
Zheng, Feipeng; Cai, Chaoyi; Ge, Shaofeng; Zhang, Xuefeng; Liu, Xin; Lu, Hong; Zhang, Yudao; Qiu, Jun; Taniguchi, Takashi; Watanabe, Kenji; Jia, Shuang; Qi, Jingshan; Chen, Jian-Hao; Sun, Dong; Feng, Ji
2016-06-01
Positive quantum spin Hall gap in mono-layer 1T'-WTe2 is consistently supported by density-functional theory calculations, ultrafast pump-probe, and electrical transport measurements. It is argued that monolayer 1T'-WTe2 , which was predicted to be a semimetallic quantum spin Hall material, is likely a truly 2D quantum spin Hall insulator with a positive quantum spin Hall gap. PMID:27115098
A path integral approach to fractional quantum Hall effect
Kvale, M.N.
1989-01-01
In this paper the author reformulates and further develops the cooperative-ring-exchange (CRE) theory of the fractional quantum Hall effect. Initially, a classical two-dimensional electron gas is considered and a guiding-center approximation is made for strong magnetic fields. The resulting Lagrangian is quantized via path integration and the integral is evaluated using the semiclassical approximation. By considering the CRE processes and a time discretization procedure, the 2DEG is mapped to two different lattice models that bracket the behavior of the system. Analysis of the behavior of the system shows an underlying modular symmetry and allows one to made some new experimental predictions. By interpreting the CRE processes as a loop-space formulation of a lattice gauge field theory, a Landau-Ginzburg action is derived that contains most of the important physics associated with the FQHE and chose ground state can be identified with the Laughlin wave function. Finally, the Laughlin wave function is derived directly from the partition function in the FQHE regime.
Quantum gas mixtures in different correlation regimes
NASA Astrophysics Data System (ADS)
Garcia-March, Miguel Angel; Busch, Thomas
2013-06-01
We present a many-body description for two-component ultracold bosonic gases when one of the species is in the weakly interacting regime and the other is either weakly or strongly interacting. In the one-dimensional limit the latter is a hybrid in which a Tonks-Girardeau gas is immersed in a Bose-Einstein condensate, which is an example of a class of quantum system involving a tunable, superfluid environment. We describe the process of phase separation microscopically as well as semiclassically in both situations and show that quantum correlations are maintained even in the separated phase.
NASA Astrophysics Data System (ADS)
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
Thin films of topological insulators (TIs) with conduction dominated by high mobility topological surface state (TSS) channel have been difficult to achieve due to increased material defects, thus making it difficult to probe TIs in quantum regime. Here by utilizing a structurally matched buffer layer based on In2Se3, we have achieved Bi2Se3 films with low defect density resulting in `order of magnitude' improvement in mobilities and carrier densities. This has led to TSS dominated transport and first observation of quantum Hall effect in Bi2Se3.
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.
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 Entanglement and the Topological Order of Fractional Hall States
NASA Astrophysics Data System (ADS)
Rezayi, Edward
2015-03-01
Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. In collaboration with Clare Abreu and Raul Herrera. Supported by DOE Grant DE-SC0002140.
Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model
NASA Astrophysics Data System (ADS)
Bauer, David; Jackson, T. S.; Roy, Rahul
2016-06-01
We study how the stability of the fractional quantum Hall effect is influenced by the geometry of band structure in lattice Chern insulators. We consider the Hofstadter model, which converges to continuum Landau levels in the limit of small flux per plaquette. This gives us a degree of analytic control not possible in generic lattice models, and we are able to obtain analytic expressions for the relevant geometric criteria. These may be differentiated by whether they converge exponentially or polynomially to the continuum limit. We demonstrate that the latter criteria play a dominant role in predicting the physics of interacting particles in Hofstadter bands in this low flux density regime. In particular, we show that the many-body gap depends monotonically on a band-geometric criterion related to the trace of the Fubini-Study metric.
Hall effect in quantum critical charge-cluster glass
NASA Astrophysics Data System (ADS)
Wu, Jie; Bollinger, Anthony T.; Sun, Yujie
2016-04-01
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.
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. 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.
NASA Astrophysics Data System (ADS)
Stepanov, Petr; Barlas, Yafis; Espiritu, Tim; Che, Shi; Watanabe, Kenji; Taniguchi, Takashi; Smirnov, Dmitry; Lau, Chun Ning
2016-08-01
The copresence of multiple Dirac bands in few-layer graphene leads to a rich phase diagram in the quantum Hall regime. Using transport measurements, we map the phase diagram of BN-encapsulated A B A -stacked trilayer graphene as a function charge density n , magnetic field B , and interlayer displacement field D , and observe transitions among states with different spin, valley, orbital, and parity polarizations. Such a rich pattern arises from crossings between Landau levels from different subbands, which reflect the evolving symmetries that are tunable in situ. At D =0 , we observe fractional quantum Hall (FQH) states at filling factors 2 /3 and -11 /3 . Unlike those in bilayer graphene, these FQH states are destabilized by a small interlayer potential that hybridizes the different Dirac bands.
Quantum Hall Effect in Black Phosphorus Two-dimensional Electron System
NASA Astrophysics Data System (ADS)
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
The recent advent of black phosphorus has greatly enriched the material base of two-dimensional electron systems (2DES). In this work, we reached a milestone in black phosphorus research - the observation of integer quantum Hall (QH) effect in high quality black phosphorus 2DES. We achieved high carrier mobility 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 Hall mobility up to 6000 cm2/Vs. The exceptional mobility enabled us, for the first time, to observe QH 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.
Stepanov, Petr; Barlas, Yafis; Espiritu, Tim; Che, Shi; Watanabe, Kenji; Taniguchi, Takashi; Smirnov, Dmitry; Lau, Chun Ning
2016-08-12
The copresence of multiple Dirac bands in few-layer graphene leads to a rich phase diagram in the quantum Hall regime. Using transport measurements, we map the phase diagram of BN-encapsulated ABA-stacked trilayer graphene as a function charge density n, magnetic field B, and interlayer displacement field D, and observe transitions among states with different spin, valley, orbital, and parity polarizations. Such a rich pattern arises from crossings between Landau levels from different subbands, which reflect the evolving symmetries that are tunable in situ. At D=0, we observe fractional quantum Hall (FQH) states at filling factors 2/3 and -11/3. Unlike those in bilayer graphene, these FQH states are destabilized by a small interlayer potential that hybridizes the different Dirac bands. PMID:27563989
Intrinsic spin hall effect induced by quantum phase transition in HgCdTe quantum wells.
Yang, Wen; Chang, Kai; Zhang, Shou-Cheng
2008-02-01
The spin Hall effect can be induced by both extrinsic impurity scattering and 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. By tuning the Cd content, the well width, or the bias electric field across the quantum well, the intrinsic spin Hall effect can be switched on or off and tuned into resonance under experimentally accessible conditions. PMID:18352404
SO(5) symmetry in the quantum Hall effect in graphene
NASA Astrophysics Data System (ADS)
Wu, Fengcheng; Sodemann, Inti; Araki, Yasufumi; MacDonald, Allan H.; Jolicoeur, Thierry
2014-12-01
Electrons in graphene have four flavors associated with low-energy spin and valley degrees of freedom. The fractional quantum Hall effect in graphene is dominated by long-range Coulomb interactions, which are invariant under rotations in spin-valley space. This SU(4) symmetry is spontaneously broken at most filling factors, and also weakly broken by atomic scale valley-dependent and valley-exchange interactions with coupling constants gz and g⊥. In this paper, we demonstrate that when gz=-g⊥ , an exact SO(5) symmetry survives which unifies the Néel spin order parameter of the antiferromagnetic state and the X Y valley order parameter of the Kekulé distortion state into a single five-component order parameter. The proximity of the highly insulating quantum Hall state observed in graphene at ν =0 to an ideal SO(5) symmetric quantum Hall state remains an open experimental question. We illustrate the physics associated with this SO(5) symmetry by studying the multiplet structure and collective dynamics of filling factor ν =0 quantum Hall states based on exact-diagonalization and low-energy effective theory approaches. This allows to illustrate how manifestations of the SO(5) symmetry would survive even when it is weakly broken.
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.
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
2014-01-01
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
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.
Emergence of integer quantum Hall effect from chaos
NASA Astrophysics Data System (ADS)
Tian, Chushun; Chen, Yu; Wang, Jiao
2016-02-01
We present an analytic microscopic theory showing that in a large class of spin-1/2 quasiperiodic quantum kicked rotors, a dynamical analog of the integer quantum Hall effect (IQHE) emerges from an intrinsic chaotic structure. Specifically, the inverse of the Planck's quantum (he) and the rotor's energy growth rate mimic the "filling fraction" and the "longitudinal conductivity" in conventional IQHE, respectively, and a hidden quantum number is found to mimic the "quantized Hall conductivity." We show that for an infinite discrete set of critical values of he, the long-time energy growth rate is universal and of order of unity ("metallic" phase), but otherwise vanishes ("insulating" phase). Moreover, the rotor insulating phases are topological, each of which is characterized by a hidden quantum number. This number exhibits universal behavior for small he, i.e., it jumps by unity whenever he decreases, passing through each critical value. This intriguing phenomenon is not triggered by the likes of Landau band filling, well known to be the mechanism for conventional IQHE, and far beyond the canonical Thouless-Kohmoto-Nightingale-Nijs paradigm for quantum Hall transitions. Instead, this dynamical phenomenon is of strong chaos origin; it does not occur when the dynamics is (partially) regular. More precisely, we find that a topological object, similar to the topological theta angle in quantum chromodynamics, emerges from strongly chaotic motion at microscopic scales, and its renormalization gives the hidden quantum number. Our analytic results are confirmed by numerical simulations. Our findings indicate that rich topological quantum phenomena can emerge from chaos and might point to a new direction of study in the interdisciplinary area straddling chaotic dynamics and condensed matter physics. This work is a substantial extension of a short paper published earlier by two of us [Y. Chen and C. Tian, Phys. Rev. Lett. 113, 216802 (2014), 10.1103/PhysRevLett.113.216802].
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.
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. PMID:27081998
Dynamical quantum Hall effect in the parameter space
Gritsev, V.; Polkovnikov, A.
2012-01-01
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. PMID:22493228
Non-perturbative approach to the quantum Hall bilayer
NASA Astrophysics Data System (ADS)
Milovanovic, Milica; Papic, Zlatko
2008-03-01
We study the disordering of the superfluid phase in the quantum Hall bilayer at the filling factor one with increasing distance between the layers. We find that the possibilities for ground state wave functions that describe the superfluid at an arbitrary distance fall into two universality classes. They correspond to (1) Berezinskii-Kosterlitz-Thouless (BKT) (2D XY) model of superfluid disordering in the presence of charged impurities and (2) λ transition (3D XY) model in a translatory invariant quantum Hall bilayer system. The BKT type of disordering likely ends with unbinding of created pairs of neutral fermionic vortices (in a transition reminiscent of the one reported in Champagne et al.). In the translatory invariant system the ensuing quantum phase transition proceeds via condensation of loops of elementary charged vortices - merons into a topological phase associated with the toric code model.
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.
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.
Bosonic Integer Quantum Hall Effect in an Interacting Lattice Model
NASA Astrophysics Data System (ADS)
He, Yin-Chen; Bhattacharjee, Subhro; Moessner, R.; Pollmann, Frank
2015-09-01
We study a bosonic model with correlated hopping on a honeycomb lattice, and show that its ground state is a bosonic integer quantum Hall (BIQH) phase, a prominent example of a symmetry-protected topological (SPT) phase. By using the infinite density matrix renormalization group method, we establish the existence of the BIQH phase by providing clear numerical evidence: (i) a quantized Hall conductance with |σx y|=2 , (ii) two counterpropagating gapless edge modes. Our simple model is an example of a novel class of systems that can stabilize SPT phases protected by a continuous symmetry on lattices and opens up new possibilities for the experimental realization of these exotic phases.
Quantum Hall effect and semiconductor-to-semimetal transition in biased black phosphorus
NASA Astrophysics Data System (ADS)
Yuan, Shengjun; van Veen, Edo; Katsnelson, Mikhail I.; Roldán, Rafael
2016-06-01
We study the quantum Hall effect of two-dimensional electron gas in black phosphorus in the presence of perpendicular electric and magnetic fields. In the absence of a bias voltage, the external magnetic field leads to a quantization of the energy spectrum into equidistant Landau levels, with different cyclotron frequencies for the electron and hole bands. The applied voltage reduces the band gap, and eventually a semiconductor-to-semimetal transition takes place. This nontrivial phase is characterized by the emergence of a pair of Dirac points in the spectrum. As a consequence, the Landau levels are not equidistant anymore but follow the ɛn∝√{n B } characteristic of Dirac crystals as graphene. By using the Kubo-Bastin formula in the context of the kernel polynomial method, we compute the Hall conductivity of the system. We obtain a σx y∝2 n quantization of the Hall conductivity in the gapped phase (standard quantum Hall effect regime) and a σx y∝4 (n +1 /2 ) quantization in the semimetallic phase, characteristic of Dirac systems with nontrivial topology.
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.
Low frequency spin dynamics in a quantum Hall canted antiferromagnet
NASA Astrophysics Data System (ADS)
Muraki, Koji
2007-03-01
In quantum Hall (QH) systems, Coulomb interactions combined with the macroscopic degeneracy of Landau levels (LLs) drive the electron system into strongly correlated phases as illustrated by the series of fractional QH effects and may also lead to various forms of broken symmetry dictated by the LL filing factor ν. When two layers of such electron systems are closely separated by a thin tunnel barrier, the addition of interlayer interactions and the layer degree of freedom brings about even richer electronic phases, opening up possibilities for different classes of symmetry breaking. In particular, at total filling factor νT = 2, where the two of the four lowest LLs split by the Zeeman and interlayer tunnel couplings are occupied, the competing degrees of freedom due to the layer and spin are predicted to lead to rich magnetic phases. Here we present results of resistively detected nuclear spin relaxation measurements in closely separated electron systems that reveal strong low-frequency spin fluctuations in the QH regime at νT = 2 [1]. As the temperature is decreased, the spin fluctuations, manifested by a sharp enhancement of the nuclear spin-lattice relaxation rate 1/T1, continue to grow down to the lowest temperature of 66 mK. The observed divergent behavior of 1/T1 signals a gapless spin excitation mode (i.e., a Goldstone mode) and is a hallmark of the theoretically predicted canted antiferromagnetic order. Our data demonstrate the realization of a two-dimensional system with broken planar spin rotational symmetry, in which fluctuations do not freeze out when approaching the zero temperature limit. [1] N. Kumada, K. Muraki, and Y. Hirayama, Science 313, 329 (2006).
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.
Arapov, Yu. G.; Gudina, S. V. Klepikova, A. S.; Neverov, V. N.; Shelushinina, N. G.; Yakunin, M. V.
2015-02-15
The dependences of the longitudinal and Hall resistances on a magnetic field in the integer quantum Hall effect regime in n-InGaAs/GaAs heterostructures with a double quantum well are measured in the range of magnetic fields B = 0–16 T and temperatures T = 0.05–4.2 K, before and after infrared illumination. Analysis of the temperature dependence of the width of transitions between plateaus of the quantum Hall effect is performed in the scope of the scaling hypothesis allowing for electron-electron interaction effects.
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. PMID:27018659
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.
Quantum Hall effect in polycrystalline CVD graphene: grain boundaries impact
NASA Astrophysics Data System (ADS)
Ribeiro-Palau, Rebeca; Lafont, Fabien; Schopfer, Felicien; Poirier, Wilfrid; Bouchiat, Vincent; Han, Zhen; Cresti, Alessandro; Cummings, Aron; Roche, Stephan
2014-03-01
It was demonstrated by Janssen et al. (New J. Phys. 2011) that graphene could surpass GaAs for quantum Hall resistance standards with an accuracy better than 10-10. Graphene should render possible the realization of a standard operating at T > 4 K and B < 4 T, easing its dissemination towards industry. To materialize this goal scalable graphene with outstanding electronic transport properties is required. We present measurements performed in large area Hall bars made of polycrystalline CVD graphene on Si/SiO2, with a carrier mobility of 0.6 T-1. Even at 20.2 T and 300 mK, the Hall resistance plateaus are insufficiently quantized at ν = +/- 2 and +/- 6 . This is due to a high dissipation manifested by a longitudinal resistance which does not drop to zero. We pointed out unusual power-law temperature dependencies of Rxx and an exponential magnetic field dependence. We do not observe the common thermally activated or VRH behaviors. This can be attributed to the grain boundaries in the sample that short-circuit the edge states, as supported by our numerical simulations. This reveals new and peculiar aspects of the quantum Hall effect in polycrystalline systems. Another unexpected feature is the observation of the ν = 0 and 1 states in such low mobility systems.
Interaction driven quantum Hall effect in artificially stacked graphene bilayers.
Iqbal, Muhammad Zahir; Iqbal, Muhammad Waqas; Siddique, Salma; Khan, Muhammad Farooq; Ramay, Shahid Mahmood; Nam, Jungtae; Kim, Keun Soo; Eom, Jonghwa
2016-01-01
The honeycomb lattice structure of graphene gives rise to its exceptional electronic properties of linear dispersion relation and its chiral nature of charge carriers. The exceptional electronic properties of graphene stem from linear dispersion relation and chiral nature of charge carries, originating from its honeycomb lattice structure. Here, we address the quantum Hall effect in artificially stacked graphene bilayers and single layer graphene grown by chemical vapor deposition. The quantum Hall plateaus started to appear more than 3 T and became clearer at higher magnetic fields up to 9 T. Shubnikov-de Hass oscillations were manifestly observed in graphene bilayers texture. These unusual plateaus may have been due to the layers interaction in artificially stacked graphene bilayers. Our study initiates the understanding of interactions between artificially stacked graphene layers. PMID:27098387
Fractionally charged skyrmions in fractional quantum Hall effect.
Balram, Ajit C; Wurstbauer, U; Wójs, A; Pinczuk, A; Jain, J K
2015-01-01
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. PMID:26608906
Interaction driven quantum Hall effect in artificially stacked graphene bilayers
Iqbal, Muhammad Zahir; Iqbal, Muhammad Waqas; Siddique, Salma; Khan, Muhammad Farooq; Ramay, Shahid Mahmood; Nam, Jungtae; Kim, Keun Soo; Eom, Jonghwa
2016-01-01
The honeycomb lattice structure of graphene gives rise to its exceptional electronic properties of linear dispersion relation and its chiral nature of charge carriers. The exceptional electronic properties of graphene stem from linear dispersion relation and chiral nature of charge carries, originating from its honeycomb lattice structure. Here, we address the quantum Hall effect in artificially stacked graphene bilayers and single layer graphene grown by chemical vapor deposition. The quantum Hall plateaus started to appear more than 3 T and became clearer at higher magnetic fields up to 9 T. Shubnikov-de Hass oscillations were manifestly observed in graphene bilayers texture. These unusual plateaus may have been due to the layers interaction in artificially stacked graphene bilayers. Our study initiates the understanding of interactions between artificially stacked graphene layers. PMID:27098387
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.
Disorder-Induced Stabilization of the Quantum Hall Ferromagnet.
Piot, B A; Desrat, W; Maude, D K; Kazazis, D; Cavanna, A; Gennser, U
2016-03-11
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. PMID:27015501
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.}
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.
2015-01-01
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. PMID:26608906
Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid
NASA Astrophysics Data System (ADS)
Parameswaran, S. A.; Kivelson, S. A.; Sondhi, S. L.; Spivak, B. Z.
2011-06-01
The Pfaffian phase in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing energy is small, i.e., in the weak-coupling, BCS limit, where the coherence length is much larger than the charge screening length. We find that, as in a type I superconductor, vortices attract so that, upon varying the magnetic field from its magic value at ν=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffians exemplify a general dichotomy between type I and type II quantum Hall fluids.
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)
Interaction driven quantum Hall effect in artificially stacked graphene bilayers
NASA Astrophysics Data System (ADS)
Iqbal, Muhammad Zahir; Iqbal, Muhammad Waqas; Siddique, Salma; Khan, Muhammad Farooq; Ramay, Shahid Mahmood; Nam, Jungtae; Kim, Keun Soo; Eom, Jonghwa
2016-04-01
The honeycomb lattice structure of graphene gives rise to its exceptional electronic properties of linear dispersion relation and its chiral nature of charge carriers. The exceptional electronic properties of graphene stem from linear dispersion relation and chiral nature of charge carries, originating from its honeycomb lattice structure. Here, we address the quantum Hall effect in artificially stacked graphene bilayers and single layer graphene grown by chemical vapor deposition. The quantum Hall plateaus started to appear more than 3 T and became clearer at higher magnetic fields up to 9 T. Shubnikov-de Hass oscillations were manifestly observed in graphene bilayers texture. These unusual plateaus may have been due to the layers interaction in artificially stacked graphene bilayers. Our study initiates the understanding of interactions between artificially stacked graphene layers.
Fractionally charged skyrmions in fractional quantum Hall effect
NASA Astrophysics Data System (ADS)
Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; Pinczuk, A.; Jain, J. K.
2015-11-01
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.
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.
Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene
NASA Astrophysics Data System (ADS)
Feldman, Benjamin E.; Krauss, Benjamin; Smet, Jurgen H.; Yacoby, Amir
2012-09-01
Graphene provides a rich platform to study many-body effects, owing to its massless chiral charge carriers and the fourfold degeneracy arising from their spin and valley degrees of freedom. We use a scanning single-electron transistor to measure the local electronic compressibility of suspended graphene, and we observed an unusual pattern of incompressible fractional quantum Hall states that follows the standard composite fermion sequence between filling factors ν = 0 and 1 but involves only even-numerator fractions between ν = 1 and 2. We further investigated this surprising hierarchy by extracting the corresponding energy gaps as a function of the magnetic field. The sequence and relative strengths of the fractional quantum Hall states provide insight into the interplay between electronic correlations and the inherent symmetries of graphene.
Contrasting energy scales of reentrant integer quantum Hall states
NASA Astrophysics Data System (ADS)
Deng, Nianpei; Watson, J. D.; Rokhinson, L. P.; Manfra, M. J.; Csáthy, G. A.
2012-11-01
We report drastically different onset temperatures of the reentrant integer quantum Hall states in the second and third Landau level. This finding is in quantitative disagreement with the Hartree-Fock theory of the bubble phases which is thought to describe these reentrant states. Our results indicate that the number of electrons per bubble in either the second or the third Landau level is likely different than predicted.
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.
Kac Moody theories for colored phase space (quantum Hall) droplets
NASA Astrophysics Data System (ADS)
Polychronakos, Alexios P.
2005-04-01
We derive the canonical structure and Hamiltonian for arbitrary deformations of a higher-dimensional (quantum Hall) droplet of fermions with spin or color on a general phase space manifold. Gauge fields are introduced via a Kaluza-Klein construction on the phase space. The emerging theory is a nonlinear higher-dimensional generalization of the gauged Kac-Moody algebra. To leading order in ℏ this reproduces the edge state chiral Wess-Zumino-Witten action of the droplets.
Quantum Hall effect in graphene decorated with disordered multilayer patches
Nam, Youngwoo; Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-412 96 Gothenburg ; 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.
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.
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
2015-12-01
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. PMID:26583739
Koirala, Nikesh; Han, Myung -Geun; Brahlek, Matthew; Salehi, Maryam; Wu, Liang; Dai, Jixia; Waugh, Justin; Nummy, Thomas; Moon, Jisoo; Zhu, Yimei; et al
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}.
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.
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.
Quantum Hall effect in exfoliated graphene affected by charged impurities: Metrological measurements
NASA Astrophysics Data System (ADS)
Guignard, J.; Leprat, D.; Glattli, D. C.; Schopfer, F.; Poirier, W.
2012-04-01
Metrological investigations of the quantum Hall effect (QHE) completed by transport measurements at low magnetic field are carried out in a-few-μm-wide Hall bars made of monolayer (ML) or bilayer (BL) exfoliated graphene transferred on Si/SiO2 substrate. From the charge carrier density dependence of the conductivity and from the measurement of the quantum corrections at low magnetic field, we deduce that transport properties in these devices are mainly governed by the Coulomb interaction of carriers with a large concentration of charged impurities. In the QHE regime, at high magnetic field and low temperature (T<1.3 K), the Hall resistance is measured by comparison with a GaAs-based quantum resistance standard using a cryogenic current comparator. In the low-dissipation limit, it is found quantized within 5 parts in 107 (one standard deviation, 1σ) at the expected rational fractions of the von Klitzing constant, respectively, RK/2 and RK/4 in the ML and BL devices. These results constitute the most accurate QHE quantization tests to date in monolayer and bilayer exfoliated graphene. It turns out that a main limitation to the quantization accuracy, which is found well above the 10-9 accuracy usually achieved in GaAs, is the low value of the QHE breakdown current being no more than 1μA. The current dependence of the longitudinal conductivity investigated in the BL Hall bar shows that dissipation occurs through quasielastic inter-Landau-level scattering, assisted by large local electric fields. We propose that charged impurities are responsible for an enhancement of such inter-Landau-level transition rate and cause small breakdown currents.
Hall effect in quantum critical charge-cluster glass
Bozovic, Ivan; Wu, Jie; Bollinger, Anthony T.; Sun, Yujie
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
Discovery of competing 5/2 fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Lin, Xi; Fu, Hailong; Wang, Pengjie; Shan, Pujia; Xiong, Lin; Pfeiffer, Loren; West, Ken; Kastner, Marc
With an even denominator, ν = 5 / 2 fractional quantum Hall state (FQH) is different from most of the other FQH states. Some of its proposed wave functions may exhibit novel non-Abelian statistics, which is related to topological quantum computation. We carried out tunneling measurements within a quantum point contact (QPC) at the 5/2 state and we were able to match the QPC's density to the two-dimensional electron gas bulk density. Such a density match guarantees the uniform filling factor inside and outside the QPC. The interaction parameter g and the effective charge e* can be extracted through the weak tunneling theory. We found g and e* similar to what people believed to be the Abelian 331 state. By tuning the confinement, we observed another region where the experimental data agree well with the weak tunneling theory, which leads to e* =0.25 and g =0.52, implying non-Abelian wavefunctions such as anti-Pfaffian or U(1)×SU2(2). Our discovery suggests that there are competing 5/2 fractional quantum Hall ground states depending on the confinement. The work at PKU was funded by NSFC and NBRPC. The work at Princeton University was funded by the Gordon and Betty Moore Foundation through the EPiQS initiative Grant GBMF4420, and by the National Science Foundation MRSEC Grant DMR-1420541.
Application of the quantum Hall effect to resistance metrology
NASA Astrophysics Data System (ADS)
Poirier, Wilfrid; Schopfer, Félicien; Guignard, Jérémie; Thévenot, Olivier; Gournay, Pierre
2011-05-01
The quantum Hall effect (QHE) discovery has revolutionized metrology by providing with a representation of the unit of resistance, R, that can be reproduced within a relative uncertainty of one part in 10 9 and is theoretically only linked to Planck's constant h and the electron charge e. This breakthrough also results from the development of resistance comparison bridges using cryogenic current comparator (CCC). The QHE experimental know-how now allows the realization of perfectly quantized Quantum Hall Array Resistance Standards (QHARS) by combining a large number of single Hall bars. In the context of an evolution of the Système International (SI) of units by fixing some fundamental constants of physics, the determination of the von Klitzing constant R through the use of the so-called Thompson-Lampard calculable capacitor and the realization of refined universality tests of the QHE are of prime importance. Finally, the fascinating graphene material might be a new turning point in resistance metrology.
Interlayer tunneling in double-layer quantum hall pseudoferromagnets.
Balents, L; Radzihovsky, L
2001-02-26
We show that the interlayer tunneling I-V in double-layer quantum Hall states displays a rich behavior which depends on the relative magnitude of sample size, voltage length scale, current screening, disorder, and thermal lengths. For weak tunneling, we predict a negative differential conductance of a power-law shape crossing over to a sharp zero-bias peak. An in-plane magnetic field splits this zero-bias peak, leading instead to a "derivative" feature at V(B)(B(parallel)) = 2 pi Planck's over 2 pi upsilon B(parallel)d/e phi(0), which gives a direct measurement of the dispersion of the Goldstone mode corresponding to the spontaneous symmetry breaking of the double-layer Hall state. PMID:11290258
Edge states and integer quantum Hall effect in topological insulator thin films.
Zhang, Song-Bo; Lu, Hai-Zhou; Shen, Shun-Qing
2015-01-01
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. PMID:26304795
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
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.
Four-Dimensional Quantum Hall Effect with Ultracold Atoms
NASA Astrophysics Data System (ADS)
Price, H. M.; Zilberberg, O.; Ozawa, T.; Carusotto, I.; Goldman, N.
2015-11-01
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.
Topological polaritons in a quantum spin Hall cavity
NASA Astrophysics Data System (ADS)
Janot, Alexander; Rosenow, Bernd; Refael, Gil
2016-04-01
We study the topological structure of matter-light excitations, so-called polaritons, in a quantum spin Hall insulator coupled to photonic cavity modes. We identify a topological invariant in the presence of time reversal (TR) symmetry, and demonstrate the existence of a TR-invariant topological phase. We find protected helical edge states with energies below the lower polariton branch and characteristic uncoupled excitonic states, both detectable by optical techniques. Applying a Zeeman field allows us to relate the topological index to the double coverage of the Bloch sphere by the polaritonic pseudospin.
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.
Topological superconductivity in quantum Hall-superconductor hybrid systems
NASA Astrophysics Data System (ADS)
Zocher, Björn; Rosenow, Bernd
2016-06-01
We develop a scenario to engineer a topological phase with Majorana edge states based on an integer quantum Hall (QH) system proximity coupled to a superconductor (SC). Due to the vortices in the SC order parameter, the SC-QH hybrid system is described by a Bloch problem with ten unpaired momenta, corresponding to the maxima and saddle points of the SC order parameter. For external potentials respecting the symmetry of the vortex lattice, the states with unpaired momenta have degeneracies such that the system always is in a trivial phase. However, an incommensurate potential can lift the degeneracies and drive the system into a topologically nontrivial phase.
Quantum Hall effect in supersymmetric Chern-Simons theories
NASA Astrophysics Data System (ADS)
Tong, David; Turner, Carl
2015-12-01
We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantize the vortices and, by relating their dynamics to a matrix model, show that their ground state wave function is in the same universality class as the Laughlin state. We further construct coherent state representations of the excitations of a finite number of vortices. These are quasiholes. By an explicit computation of the Berry phase, without resorting to a plasma analogy, we show that these excitations have fractional charge and spin.
Quantum Hall States and Phase Diagram of Bilayer Graphene
NASA Astrophysics Data System (ADS)
Jia, Junji
2013-03-01
The quantum Hall states of bilayer graphene for filling factor ν from 0 to 4 are investigated using lowest Landau level approximation. A critical line in the E⊥B plane for both the ν = 0 and 1 case is found. This line separates the (partially) spin polarized and (partially) layer polarized phases in the ν = 0 (1) case. The gaps for all ν are found to scale linearly with B. The existence of phase separation line, the linearity of the gaps, and the hierarchy for gaps of different ν agree well with experiments.
Magnetic phase diagram of ν=2 quantum Hall systems
NASA Astrophysics Data System (ADS)
Yoshizawa, Kanako; Takayanagi, Kazuo
2009-03-01
We present the magnetic phase diagram of the ν=2 quantum Hall system on the whole (rs,EZ) plane. We fix the phase boundaries of the paramagnetic and ferromagnetic states by looking for a softening of spin-density excitations in the time-dependent Hartree-Fock theory. A nontrivial phase is obtained in the self-consistent Hartree-Fock theory for rs˜2 and EZ≲0.06ℏωc , where both the paramagnetic and ferromagnetic states show spin instability. We show that the obtained phase is the spin-density wave (SDW) state, and explain the mechanism how the SDW stabilizes.
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.
Matrix method analysis of quantum Hall effect device connections
NASA Astrophysics Data System (ADS)
Ortolano, M.; Callegaro, L.
2012-02-01
The modelling of electrical connections of single, or several, multiterminal quantum Hall effect (QHE) devices is relevant for electrical metrology: it is known, in fact, that certain particular connections allow (i) the realization of multiples or fractions of the quantized resistance, or (ii) the rejection of stray impedances, so that the configuration maintains the status of quantum standard. Ricketts-Kemeny and Delahaye equivalent circuits are known to be accurate models of the QHE: however, the numerical or analytical solution of electrical networks including these equivalent circuits can be difficult. In this paper, we introduce a method of analysis based on the representation of a QHE device by means of the indefinite admittance matrix: external connections are then represented with another matrix, easily written by inspection. Some examples, including the solution of double- and triple-series connections, are shown.
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.
Quantum Hall effect in a system with an electron reservoir
NASA Astrophysics Data System (ADS)
Dorozhkin, S. I.
2016-04-01
Precise measurements of the magnetic-field and gate-voltage dependences of the capacitance of a field-effect transistor with an electron system in a wide GaAs quantum well have been carried out. It has been found that the capacitance minima caused by the gaps in the Landau spectrum of the electron system become anomalously wide when two size-quantization subbands are occupied. The effect is explained by retention of the chemical potential in the gap between the Landau levels of one of the subbands owing to redistribution of electrons between the subbands under a change in the magnetic field. The calculation taking into account this redistribution has been performed in a model of the electron system formed by two two-dimensional electron layers. The calculation results describe both the wide capacitance features and the observed disappearance of certain quantum Hall effect states.
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.
Optical Imaging of Quantum Hall Current in GaAs/AlGaAs Two-dimensional Electron System
NASA Astrophysics Data System (ADS)
Oto, K.; Kaneko, S.; Inaba, R.; Takada, Y.; Yamada, T.; Muro, K.
2010-01-01
We have measured the current distribution in GaAs/AlGaAs two-dimensional electron system at quantum Hall effect regime, where the critical current shows sub-linear dependence on the channel width. An optical-fiber-based potential imaging system by Pockels effect is improved by using a twin-optical bridge detector which reduces retardation noise in the optical fiber. We have also mapped the resistance change by the local photo-excitation in the QHE regime. Both the observed images show the evidence of current concentration at center region of the channel, and the extent of current concentration increases with increasing the current.
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 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 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.
Missing fractional quantum Hall states in ZnO
NASA Astrophysics Data System (ADS)
Luo, Wenchen; Chakraborty, Tapash
2016-04-01
We have analyzed the crucial role a proper form of the Coulomb interaction plays on the even and odd denominator fractional quantum Hall effects in a two-dimensional electron gas (2DEG) in the ZnO heterointerface. In this system, the Landau level gaps are much smaller than those in conventional GaAs systems. The Coulomb interaction is also very large compared to the Landau level gap even in very high magnetic fields. We therefore consider the influence of higher Landau levels by considering the screened Coulomb potential in the random-phase approximation. Interestingly, our exact diagonalization studies of the collective modes with this screened potential successfully explain recent experiments of even and odd denominator fractional quantum Hall effects, in particular, the unexpected absence of the 5/2 state and the presence of the 9/2 state in ZnO. Additionally, our study also reveals a strong presence of spin-reversed excitations in the 7/2 state in accordance with the experimental observation.
Quantum anomalous Hall effect in magnetic topological insulators
NASA Astrophysics Data System (ADS)
Wang, Jing; Lian, Biao; Zhang, Shou-Cheng
2015-12-01
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. 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.
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
Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene
NASA Astrophysics Data System (ADS)
Feldman, Benjamin; Krauss, Benjamin; Smet, Jurgen; Yacoby, Amir
2012-02-01
Graphene provides a unique platform to study many-body correlations due to the relativistic nature of its charge carriers and their fourfold degeneracy. We report local electronic compressibility measurements of a suspended graphene flake performed using a scanning single-electron transistor. Between filling factors v = 0 and 1, our measurements reveal incompressible fractional quantum Hall states at v = 1/3, 2/3, 2/5, 3/5, 3/7, 4/7 and 4/9, which clearly follow the standard composite fermion sequence. In contrast, between v = 1 and 2, incompressible states occur only at v = 4/3, 8/5, 10/7 and 14/9. These fractions correspond to a subset of the composite fermion sequence involving only even numerators, suggesting a robust underlying symmetry. We extract the energy gaps of each fractional quantum Hall state as a function of magnetic field and find that v = 1/3, 2/3, 4/3, and 8/5 are strongest at low field, persisting below 1.5 T. Our results provide insight into the interplay between electronic correlations and SU(4) symmetry in graphene.
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. PMID:26722936
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.
NASA Astrophysics Data System (ADS)
Lewis, Rupert Murray
The quantum Hall effect appears in two-dimensional electron gases (2DEG's) confined at the interfaces of semiconductor heterostructures. The plateau regions are electrical insulators while the transition between the plateaus is metallic. Two techniques have been used to study aspects of this insulating behavior; heating experiments using DC techniques and localization length spectroscopy through high frequency transport experiments. Heating experiments pump energy into a system while the experimenter observes the physical mechanisms that nature uses to remove this energy. The principle mechanism for energy removal from 2DEG's is the interaction of electrons with phonons. We have performed heating experiments from the center of the plateaus, moving outwards towards the transition region. A relationship between the input power and the effective electron temperature P ˜ Tp+2 is found to exist. At the center of the plateaus p + 2 = 5 but near the plateau edges p + 2 ≈ 4. Simultaneously, the phonon emission rate ( t-1e-ph ) from the hot electron system has been measured. We find t-1e-ph to be about 1 x 108 T 3 K-3s-1 at odd plateaus and about 10 times smaller (1 x 107 T 3 K-3s-1) at even plateaus. A new technique for probing the electron localization length via microwave transport measurements has been developed. Using a resonant technique, the real and imaginary parts of the longitudinal conductivity (sigma xx) are measured for frequencies 1.25 ≤ f ≤ 10 GHz. This is the first experiment to closely examine the insulating quantum Hall plateau regime at these frequencies whereas previous experiments have focused on the sigmaxx peaks between plateaus. The real part of sigmaxx is found to scale linearly with frequency, i.e. sigmaxx ˜ xi f where xi is the localization length. The scaled conductivity allows calculation of the localization length of electrons in the quantum Hall plateaus. The measurement agrees with localization length measurements made at DC.
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.
Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
NASA Astrophysics Data System (ADS)
Mong, Roger
2014-03-01
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p + ip superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the Z3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge- 2 e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that--unlike Ising anyons--allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics.
Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure
NASA Astrophysics Data System (ADS)
Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul; Nayak, Chetan; Oreg, Yuval; Stern, Ady; Berg, Erez; Shtengel, Kirill; Fisher, Matthew P. A.
2014-01-01
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the Z3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that—unlike Ising anyons—allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a twofold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types, yet depending on nonuniversal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.
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).
Deconstructing the Liouvillian approach to the quantum Hall plateau transition
NASA Astrophysics Data System (ADS)
Oganesyan, Vadim; Chalker, J. T.; Sondhi, S. L.
2003-07-01
We examine the Liouvillian approach to the quantum Hall plateau transition, as introduced recently by Sinova, Meden, and Girvin [Phys. Rev. B 62, 2008 (2000)] and developed by Moore, Zee, and Sinova [Phys. Rev. Lett. 87, 046801 (2001)]. We show that, despite appearances to the contrary, the Liouvillian approach is not specific to the quantum mechanics of particles moving in a single Landau level: we formulate it for a general disordered single-particle Hamiltonian. We next examine the relationship between Liouvillian perturbation theory and conventional calculations of disorder-averaged products of Green functions and show that each term in Liouvillian perturbation theory corresponds to a specific contribution to the two-particle Green function. As a consequence, any Liouvillian approximation scheme may be reexpressed in the language of Green functions. We illustrate these ideas by applying Liouvillian methods (including their extension to NL>1 Liouvillian flavors) to random matrix ensembles, using numerical calculations for small integer NL and an analytical analysis for large NL. We find that the behavior at NL>1 is different in qualitative ways from that at NL=1. In particular, the NL=∞ limit expressed using Green functions generates a pathological approximation, in which two-particle correlation functions fail to factorize correctly at large separations of their energy, and exhibit spurious singularities inside the band of random matrix energy levels. We also consider the large-NL treatment of the quantum Hall plateau transition, showing that the same undesirable features are present there, too. We suggest that failings of this kind are likely to be generic in Liouvillian approximation schemes.
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.
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.
Superconducting proximity effect in graphene: Injecting Cooper pairs in quantum Hall edge states
NASA Astrophysics Data System (ADS)
Komatsu, Katsuyoshi; Li, Chuan; Autier-Laurent, Sandrine; Kasumov, Alik; Bouchiat, Helene; Gueron, Sophie
2012-02-01
A superconductor-graphene(SG) hybrid system, such as an SGS junction or an SG interface, provides an ideal platform to investigate the relativistic nature of Dirac fermions combined with superconductivity. Instead of the retro-reflection of carriers in an ordinary superconductor-normal metal interface, an SG interface is theoretically predicted to show the specular reflection of quasiparticle carriers. We show that a supercurrent flows through a SGS junction with Nb electrodes even through a very long graphene distance of 1.2μm, more than 3 times the length previously reported. This supercurrent disappears in the vicinity of the Dirac point, indicating a strong sensitivity of the transmission of Andreev pairs to the formation of charge puddles with size greater than the superconducting coherence length. We also present data on similar size graphene samples with superconducting electrodes with a high critical field (more than 7Tesla) for which the properties of the normal state are dominated by quantum Hall physics. Whereas the behavior of the supercurrent is similar to the Nb/Graphene/Nb system in zero field, new features are observed in the high field quantum Hall regime.
Edge mode velocities in the quantum Hall effect from a dc measurement
NASA Astrophysics Data System (ADS)
Zucker, P. T.; Feldman, D. E.
2015-11-01
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.
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.
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
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.
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.
Local compressibility of bilayer graphene in the quantum hall regime
NASA Astrophysics Data System (ADS)
Levin, Andrei; Kou, Angela; Feldman, Benjamin; Halperin, Bertrand; Watanabe, Kenji; Taniguchi, Takashi; Yacoby, Amir
2014-03-01
In the presence of a strong magnetic field, the charge carriers in bilayer graphene (BLG) condense into a set of flat energy bands called Landau levels (LLs). Electronic compressibility measurements have historically been a powerful tool in studying the physics of partially filled LLs in two-dimensional electronic systems. In particular, electron-electron correlations arising from Coulomb interactions can introduce a negative component to the compressibility. Here we present measurements of electronic compressibility in BLG, performed locally using a scanning single electron transistor. We find that while the inverse compressibility is close to zero for 4 < | ν | < 8 , it is markedly more negative in the lowest LL, | ν | < 4 . Moreover, within the lowest LL, the background inverse compressibility between integer filling also exhibits a stark even-odd asymmetry. It is more negative when starting to fill from an even filling factor than when starting to fill from an odd filling factor, exhibiting a ν --> ν + 2 symmetry and indicating the important role of the orbital degeneracy uniquely present in bilayer graphene.
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.
Partial heating between counter propagating quantum Hall edge channels
NASA Astrophysics Data System (ADS)
Washio, Kazuhisa; Nakazawa, Ryo; Hashisaka, Masayuki; Muraki, Koji; Fujisawa, Toshimasa
2014-03-01
In contrast to clear unidirectional charge flow in quantum Hall edge channels, heat transport and equilibration remain veiled. Most of the previous works were concentrated on heating between co-propagating edge channels, where co-propagating charge and spin modes are formed by the Coulomb interaction. Here, we investigate heating between counter propagating edge channels separated by a narrow surface gate of the width 0.1 μm, where the plasmon coupling forms counter-propagating dragging modes. One edge channel is directly heated up by a quantum point contact at its half transmission, and energy spectrum of the other edge channel is evaluated by quantum dot thermometry. We observed partial heating in the spectrum, where a small fraction (1-5 percent) of electrons is highly excited over the original Fermi distribution, for an interaction length of 5-10 μm in the coupled channels. This can be understood by considering weak scattering process between the channels. The flow of this non-equilibrium distribution will be discussed with different configurations of heating and detecting channels in terms of the chirality and the dragging modes. JSPS KAKENHI Grant Numbers 21000004, 24009291.
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
Pure scaling operators at the integer quantum Hall plateau transition.
Bondesan, R; Wieczorek, D; Zirnbauer, M R
2014-05-01
Stationary wave functions at the transition between plateaus of the integer quantum Hall effect are known to exhibit multifractal statistics. Here we explore this critical behavior for the case of scattering states of the Chalker-Coddington network model with point contacts. We argue that moments formed from the wave amplitudes of critical scattering states decay as pure powers of the distance between the points of contact and observation. These moments in the continuum limit are proposed to be correlation functions of primary fields of an underlying conformal field theory. We check this proposal numerically by finite-size scaling. We also verify the conformal field theory prediction for a three-point function involving two primary fields. PMID:24856714
Braiding non-Abelian quasiholes in fractional quantum Hall states.
Wu, Yang-Le; Estienne, B; Regnault, N; Bernevig, B Andrei
2014-09-12
Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the Z_{3} Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the Z_{3} Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the nonunitary Gaffnian wave function. PMID:25259996
Quantum hall plateau transition at order 1/N.
Moore, J E; Zee, A; Sinova, J
2001-07-23
The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law delocalization near the discrete extended-state energies E(n) = Planck's over 2piomega(c)(n+1 / 2), we study a generalization of the disorder-averaged Liouvillian framework for the lowest Landau level to N flavors of electron densities ( N = 1 for the physical case). We find analytically the large- N limit and 1/N corrections for all disorder strengths: at N = infinity this gives an estimate of the critical conductivity, and at order 1/N an estimate of the localization exponent nu. PMID:11461633
Unconventional spin texture in a noncentrosymmetric quantum spin Hall insulator
NASA Astrophysics Data System (ADS)
Mera Acosta, C.; Babilonia, O.; Abdalla, L.; Fazzio, A.
2016-07-01
We propose that the simultaneous presence of both Rashba and band inversion can lead to a Rashba-like spin splitting formed by two bands with the same in-plane helical spin texture. Because of this unconventional spin texture, the backscattering is forbidden in edge and bulk conductivity channels. We propose a noncentrosymmetric honeycomb-lattice quantum spin Hall (QSH) insulator family formed by the IV, V, and VII elements with this property. The system formed by Bi, Pb, and I atoms is mechanically stable and has both a large Rashba spin splitting of 60 meV and a large nontrivial band gap of 0.14 eV. Since the edge and the bulk states are protected by the time-reversal (TR) symmetry, contrary to what happens in most doped QSH insulators, the bulk states do not contribute to the backscattering in the electronic transport, allowing the construction of a spintronic device with less energy loss.
Electronic simulation of a multiterminal quantum Hall effect device
NASA Astrophysics Data System (ADS)
Sosso, A.; Capra, P. P.
1999-04-01
A circuit with only resistors and unity gain amplifiers can be proven to be equivalent to the Ricketts and Kemeny electrical model of multiterminal quantum Hall effect (QHE) devices. By means of the new equivalent circuit, commercial software for electronic circuit analysis can be used to study a QHE measurement system. Moreover, it can be easily implemented, and we were able to build a circuit that simulates the electrical behavior of a QHE device. Particular care was taken in the design to reduce the effect of parasitic capacitances, which act as loads connected to the device terminals. Bootstrap buffers have been adopted to significantly reduce the capacitance of input stage. The small residual loading effect can be calculated and eliminated, allowing simulation of a QHE device with good accuracy.
Aspects of anisotropic fractional quantum Hall effect in phosphorene
NASA Astrophysics Data System (ADS)
Ghazaryan, Areg; Chakraborty, Tapash
2015-10-01
We have analyzed the effects of the anisotropic energy bands of phosphorene on magnetoroton branches for electrons and holes in the two Landau levels close to the band edges. We have found that the fractional quantum Hall effect gap in the lowest (highest) Landau level in the conduction (valence) band is slightly larger than that for conventional semiconductor systems and therefore the effect should be experimentally observable in phosphorene. We also found that the magnetoroton mode for both electrons and holes consists of two branches with two minima due to the anisotropy. Most importantly, in the long-wavelength limit a second mode with upward dispersion, well separated from the magnetoroton mode was found to appear, that is entirely a consequence of the anisotropy in the system. These novel features of the collective mode, unique to phosphorene, can be observed in resonant inelastic light-scattering experiments.
Geometry of quantum Hall states: Gravitational anomaly and transport coefficients
NASA Astrophysics Data System (ADS)
Can, Tankut; Laskin, Michael; Wiegmann, Paul B.
2015-11-01
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.
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. PMID:18764355
Theory of Activated Transport in Bilayer Quantum Hall Systems
NASA Astrophysics Data System (ADS)
Roostaei, Bahman; Fertig, Herbert; Mullen, Kieran; Simon, Steven
2008-03-01
We analyze the transport properties of bilayer quantum Hall systems at total filling factor ν= 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. We conclude with predictions for future experiments.
Theory of Activated Transport in Bilayer Quantum Hall Systems
NASA Astrophysics Data System (ADS)
Roostaei, B.; Mullen, K. J.; Fertig, H. A.; Simon, S. H.
2008-07-01
We analyze the transport properties of bilayer quantum Hall systems at total filling factor ν=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.
Observing the Quantum Spin Hall Effect with Ultracold Atoms
NASA Astrophysics Data System (ADS)
Vaishnav, J. Y.; Stanescu, Tudor D.; Clark, Charles W.; Galitski, Victor
2009-03-01
The quantum spin Hall (QSH) state is a topologically nontrivial state of matter proposed to exist in certain 2-D systems with spin-orbit coupling. While the electronic states of a QSH insulator are gapped in the bulk, a QSH insulator is characterized by gapless edge states of different spins which counterpropagate at a given edge; the spin is correlated with the direction of propagation. Recent proposals ootnotetextT. D. Stanescu, C. Zhang, V. Galitski, Physical Review Letters 99, 110403 (2007), J. Y. Vaishnav, Charles W. Clark, Physical Review Letters 100, 153002 (2008). suggest that synthetic spin-orbit couplings can be created for cold atoms moving in spatially varying light fields. Here, we identify an optical lattice setup which generates an effective QSH effect for cold, multilevel atoms. We also discuss methods for experimental detection of the atomic QSH effect.
Quantum Hall Exciton Condensation at Full Spin Polarization
NASA Astrophysics Data System (ADS)
Finck, A. D. K.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2010-03-01
Using Coulomb drag as a probe, we explore the excitonic phase transition in quantum Hall bilayers at νT=1 as a function of Zeeman energy, EZ. The critical layer separation (d/l)c for exciton condensation initially increases rapidly with EZ, but then reaches a maximum and begins a gentle decline. At high EZ, 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 EZ 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 Hall Exciton Condensation at Full Spin Polarization
NASA Astrophysics Data System (ADS)
Finck, A. D. K.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2010-01-01
Using Coulomb drag as a probe, we explore the excitonic phase transition in quantum Hall bilayers at νT=1 as a function of Zeeman energy EZ. The critical layer separation (d/ℓ)c for exciton condensation initially increases rapidly with EZ, but then reaches a maximum and begins a gentle decline. At high EZ, 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 EZ 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.
Spin quantum Hall effects in featureless nonfractionalized spin-1 magnets
NASA Astrophysics Data System (ADS)
Lu, Yuan-Ming; Lee, Dung-Hai
2014-05-01
The Affleck-Kennedy-Lieb-Tasaki state (or Haldane phase) in a spin-1 chain represents a large class of gapped topological paramagnets that host symmetry-protected gapless excitations on the boundary. In this work, we show how to realize this type of featureless spin-1 state on a generic two-dimensional lattice. These states have a gapped spectrum in the bulk, but they support gapless edge states protected by spin rotational symmetry along a certain direction, and they exhibit the spin quantum Hall effect. Using a fermion representation of integer spins, we show a concrete example of such spin-1 topological paramagnets on a kagome lattice, and we suggest a microscopic spin-1 Hamiltonian that may realize it.
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.
Quantum spin hall insulators in strain-modified arsenene
NASA Astrophysics Data System (ADS)
Zhang, Haijun; Ma, Yandong; Chen, Zhongfang
2015-11-01
By means of density functional theory (DFT) computations, we predict that the suitable strain modulation of honeycomb arsenene results in a unique two-dimensional (2D) topological insulator (TI) with a sizable bulk gap (up to 696 meV), which could be characterized and utilized at room temperature. Without considering any spin-orbit coupling, the band inversion occurs around the Gamma (G) point at tensile strains larger than 11.7%, which indicates the quantum spin Hall effect in arsenene at appropriate strains. The nontrivial topological phase was further confirmed by the topological invariant ν = 1 and edge states with a single Dirac-type crossing at the G point. Our results provide a promising strategy for designing 2D TIs with large bulk gaps from commonly used materials.By means of density functional theory (DFT) computations, we predict that the suitable strain modulation of honeycomb arsenene results in a unique two-dimensional (2D) topological insulator (TI) with a sizable bulk gap (up to 696 meV), which could be characterized and utilized at room temperature. Without considering any spin-orbit coupling, the band inversion occurs around the Gamma (G) point at tensile strains larger than 11.7%, which indicates the quantum spin Hall effect in arsenene at appropriate strains. The nontrivial topological phase was further confirmed by the topological invariant ν = 1 and edge states with a single Dirac-type crossing at the G point. Our results provide a promising strategy for designing 2D TIs with large bulk gaps from commonly used materials. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr05006e
Repulsive interactions in quantum Hall systems as a pairing problem
NASA Astrophysics Data System (ADS)
Ortiz, G.; Nussinov, Z.; Dukelsky, J.; Seidel, A.
2013-10-01
A subtle relation between quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin-type Hamiltonians that arise in (px+ipy) superconductivity. Specifically, we show that general Haldane pseudopotentials (and their sums) can be expressed as a sum of repulsive noncommuting (px+ipy)-type pairing Hamiltonians. The determination of the spectrum and individual null spaces of each of these noncommuting Richardson-Gaudin-type Hamiltonians is nontrivial yet is Bethe ansatz solvable. For the Laughlin sequence, it is observed that this problem is frustration free and zero-energy ground states lie in the common null space of all of these noncommuting Hamiltonians. This property allows for the use of a new truncated basis of pairing configurations in which to express Laughlin states at general filling factors. We prove separability of arbitrary Haldane pseudopotentials, providing explicit expressions for their second quantized forms, and further show by explicit construction how to exploit the topological equivalence between different geometries (disk, cylinder, and sphere) sharing the same topological genus number, in the second quantized formalism, through similarity transformations. As an application of the second quantized approach, we establish a “squeezing principle” that applies to the zero modes of a general class of Hamiltonians, which includes but is not limited to Haldane pseudopotentials. We also show how one may establish (bounds on) “incompressible filling factors” for those Hamiltonians. By invoking properties of symmetric polynomials, we provide explicit second quantized quasihole generators; the generators that we find directly relate to bosonic chiral edge modes and further make aspects of dimensional reduction in the quantum Hall systems
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. PMID:26372787
Long-lived binary tunneling spectrum in the quantum Hall Tomonaga-Luttinger liquid
NASA Astrophysics Data System (ADS)
Washio, K.; Nakazawa, R.; Hashisaka, M.; Muraki, K.; Tokura, Y.; Fujisawa, T.
2016-02-01
The existence of long-lived nonequilibrium states without showing thermalization, which has previously been demonstrated in time evolution of ultracold atoms, suggests the possibility of their spatial analog in transport behavior of interacting electrons in solid-state systems. Here we report long-lived nonequilibrium states in one-dimensional edge channels in the integer quantum Hall regime. An indirect heating scheme in a counterpropagating configuration is employed to generate a nontrivial binary spectrum consisting of high- and low-temperature components. This unusual spectrum is sustained even after traveling 5-10 μ m , much longer than the length for electronic relaxation (about 0.1 μ m ), without showing significant thermalization. This observation is consistent with the integrable model of Tomonaga-Luttinger liquid. The long-lived spectrum implies that the system is well described by noninteracting plasmons, which are attractive for carrying information for a long distance.
Evidence for a fractional fractal quantum Hall effect in graphene superlattices.
Wang, Lei; Gao, Yuanda; Wen, Bo; Han, Zheng; Taniguchi, Takashi; Watanabe, Kenji; Koshino, Mikito; Hone, James; Dean, Cory R
2015-12-01
The Hofstadter energy spectrum provides a uniquely tunable system to study emergent topological order in the regime of strong interactions. Previous experiments, however, have been limited to low Bloch band fillings where only the Landau level index plays a role. We report measurements of high-mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. We observed coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal Hofstadter spectrum. At large magnetic field, we observed signatures of another series of states, which appeared at fractional Bloch filling index. These fractional Bloch band QHE states are not anticipated by existing theoretical pictures and point toward a distinct type of many-body state. PMID:26785484
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.
Edge structure of graphene monolayers in the ν =0 quantum Hall state
NASA Astrophysics Data System (ADS)
Knothe, Angelika; Jolicoeur, Thierry
2015-10-01
Monolayer graphene at neutrality in the quantum Hall regime has many competing ground states with various types of ordering. The outcome of this competition is modified by the presence of the sample boundaries. In this paper we use a Hartree-Fock treatment of the electronic correlations allowing for space-dependent ordering. The armchair edge influence is modeled by a simple perturbative effective magnetic field in valley space. We find that all phases found in the bulk of the sample, ferromagnetic, canted antiferromagnetic, charge-density wave, and Kekulé distortion, are smoothly connected to a Kekulé-distorted edge. The single-particle excitations are computed taking into account the spatial variation of the order parameters. An eventual metal-insulator transition as a function of the Zeeman energy is not simply related to the type of bulk order.
Inverse spin Hall effect in a HgTe quantum well
NASA Astrophysics Data System (ADS)
Luo, Wei; Deng, W. Y.; Chen, M. N.; Sheng, L.; Xing, D. Y.
2016-03-01
The inverse spin Hall effect (ISHE) is a phenomenon due to spin-orbit coupling, in which a longitudinal spin current can generate a transverse charge current and electrical voltage difference. We investigate the ISHE in a topological insulator material, a HgTe quantum well, assuming that the Fermi energy is in the conduction band. The transverse charge current and voltage difference are calculated in the ballistic regime. It is found that in this system a Rashba spin-orbit coupling can cause the occurrence of the ISHE. The induced transverse voltage difference is maximized when the spin current is polarized in the longitudinal direction, and vanishes when the spin current is polarized in the transverse directions.
Quantum Hall effect on centimeter scale chemical vapor deposited graphene films
NASA Astrophysics Data System (ADS)
Shen, Tian; Wu, Wei; Yu, Qingkai; Richter, Curt A.; Elmquist, Randolph; Newell, David; Chen, Yong P.
2011-12-01
We report observations of well developed half integer quantum Hall effect on mono layer graphene films of 7 mm × 7 mm in size. The graphene films are grown by chemical vapor deposition on copper, then transferred to SiO2/Si substrates, with typical carrier mobilities ≈4000 cm2/Vs. The large size graphene with excellent quality and electronic homogeneity demonstrated in this work is promising for graphene-based quantum Hall resistance standards and can also facilitate a wide range of experiments on quantum Hall physics of graphene and practical applications exploiting the exceptional properties of graphene.
Quantum Hall effect on centimeter scale chemical vapor deposited graphene films
NASA Astrophysics Data System (ADS)
Shen, Tian; Wu, Wei; Yu, Qingkai; Richter, Curt; Elmquist, Randolph; Newell, David; Chen, Yong
2012-02-01
We report observations of well developed half integer quantum Hall effect on mono layer graphene films of 7 mm by 7 mm in size. The graphene films are grown by chemical vapor deposition on copper, then transferred to SiO2/Si substrates, with typical carrier mobilities 4000 cm^2/Vs. The large size graphene with excellent quality and electronic homogeneity demonstrated in this work is promising for graphene-based quantum Hall resistance standards, and can also facilitate a wide range of experiments on quantum Hall physics of graphene and practical applications exploiting the exceptional properties of graphene.
Electronic transport and the localization length in the quantum Hall effect
NASA Astrophysics Data System (ADS)
Furlan, M.
1998-06-01
We report on recent experimental results from transport measurements with large Hall bars made of high- mobility GaAs/AlxGa1-xAs heterostructures. Thermally activated conductivities and hopping transport were investigated in the integer quantum Hall regime. The predominant transport processes in two dimensions are discussed. The implications of transport regime on prefactor universality and on the relation between ρxx and ρxy are studied. Particularly in the Landau-level tails, a strictly linear dependence δρxy(ρxx) was found, with pronounced asymmetries with respect to the plateau center. At low temperatures, Ohmic (temperature-dependent) as well as non-Ohmic (current-dependent) transport were investigated and analyzed on the basis of variable-range hopping theory. The non-Ohmic regime could successfully be described by an effective electron temperature model. The results from either the Ohmic transport or from a comparison of Ohmic and non-Ohmic data allowed us to determine the localization length ξ in two different ways. The observed divergence of ξ(ν) with the filling factor ν approaching a Landau-level center, is in qualitative agreement with scaling theories of electron localization. The absolute values of ξ far from the ρxx peaks are compared with theoretical predictions. On one hand, discrepancies between the ξ results obtained from the two experimental methods are attributed to an inhomogeneous electric-field distribution. Extrapolation yields an effective width of dominant potential drop of about 100 μm. On the other hand, our analysis suggests a divergence of the dielectric function ɛr~ξβ with β~=1.
Quantum Hall Effect near the charge neutrality point in graphene
NASA Astrophysics Data System (ADS)
Leon, Jorge; Gusev, Guennadii; Plentz, Flavio
2013-03-01
The Quantum Hall effect (QHE) of a two-dimensional (2D) electron gas in a strong magnetic field is one of the most fascinating quantum phenomena discovered in condensed matter physics. In this work we propose to study the transport properties of the single layer and bilayer of graphene at the charge neutrality point (CNP) and compare it with random magnetic model developed in theoretical papers in which we argue that at CNP graphene layer is still inhomogeneous, very likely due to random potential of impurities. The random potential fluctuations induce smooth fluctuations in the local filling factor around ν = 0. In this case the transport is determined by special class of trajectories, ``the snake states'', propagating along contour ν = 0. The situation is very similar to the transport of a two-dimensional particles moving in a spatially modulated random magnetic field with zero mean value. We especially emphasize that our results may be equally relevant to the composite fermions description of the half-filled Landau level. The authors thank to CNPq and FAPESP for financial support for this work.
Fibonacci anyons from Abelian bilayer quantum Hall states.
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. PMID:25526149
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.
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.
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.
Anisotropic Quantum Hall Liquid States with No Translational Invariance in the Lowest Landau Level
NASA Astrophysics Data System (ADS)
Ciftja, Orion
2016-05-01
Strongly correlated two-dimensional electron systems in a high perpendicular magnetic field have displayed remarkable new physics leading to the discovery of phenomena such as the integer and the fractional quantum Hall effect, to mention a few. Laughlin's theoretical model and the composite fermion's (CFs) approach provide a good description of the liquid electronic phases in the lowest Landau level (LLL) at relatively large filling factors. Other electronic phases at smaller filling factors of the LLL likely represent electronic Wigner solid states. It is believed that no other phases with intermediate order stabilize at the liquid-solid transition region. The current study deals with filling factor 1/6 in the LLL, a state which is very close to the critical filling factor where the liquid-solid transition takes place. With the assumption that the underlying signs of crystalline order are starting to appear at this transitional regime, we focus our attention and study the properties of a hybrid electronic phase that lacks translational invariance. To describe such a state, we consider a wave function that lies entirely in the LLL but, unlike a typical quantum Hall liquid phase, does not possess translational invariance. Although inspired by Laughlin's approach, the wave function we introduce differs from Laughlin's or CFs wave functions that describe translationally invariant uniform electronic phases. We perform quantum Monte Carlo simulations in a standard disk geometry to gain a better understanding of the properties of this wave function that may be considered as a precursor to the more conventional Wigner crystal phase.
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.
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.
NASA Astrophysics Data System (ADS)
Kazakov, Alexander; Kolkovsky, V.; Adamus, Z.; Karczewski, G.; Wojtowicz, T.; Rokhinson, Leonid
2015-03-01
Several experiments detected signatures of Majorana fermions in nanowires, and the focus of current research is shifting toward systems where non-Abelian statistics of excitations can be demonstrated. To achieve this goal we are developing a new 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. The system is based on CdTe quantum wells non-uniformly doped with paramagnetic impurities, which result in a complicate field-dependence of Zeeman splitting. A unique property of the system is that at high fields we can form a quantum Hall ferromagnet with gate-controllable spin polarization. Helical 1D edge channels formed along the edges of electrostatic gates may support generalized non-Abelian excitations in the fractional qunatum Hall regime, and Majorana and parafermion excitations in the presence of induced superconductivity. We will present results on the gate control of s-d exchange in specially designed heterostructures, demonstrate gate control of spin polarization at filling factor ν = 2 , and show spatial separation of quantum Hall states with different spin polarization using lithographically defined gates.
Electrically tunable spin polarization of chiral edge modes in a quantum anomalous Hall insulator
NASA Astrophysics Data System (ADS)
Zhang, Rui-Xing; Hsu, Hsiu-Chuan; Liu, Chao-Xing
2016-06-01
In the quantum anomalous Hall effect, chiral edge modes are expected to conduct spin polarized current without dissipation and thus hold great promise for future electronics and spintronics with low energy consumption. However, spin polarization of chiral edge modes has never been established in experiments. In this work, we theoretically study spin polarization of chiral edge modes in the quantum anomalous Hall effect, based on both the effective model and more realistic tight-binding model constructed from first-principles calculations. We find that spin polarization can be manipulated by tuning either a local gate voltage or the Fermi energy. We also propose to extract spin information of chiral edge modes by contacting the quantum anomalous Hall insulator to a ferromagnetic lead. The establishment of spin polarization of chiral edge modes, as well as the manipulation and detection in a fully electrical manner, will pave the way to the applications of the quantum anomalous Hall effect in spintronics.
Long-term research in Inmetro on samples of quantum Hall resistance standards made by PTB
NASA Astrophysics Data System (ADS)
Carvalho, H. R.; Briones, R. E. M.; Pierz, K.; Gotz, M.
2016-07-01
This paper shows up to date results of Inmetro's investigations on aging effects of quantum Hall samples fabricated by PTB in the frame of a mutual scientific agreement established between the Brazilian and German National Metrology Institutes.
Long-lived non-equilibrium states in a quantum-Hall Tomonaga-Luttinger liquid
NASA Astrophysics Data System (ADS)
Fujisawa, Toshimasa; Washio, Kazuhisa; Nakazawa, Ryo; Hashisaka, Masayuki; Muraki, Koji; Tokura, Yasuhiro
The existence of long-lived non-equilibrium states without showing thermalization, which has previously been demonstrated in time evolution of ultracold atoms (quantum quench), suggests the possibility of their spatial analogue in transport behavior of interacting electrons in solid-state systems. Here we report long-lived non-equilibrium states in one-dimensional edge channels in the integer quantum Hall regime. For this purpose, non-trivial binary spectrum composed of hot and cold carriers is prepared by an indirect heating scheme using weakly coupled counterpropagating edge channels in an AlGaAs/GaAs heterostructure. Quantum dot spectroscopy clearly reveals that the carriers with the non-trivial binary spectrum propagate over a long distance (5 - 10 um), much longer than the length required for electronic relaxation (about 0.1 um), without thermalization into a trivial Fermi distribution. This observation is consistent with the integrable model of Tomonaga-Luttinger liquid. The long-lived spectrum implies that the system is well described by non-interacting plasmons, which are attractive for carrying information for a long distance. This work was supported by the JSPS 26247051 and 15H05854, and Nanotechnology Platform Program of MEXT.
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.
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. PMID:27166762
The Bulk-Edge Correspondence for the Quantum Hall Effect in Kasparov Theory
NASA Astrophysics Data System (ADS)
Bourne, Chris; Carey, Alan L.; Rennie, Adam
2015-09-01
We prove the bulk-edge correspondence in K-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This approach allows us to represent bulk topological invariants explicitly as a Kasparov product of boundary invariants with the extension class linking the algebras. This paper focuses on the example of the discrete integer quantum Hall effect, though our general method potentially has much wider applications.
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
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
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.
2011-01-01
A direct insulator-quantum Hall (I-QH) transition corresponds to a crossover/transition from the insulating regime to a high Landau level filling factor ν > 2 QH state. Such a transition has been attracting a great deal of both experimental and theoretical interests. In this study, we present three different two-dimensional electron systems (2DESs) which are in the vicinity of nanoscaled scatterers. All these three devices exhibit a direct I-QH transition, and the transport properties under different nanaoscaled scatterers are discussed. PMID:21711637
NASA Astrophysics Data System (ADS)
Mirza, Babur M.
2016-05-01
A microscopic theory of integer and fractional quantum Hall effects is presented here. In quantum density wave representation of charged particles, it is shown that, in a two-dimensional electron gas coherent structures form under the low temperature and high density conditions. With a sufficiently high applied magnetic field, the combined N particle quantum density wave exhibits collective periodic oscillations. As a result the corresponding quantum Hall voltage function shows a step-wise change in multiples of the ratio h/e2. At lower temperatures further subdivisions emerge in the Hall resistance, exhibiting the fractional quantum Hall effect.
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.
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.
Real Spin in Pseudospin Quasiparticles of Bilayer Quantum Hall systems
NASA Astrophysics Data System (ADS)
Roostaei, Bahman; Fertig, H. A.; Mullen, Kieran
2005-03-01
Recent experiments have observed enhanced nuclear spin relaxation in double layer quantum Hall systems near the phase boundary between compressible and incompressible states(1). We investigate the electronic spin structure of such systems by calculating the groundstate close to ν= 1 using the Hartree-Fock approximation. This state is a quasiparticle lattice, and we examine the possibility of optimizing its energy by allowing the real spin to tilt away from the majority direction in the quasiparticle cores, analogous to what has been suggested in field theoretic studies of single quasiparticles(2). A broken symmetry of these states introduces low energy spin modes which may couple to the nuclear spins. We calculate both the spin and pseudospin textures for the system near the transition and discuss whether they can account for the observed relaxation rates.1) I.B. Spielman et al., cond-mat/0410092; N. Kumada et al., cond-mat/04104952) S. Ghosh and R. Rajaraman, Phys. Rev. B63, 035304 (2001); Z.F. Izawa and G. Tsitsishvili, cond- mat/0311406.Grants: NSF MRSEC DMR-0080054, NSF EPS-9720651 and NSF DMR- 0454699
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.
Electronic properties and the quantum Hall effect in bilayer graphene.
Fal'ko, Vladimir I
2008-01-28
In this paper, I review the quantum Hall effect (QHE) and far-infra red (FIR) absorption properties of bilayer graphene in a strong magnetic field. This includes a derivation of the effective low-energy Hamiltonian for this system and the consequences of this Hamiltonian for the sequencing of the Landau levels in the material: the form of this effective Hamiltonian gives rise to the presence of a level with doubled degeneracy at zero energy. The effect of a potential difference between the layer of a bilayer is also investigated. It is found that there is a density-dependent gap near the K points in the band structure. The consequences of this gap on the QHE are then described. Also, the magneto-absorption spectrum is investigated and an experiment proposed to distinguish between model groundstates of the bilayer QHE system based on the different absorption characteristics of right- and left-handed polarization of FIR light. Finally, the effects of trigonal warping are taken into account in the absorption picture. PMID:18024357
Andreev conversion of quantum Hall edge state in graphene
NASA Astrophysics Data System (ADS)
Lee, Gil-Ho; Hart, Sean; Wei, Di; Huang, Katie; Efetov, Dmitri; Taniguchi, Takashi; Watanabe, Kenji; Yacoby, Amir; Kim, Philip
Understanding the interplay between superconductivity (SC) and quantum Hall effect (QHE) has been a long-sought theoretical and experimental problem. SC contacts to QHE systems enable us to study interesting physics, such as Cooper pair injection into ballistic 2D channels, Andreev edge states, and emergent excitations of non-Abelian anyons. We developed an in-situ etching technique for highly transparent superconducting contact (NbN) to hBN encapsulated graphene channels. The high critical field of NbN electrodes (Hc 2 > 30 T) and the high quality of our graphene devices allows us to experimentally access a wide range of magnetic field where SC and QHE coexist. In order to probe the Andreev conversion of QH edge states, we measure the chemical potential of normal electrodes located on the upstream and the downstream QH edge states relative to a narrow grounded superconducting electrode. We observed that the chemical potential in downstream has sign opposite to the one measured in upstream suggesting Andreev conversion of incident electrons to outgoing holes across the narrow superconducting contact. We systematically investigated this phenomena as a function of temperature, magnetic field, bias voltage and the width and length of the superconducting electrode.
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
Giant quantum Hall plateaus generated by charge transfer in epitaxial graphene
NASA Astrophysics Data System (ADS)
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.
2016-07-01
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.
Hartree simulations of coupled quantum Hall edge states in corner-overgrown heterostructures
NASA Astrophysics Data System (ADS)
Steinke, L.; Cantwell, P.; Stach, E.; Schuh, D.; Fontcuberta i Morral, A.; Bichler, M.; Abstreiter, G.; Grayson, M.
2013-04-01
The electronic states in a corner-overgrown bent GaAs/AlGaAs quantum well heterostructure are studied with numerical Hartree simulations. Transmission electron microscope pictures of the junction sharpness are shown to justify the sharp-corner potential assumed for these calculations. In a tilted magnetic field, both facets of the bent quantum well are brought to a quantum Hall (QH) state, and the corner hosts an unconventional hybrid system of coupled counter-propagating quantum Hall edges and an additional 1D accumulation wire. We show how, in contrast to coplanar barrier-junctions of QH systems, the coupling between the three subsystems increases as a function of the applied magnetic field, and discuss the implications of the numerical results for the interpretation of experimental data on bent quantum Hall systems reported elsewhere.
a Variational Ground State for the Fractional Quantum Hall Effect.
NASA Astrophysics Data System (ADS)
Galejs, Robert Julian
1987-09-01
The fractional quantum Hall effect has aroused much interest in recent years. A large portion of the research in this field has centered on the theoretical understanding of the ground state properties of a system of two-dimensional electrons in a perpendicular magnetic field. One of the most successful models for such a system is that of Laughlin, who proposed a trial wavefunction to model the ground state for certain electron densities. The present work examines the ground state of this system variationally for three and four electrons. The ground state was modeled as a sum of Slater determinants composed of one-electron functions from the lowest Landau level. This wavefunction was placed on a disk of neutralizing charge and the coefficients of the determinants varied to minimize the energy. This variational wavefunction may be compared directly with Laughlin's, as well as model densities not described by Laughlin. The energy per electron was found to vary smoothly as a function of filling factor except at discrete points where there was an upward cusp. Downward cusps, as found by other investigators, were not found in this work. In the smooth portions, the wavefunction is incompressible whereas at the cusps, the wavefunction undergoes a drastic change. In the presence of impurities, these upward cusps smooth out and the wavefunction is now charge-density-wave -like near the former location of the cusps. This variation between incompressible and charge-density-wave behavior may give an explanation of the behavior of the Hall plateau widths as a function of impurity concentration. At a filling factor of 1/3 it was found that the Laughlin wavefunction is a very good approximation to the ground state, giving a very large overlap with and only a slightly higher energy than the variational state calculated here. Laughlin's excited states appear to be a good approximation as well, although the details of their charge density may not be. A new class of wavefunctions was
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.
The ν = 5 / 2 Fractional Quantum Hall State in presence of Alloy Disorder
NASA Astrophysics Data System (ADS)
Deng, Nianpei; Gardner, Geoffrey; Mondal, Sumit; Kleinbaum, Ethan; Manfra, Michael; Csathy, Gabor
2014-03-01
Disorder plays a prominent role in the formation and the strength of all fractional quantum Hall states, including the one forming at filling factor ν = 5 / 2 . Many aspects of the disorder are, however, poorly understood. At the root of this lack of understanding one often finds our inability to control and characterize disorder. We have investigated the effect of a specific type of disorder, alloy disorder, on the ν = 5 / 2 state. The alloy disorder is controllably introduced into the electron channel by growing a series of Al0.24Ga0.76As/AlxGa1-xAs/Al0.24Ga0.76As quantum well samples with different aluminum molar fraction x using Molecular Beam Epitaxy techniques. We find a suppression of the energy gap of ν = 5 / 2 state with increasing x. To our surprise, we observe a fully quantized ν = 5 / 2 state in an extremely low mobility regime in which, based on existing data, we did not expect the ν = 5 / 2 state to develop. Such a result indicates that ν = 5 / 2 state is unusually robust to the short-ranged alloy disorder. This work was supported by the DOE BES contract no. DE-SC0006671.
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.
Scanning gate spectroscopy of transport across a quantum Hall nano-island
NASA Astrophysics Data System (ADS)
Martins, F.; Faniel, S.; Rosenow, B.; Pala, M. G.; Sellier, H.; Huant, S.; Desplanque, L.; Wallart, X.; Bayot, V.; Hackens, B.
2013-01-01
We explore transport across an ultra-small quantum Hall island (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 first localize and then study a single QHI near a quantum point contact. The presence of Coulomb diamonds in the 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.
NASA Astrophysics Data System (ADS)
Faniel, S.; Martins, F.; Bayot, V.; Hackens, B.; Desplanque, L.; Wallart, X.; Rosenow, B.; Melinte, S.
2013-03-01
We report low temperature (~ 100 mK) magnetotransport, scanning gate microscopy and scanning gate spectroscopy measurements in an In0 . 7Ga0 . 3 As /In0 . 52Al0 . 48 As quantum point contact (QPC). The magnetoresistance of the QPC shows oscillations in the vicinity of integer quantum Hall states. We attribute these magnetoresistance oscillations to the formation of an electron interferometer around a small, disorder-induced quantum Hall island located within the constriction. The magnetic field B tunes the edge states configuration in the QPC, leading to different signatures in the transport measurements. Interestingly, near the Landau level filling factor ν = 3 , the spectroscopy measurements performed on the quantum Hall interferometer, as a function of B or scanning gate tip voltage, exhibit a smooth transition from Coulomb diamonds to a checkerboard pattern.
8 π -periodic Josephson effects in a quantum dot/ quantum spin-Hall josephson junction system
NASA Astrophysics Data System (ADS)
Hui, Hoi-Yin; Sau, Jay
2015-03-01
Josephson junctions made of conventional s-wave superconductors display 2 π periodicity. On the other hand, 4 π -periodic fractional Josephson effect is known to be a characteristic signature of topological superconductors and Majorana fermions [1]. Zhang and Kane have shown that Josephson junctions made of topological superconductors are 8 π -periodic if interaction is used to avoid dissipation [2]. Here we present a general argument for how time-reversal symmetry and Z2 non-trivial topology constrains the Josephson periodicity to be 8 π . We then illustrate this through a microscopic model of a quantum dot in a quantum spin-hall Josephson junction. Work supported by NSF-JQI-PFC, LPS-CMTC and Microsoft Q.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Liu, Zhao; Bhatt, R. N.
The conventional method to study phase transitions from fractional quantum Hall (FQH) liquids to a localized phase induced by disorder has relied on the collapse of the mobility gap and Hall conductance. Here, we scrutinize this issue from the perspective of quantum entanglement. We consider electrons in the disordered lowest Landau level at Laughlin filling fractions ν = 1 / m with either Haldane's pseudopotentials or Coulomb interaction. We find that the derivative of the orbital-cut von-Neumann entropy with respect to the disorder strength has a sharp peak, which diverges with system size, providing a clear fingerprint of the transition from FQH liquids to a localized phase. Further, the fluctuation of the entropy with different cut boundaries is utilized to examine whether the ground states are localized in some region. We also investigate the level statistics of the entanglement spectrum, as well as the low-lying spectrum of the Hamiltonian to extract more information about the phase transition. Our method can be applied to study many-body localization in other topological systems. This work was supported by US Department of Energy, Office of Basic Energy Sciences, through Grant No. DE-SC0002140.
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)
Ghaemi, Pouyan; Ryu, Shinsei; Lee, Dung-Hai
2010-02-01
We show that when superconductivity is induced in graphene through proximity effect, a superconducting vortex is dressed with an interesting pattern of textured order parameters. Furthermore, passing a supercurrent in a superconducting graphene sample induces accumulation of valley pseudospin quantum number at edges: the “quantum valley Hall effect” will be observable in superconducting graphene. These effects reveal a quantum duality between different order parameters that is at heart of the Wess-Zumino-Witten term.
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. PMID:26639023
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
Disorder-assisted quantum transport in suboptimal decoherence regimes
NASA Astrophysics Data System (ADS)
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.
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.
Signature candidate of quantum chaos far from the semiclassical regime
Li, Shang-Bin Xu, Zhengyuan
2014-03-15
We numerically investigated the entanglement product in the simplest coupled kicked top model with the spin j = 1. Different from the dynamical pattern of entanglement in the semiclassical regime, two similar initial states may have discordant entanglement oscillations. A candidate of the quantum signature of this classical chaotic system was proposed. The potential antimonotonic relation between the rank correlation coefficient qualifying the concordant of two entanglement evolutions and the stationary entanglement was preliminarily revealed.
Quantum scattering in the strip: From ballistic to localized regimes
NASA Astrophysics Data System (ADS)
Gebarowski, R.; Šeba, P.; Życzkowski, K.; Zakrzewski, J.
1998-11-01
Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition between the ballistic and the localized regimes. By considering the cylinder geometry and introducing the magnetic flux we are able to study time reversal symmetry breaking in the system. Both macroscopic (conductance) and microscopic (eigenphases distribution, statistics of S-matrix elements) characteristics of the system are examined.
Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Gromov, Andrey; Abanov, Alexander; Cho, Gil Young; You, Yizhi; Fradkin, Eduardo
2015-03-01
While the classical Chern-Simons theory is topological, it's quantum version is not as it depends on the metric of the base manifold through the path integral measure. This phenomenon is known as the framing anomaly. It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions of fractional quantum Hall systems (FQH). In the lowest order in gradients the effective action includes Chern-Simons, Wen-Zee and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and generates a ``finite size correction'' to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses of non-Abelian FQH states.
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.
Parity effect of bipolar quantum Hall edge transport around graphene antidots
NASA Astrophysics Data System (ADS)
Matsuo, Sadashige; Nakaharai, Shu; Komatsu, Katsuyoshi; Tsukagoshi, Kazuhito; Moriyama, Takahiro; Ono, Teruo; Kobayashi, Kensuke
2015-06-01
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.
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. PMID:26894724
Spin Hamiltonian for the quantum Hall state in a ladder geometry
NASA Astrophysics Data System (ADS)
Kapit, E.; Luitel, P.; Schroeter, D. F.
2006-02-01
The first calculation of the true ground state of the parent Hamiltonian proposed by Laughlin [Laughlin, Ann. Phys. 191, 163 (1989)] for the m=2 fractional quantum Hall state on a torus is presented. Laughlin’s model is generalized to the case of a system in a ladder geometry and rewritten in terms of familiar spin-spin interactions, demonstrating that the model corresponds to a long-range Heisenberg Hamiltonian with an additional four-site interaction. The exact diagonalization of the Hamiltonian is performed to extract the energies, correlation functions, sublattice magnetization, and overlap with the quantum Hall state. Our results confirm the recent work showing that the model is not exact [Schroeter, Ann. Phys. 310, 155 (2004)] and also show it to be not without merit: the overlap between the quantum Hall (QH) state and exact ground state approaches the significant value of 0.83 in the limit that the ladder becomes infinitely long.
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.
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
Engineering the quantum anomalous Hall effect in graphene with uniaxial strains
Diniz, G. S. Guassi, M. R.; Qu, F.
2013-12-28
We theoretically investigate the manipulation of the quantum anomalous Hall effect (QAHE) in graphene by means of the uniaxial strain. The values of Chern number and Hall conductance demonstrate that the strained graphene in presence of Rashba spin-orbit coupling and exchange field, for vanishing intrinsic spin-orbit coupling, possesses non-trivial topological phase, which is robust against the direction and modulus of the strain. Besides, we also find that the interplay between Rashba and intrinsic spin-orbit couplings results in a topological phase transition in the strained graphene. Remarkably, as the strain strength is increased beyond approximately 7%, the critical parameters of the exchange field for triggering the quantum anomalous Hall phase transition show distinct behaviors—decrease (increase) for strains along zigzag (armchair) direction. Our findings open up a new platform for manipulation of the QAHE by an experimentally accessible strain deformation of the graphene structure, with promising application on novel quantum electronic devices with high efficiency.
Suppression of interference in quantum Hall Mach-Zehnder geometry by upstream neutral modes
NASA Astrophysics Data System (ADS)
Gefen, Yuval; Goldstein, Moshe
Mach-Zehnder interferometry has been suggested as a probe for anyonic quasiparticles in fractional quantum Hall states. However, all experimental attempts to measure such an interference signal have failed to date, despite the high visibility of interference fringes in the integer quantum Hall case. In our work we have studied the relation between this null result and another recent surprising experimental finding, namely the detection of upstream neutral modes in virtually all fractional quantum Hall states (including, e.g., filling 1/3), not only in hole-like filling factors (such as 2/3). We have found that the excitation of upstream modes makes the interference visibility in the Mach-Zehnder geometry decay exponentially with the total length of the interferometer arms, even when the lengths are exactly equal. We also suggest ways to overcome this suppression.
Metallic phase of the quantum Hall effect in four-dimensional space
NASA Astrophysics Data System (ADS)
Edge, Jonathan; Tworzydlo, Jakub; Beenakker, Carlo
2013-03-01
We study the phase diagram of the quantum Hall effect in four-dimensional (4D) space. Unlike in 2D, in 4D there exists a metallic as well as an insulating phase, depending on the disorder strength. The critical exponent ν ~ 1 . 2 of the diverging localization length at the quantum Hall insulator-to-metal transition differs from the semiclassical value ν = 1 of 4D Anderson transitions in the presence of time-reversal symmetry. Our numerical analysis is based on a mapping of the 4D Hamiltonian onto a 1D dynamical system, providing a route towards the experimental realization of the 4D quantum Hall effect. NanoCTM, FOM/NWO, ERC
NASA Astrophysics Data System (ADS)
Eaves, L.
The breakdown of the dissipationless state of the quantum Hall effect at high currents sometimes occurs as a series of regular steps in the dissipative voltage drop measured along the Hall bar. The steps were first seen clearly in two of the Hall bars used to maintain the US Resistance Standard, but have also been reported in other devices. This paper describes a model to account for the origin of the steps. It is proposed that the dissipationless flow of the quantum Hall fluid is unstable at high flow rates due to inter-Landau level tunnelling processes in local microscopic regions of the Hall bar. Electron-hole pairs are generated in the quantum Hall fluid in these regions and the electronic motion can be envisaged as a quantum analogue of the von Karman vortex street which forms when a classical fluid flows past an obstacle.
Space-charge-limited flow in quantum regime
NASA Astrophysics Data System (ADS)
Ang, Lay Kee
2005-10-01
Space-charge-limited (SCL) flow has been an area of active research in the development of non-neutral plasma physics, high current diodes, high power microwave sources, vacuum microelectronics and sheath physics. According to the classical Child-Langmuir (CL) law for the planar diodes, the current density scales as 3/2's power of gap voltage and to the inverse squared power of gap spacing. In the past decade, there have been renewed interests in extending the classical CL law to multi-dimensional models both numerically and analytically. The study of SCL flow in quantum regime has also attracted considerable interests in the past 3 years [1-3]. With the recent advances in nanotechnology, electron beam with very high current density may be transported in a nano-scale gap with a relatively low gap voltage. In this new operating regime, where the electron wavelength is comparable or larger than the gap spacing, the quantum effects become important. In this talk, the quantum theory of CL law will be introduced to reveal that the classical CL law is enhanced by a large factor due to electron tunneling and exchange-correlation effects, and there is a new quantum scaling for the current density, which is proportional to the 1/2's power of gap voltage, and to the inverse fourth-power of gap spacing [1-2]. Quasi-2D and 3D models with finite emission area will be shown [3]. We will also show that the classical properties of the SCL flow such as bipolar flow, beam-loaded capacitance, transit time and noise will require a complete revision in the quantum regime. The implications of the emission law of Fowler-Nordheim in the presence of intense space charge over the nanometer scale will be discussed.[1] L. K. Ang, T. J. T. Kwan, and Y. Y. Lau, ``New Scaling of Child-Langmuir Law in the Quantum Regime,'' Phys. Rev. Lett. 91, 208303 (2003). [2] L. K. Ang, Y. Y. Lau, and T. J. T. Kwan, ``Simple Derivation of Quantum Scaling in Child-Langmuir law,'' IEEE Trans Plasma Sci. 32, 410
The theoretical studies of topology electronic states in HgTe Hall Bar and Quantum Dot
NASA Astrophysics Data System (ADS)
Qu, Jin-Xian; Zhang, Shu-Hui; Yang, Wen
In recent years, there is an extensive attention on the new properties of topology materials and their potential applications. Our interest is on the physics in the quantum confined systems based on topology materials. To consider two such systems, i.e., quantum dot and Hall bar constructed on the HgTe quantum well, we study the electronic properties and their dependence on various material parameters with and without an in-plane electric field. For both systems, we find that 1) the exotic edge states appear in bulk energy gap, resulting from the non-trivial topological property of quantum well system. 2) by the magnetic doping, there are tunable phase transitions, e.g., transition from trivial insulating phase to topological insulating phase or anomalous quantum Hall insulating phase. 3) the in-plane electric field can introduce effective control on the electronic states.
Loop Quantum Gravity and the Planck Regime of Cosmology
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay
The very early universe provides the best arena we currently have to test quantum gravity theories. The success of the inflationary paradigm in accounting for the observed inhomogeneities in the cosmic microwave background already illustrates this point to a certain extent because the paradigm is based on quantum field theory on the curved cosmological space-times. However, this analysis excludes the Planck era because the background space-time satisfies Einstein's equations all the way back to the big bang singularity. Using techniques from loop quantum gravity, the paradigm has now been extended to a self-consistent theory from the Planck regime to the onset of inflation, covering some 11 orders of magnitude in curvature. In addition, for a narrow window of initial conditions, there are departures from the standard paradigm, with novel effects, such as a modification of the consistency relation involving the scalar and tensor power spectra and a new source for non-Gaussianities. The genesis of the large scale structure of the universe can be traced back to quantum gravity fluctuations in the Planck regime. This report provides a bird's eye view of these developments for the general relativity community.
ab initio based tight-binding investigation of quantum spin Hall effect in InAs/GaSb quantum wells
NASA Astrophysics Data System (ADS)
Wu, Quansheng; Soluyanov, Alexey; Troyer, Matthias
Quantum spin Hall state is a topologically non-trivial quantum state, which can be used for designing various quantum devices including those potentially useful for quantum computing. Type-II InAs/GaSb semiconductor quantum well was predicted to realize this state of matter. In this work, we systematically investigate topological properties of this system using symmetrized Wannier-based tight-binding models. The model parameters are derived from first-principles hybrid functional calculations, which capture the right band gap and effective masses of both InAs and GaSb. By varying the thickness of InAs and GaSb layers, three possible phases are obtained: normal insulator, quantum spin Hall insulator, and semimetal, allowing us to optimize the growth conditions for the quantum spin Hall phase realization. Most importantly, we identify optimal growth directions, showing that a significant increase of the topological gap can be obtained by growing the quantum well in the [111]-direction. Phase diagrams are obtained for different layer thicknesses and growth directions. Effects of strain and applied electric fields are also discussed.
NASA Astrophysics Data System (ADS)
Zhou, Jian; Sun, Qiang; Wang, Qian; Kawazoe, Yoshiyuki; Jena, Puru
2016-05-01
Exploring a two-dimensional intrinsic quantum spin Hall state with a large band gap as well as an anomalous Hall state in realizable materials is one of the most fundamental and important goals for future applications in spintronics, valleytronics, and quantum computing. Here, by combining first-principles calculations with a tight-binding model, we predict that Sb or Bi can epitaxially grow on a stable and ferromagnetic MnO2 thin film substrate, forming a flat honeycomb sheet. The flatness of Sb or Bi provides an opportunity for the existence of Dirac points in the Brillouin zone, with its position effectively tuned by surface hydrogenation. The Dirac points in spin up and spin down channels split due to the proximity effects induced by MnO2. In the presence of both intrinsic and Rashba spin-orbit coupling, we find two band gaps exhibiting a large band gap quantum spin Hall state and a nearly quantized anomalous Hall state which can be tuned by adjusting the Fermi level. Our findings provide an efficient way to realize both quantized intrinsic spin Hall conductivity and anomalous Hall conductivity in a single material.Exploring a two-dimensional intrinsic quantum spin Hall state with a large band gap as well as an anomalous Hall state in realizable materials is one of the most fundamental and important goals for future applications in spintronics, valleytronics, and quantum computing. Here, by combining first-principles calculations with a tight-binding model, we predict that Sb or Bi can epitaxially grow on a stable and ferromagnetic MnO2 thin film substrate, forming a flat honeycomb sheet. The flatness of Sb or Bi provides an opportunity for the existence of Dirac points in the Brillouin zone, with its position effectively tuned by surface hydrogenation. The Dirac points in spin up and spin down channels split due to the proximity effects induced by MnO2. In the presence of both intrinsic and Rashba spin-orbit coupling, we find two band gaps exhibiting a large
Morimoto, Takahiro; Aoki, Hideo
2013-12-04
Flow diagram of (σ{sub xx},σ{sub xy}) in finite-frequency (ω) regime is numerically studied for the graphene quantum Hall effect (QHE). In a small-ω regime, the ac flow diagram exhibits a behavior qualitatively similar to the dc flow diagram, where the dynamical length scale acts as a cutoff in the ac region, and the flows are between σ{sub xy} = ±(1/2)e{sup 2}/h reflecting the graphene QHE. The dynamical flow is compared with the temperature-driven flow.
Large-Chern-number quantum anomalous Hall effect in thin-film topological crystalline insulators.
Fang, Chen; Gilbert, Matthew J; Bernevig, B Andrei
2014-01-31
We theoretically predict that thin-film topological crystalline insulators can host various quantum anomalous Hall phases when doped by ferromagnetically ordered dopants. Any Chern number between ±4 can, in principle, be reached as a result of the interplay between (a) the induced Zeeman field, depending on the magnetic doping concentration, (b) the structural distortion, either intrinsic or induced by a piezoelectric material through the proximity effect, and (c) the thickness of the thin film. We propose a heterostructure to realize quantum anomalous Hall phases with Chern numbers that can be tuned by electric fields. PMID:24580476
Spin-orbit coupling and quantum spin Hall effect for neutral atoms without spin flips.
Kennedy, Colin J; Siviloglou, Georgios A; Miyake, Hirokazu; Burton, William Cody; Ketterle, Wolfgang
2013-11-27
We propose a scheme which realizes spin-orbit coupling and the quantum spin Hall effect for neutral atoms in optical lattices without relying on near resonant laser light to couple different spin states. The spin-orbit coupling is created by modifying the motion of atoms in a spin-dependent way by laser recoil. The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient. Alternatively, a quantum spin Hall Hamiltonian can be created by all-optical means using a period-tripling, spin-dependent superlattice. PMID:24329453
Tomimatsu, Toru Shirai, Shota; Hashimoto, Katsushi Sato, Ken; Hirayama, Yoshiro
2015-08-15
Electric-field-induced nuclear resonance (NER: nuclear electric resonance) involving quantum Hall states (QHSs) was studied at various filling factors by exploiting changes in nuclear spins polarized at quantum Hall breakdown. Distinct from the magnetic dipole interaction in nuclear magnetic resonance, the interaction of the electric-field gradient with the electric quadrupole moment plays the dominant role in the NER mechanism. The magnitude of the NER signal strongly depends on whether electronic states are localized or extended. This indicates that NER is sensitive to the screening capability of the electric field associated with QHSs.
Exact conductance through point contacts in the {nu}=1/3 fractional quantum Hall Effect
Fendley, P.; Ludwig, A.W.W.; Saleur, H. |
1995-04-10
The conductance for tunneling through an impurity in a Luttinger liquid is described by a universal scaling function. We compute this scaling function exactly, by using the thermodynamic Bethe ansatz and a kinetic (Boltzmann) equation. This model has been proposed to describe resonant tunneling through a point contact between two {nu}=1/3 quantum Hall edges. Recent experiments on quantum Hall devices agree well with our exact results. We also derive the exact conductance and {ital I}({ital V}) curve, out of equilibrium, in this fully interacting system.
Hořava-Lifshitz gravity and effective theory of the fractional quantum Hall effect
NASA Astrophysics Data System (ADS)
Wu, Chaolun; Wu, Shao-Feng
2015-01-01
We show that Hořava-Lifshitz gravity theory can be employed as a covariant framework to build an effective field theory for the fractional quantum Hall effect that respects all the spacetime symmetries such as non-relativistic diffeomorphism invariance and anisotropic Weyl invariance as well as the gauge symmetry. The key to this formalism is a set of correspondence relations that maps all the field degrees of freedom in the Hořava-Lifshitz gravity theory to external background (source) fields among others in the effective action of the quantum Hall effect, according to their symmetry transformation properties. We originally derive the map as a holographic dictionary, but its form is independent of the existence of holographic duality. This paves the way for the application of Hořava-Lifshitz holography on fractional quantum Hall effect. Using the simplest holographic Chern-Simons model, we compute the low energy effective action at leading orders and show that it captures universal electromagnetic and geometric properties of quantum Hall states, including the Wen-Zee shift, Hall viscosity, angular momentum density and their relations. We identify the shift function in Hořava-Lifshitz gravity theory as minus of guiding center velocity and conjugate to guiding center momentum. This enables us to distinguish guiding center angular momentum density from the internal one, which is the sum of Landau orbit spin and intrinsic (topological) spin of the composite particles. Our effective action shows that Hall viscosity is minus half of the internal angular momentum density and proportional to Wen-Zee shift, and Hall bulk viscosity is half of the guiding center angular momentum density.
Fermi pockets and quantum oscillations of the Hall coefficient in high-temperature superconductors
Chakravarty, Sudip; Kee, Hae-Young
2008-01-01
Recent quantum oscillation measurements in high-temperature superconductors in high magnetic fields and low temperatures have ushered in a new era. These experiments explore the normal state from which superconductivity arises and provide evidence of a reconstructed Fermi surface consisting of electron and hole pockets in a regime in which such a possibility was previously considered to be remote. More specifically, the Hall coefficient has been found to oscillate according to the Onsager quantization condition, involving only fundamental constants and the areas of the pockets, but with a sign that is negative. Here, we explain the observations with the theory that the alleged normal state exhibits a hidden order, the d-density wave, which breaks symmetries signifying time reversal, translation by a lattice spacing, and a rotation by an angle π/2, while the product of any two symmetry operations is preserved. The success of our analysis underscores the importance of spontaneous breaking of symmetries, Fermi surface reconstruction, and conventional quasiparticles. We primarily focus on the version of the order that is commensurate with the underlying crystalline lattice, but we also touch on the consequences if the order were to incommensurate. It is shown that whereas commensurate order results in two independent oscillation frequencies as a function of the inverse of the applied magnetic field, incommensurate order leads to three independent frequencies. The oscillation amplitudes, however, are determined by the mobilities of the charge carriers comprising the Fermi pockets. PMID:18577585
Fractional quantum Hall physics with ultracold Rydberg gases in artificial gauge fields
NASA Astrophysics Data System (ADS)
Grusdt, F.; Fleischhauer, M.
2013-04-01
We study ultracold Rydberg-dressed Bose gases subject to artificial gauge fields in the fractional quantum Hall (FQH) regime. The characteristics of the Rydberg interaction give rise to interesting many-body ground states different from standard FQH physics in the lowest Landau level. The nonlocal but rapidly decreasing interaction potential favors crystalline ground states for very dilute systems. While a simple Wigner crystal becomes energetically favorable compared to the Laughlin liquid for filling fractions ν<1/12, a correlated crystal of composite particles emerges already for ν≤1/6 with a large energy gap to the simple Wigner crystal. The presence of a new length scale, the Rydberg blockade radius aB, gives rise to a bubble crystal phase for ν≲1/4 when the average particle distance becomes less than aB, which describes the region of saturated, almost constant interaction potential. For larger fillings indications for strongly correlated cluster liquids are found.
Quantum Hall effect at a tunably sharp cleaved-edge potential
NASA Astrophysics Data System (ADS)
Zhou, Chuanle; Grayson, M.; Steinke, L.; Uccelli, E.; Koblmueller, G.; Bichler, M.; Abstreiter, G.; Schmult, S.; Dietsche, W.
2010-03-01
We study magnetotransport in the quantum Hall (QH) regime of a two-dimensional electron system with an epitaxially overgrown sharp cleaved-edge. A thick insulating barrier is overgrown at the cleaved-edge followed by a doped layer, serving as a side gate which can control depletion or accumulation at the sharp edge, hence can convert a sharp edge into a soft edge by changing the gate bias. This geometry leads to a tunable edge potential with either the standard incompressible strips in the ``soft edge'' limit, or thin or vanishing incompressible strips in the ``sharp edge'' limit. DC magnetotransport measurements show evidence of a longitudinal resistance minimum whose width depends on the current direction. This experimental result is consistent with recent theory on the role of edge potentials in defining the QH in small samples [1]. Size effect and gate bias dependence are studied. We also report an unexplained magnetic field hysteresis at the high field side of filling factors ν=1, 2, 3, 4 in the limit of negative side-gate bias.[4pt] [1] A. Siddiki, Euro. Phys. Lett. 87, 17008(2009)
NASA Astrophysics Data System (ADS)
Pino, H.; Alba, E.; Taron, J.; Garcia-Ripoll, J. J.; Barberán, N.
2013-05-01
Interacting bosonic atoms under strong gauge fields undergo a series of phase transitions that take the cloud from a simple Bose-Einstein condensate all the way to a family of fractional-quantum-Hall-type states [M. Popp, B. Paredes, and J. I. Cirac, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.70.053612 70, 053612 (2004)]. In this work we demonstrate that the Hall response of the atoms can be used to locate the phase transitions and characterize the ground state of the many-body state. Moreover, the same response function reveals within some regions of the parameter space, the structure of the spectrum and the allowed transitions to excited states. We verify numerically these ideas using exact diagonalization for a small number of atoms, and provide an experimental protocol to implement the gauge fields and probe the linear response using a periodically driven optical lattice. Finally, we discuss our theoretical results in relation to recent experiments with condensates in artificial magnetic fields [L. J. LeBlanc, K. Jimenez-Garcia, R. A. Williams, M. C. Beeler, A. R. Perry, W. D. Phillips, and I. B. Spielman, Proc. Natl. Acad. Sci. USAPNASA60027-842410.1073/pnas.1202579109 109, 10811 (2012)] and we analyze the role played by vortex states in the Hall response.
Condensation of lattice defects and melting transitions in quantum Hall phases
NASA Astrophysics Data System (ADS)
Cho, Gil Young; Parrikar, Onkar; You, Yizhi; Leigh, Robert G.; Hughes, Taylor L.
2015-01-01
Motivated by recent progress in understanding the interplay between lattice and electronic topological phases, we consider quantum-melting transitions of weak quantum liquid crystals, a crystal and a nematic phase, in which electrons form a quantum Hall state. In certain classes of Chern band insulators and quantum Hall phases, it has been previously demonstrated that there are topological Chern-Simons terms such as a Hall viscosity term and a gravitational Chern-Simons term for local lattice deformations. The Chern-Simons terms can induce anyonic statistics for the topological lattice defects and, furthermore, dress the defects with certain symmetry quantum numbers. On the other hand, the melting transitions of such liquid-crystalline orders are driven by the condensation of lattice defects. Based on these observations, we show how the topological terms can change the nature of the proximate disordered phases of the quantum liquid-crystalline phases. We derive and study the effective dual field theories for the liquid-crystalline phases with the geometric Chern-Simons terms, and carefully examine the symmetry quantum numbers and statistics of defects. We show that a crystal may go through a continuous phase transition into another crystal with the different discrete translational symmetries because the dislocation, the topological defect in the crystal, carries nonzero crystal momentum due to the Hall viscosity term. For the nematic phase, the disclination will condense at the phase transition to the isotropic phase, and we show that the isotropic phase may support a deconfined fractionally charged excitation due to the Wen-Zee term, and thus the isotropic phase and the nematic phase have different electromagnetic Hall responses.
A prototype of RK/200 quantum Hall array resistance standard on epitaxial graphene
NASA Astrophysics Data System (ADS)
Lartsev, A.; Lara-Avila, S.; Danilov, A.; Kubatkin, S.; Tzalenchuk, A.; Yakimova, R.
2015-07-01
Epitaxial graphene on silicon carbide is a promising material for the next generation of quantum Hall resistance standards. Single Hall bars made of graphene have already surpassed their state-of-the-art GaAs based counterparts as an R K / 2 ( R K = h / e 2 ) standard, showing at least the same precision and higher breakdown current density. Compared to single devices, quantum Hall arrays using parallel or series connection of multiple Hall bars can offer resistance values spanning several orders of magnitude and (in case of parallel connection) significantly larger measurement currents, but impose strict requirements on uniformity of the material. To evaluate the quality of the available material, we have fabricated arrays of 100 Hall bars connected in parallel on epitaxial graphene. One out of four devices has shown quantized resistance that matched the correct value of R K / 200 within the measurement precision of 10 - 4 at magnetic fields between 7 and 9 T. The defective behaviour of other arrays is attributed mainly to non-uniform doping. This result confirms the acceptable quality of epitaxial graphene, pointing towards the feasibility of well above 90% yield of working Hall bars.
Quantum spin Hall effect in α -Sn /CdTe(001 ) quantum-well structures
NASA Astrophysics Data System (ADS)
Küfner, Sebastian; Matthes, Lars; Bechstedt, Friedhelm
2016-01-01
The electronic and topological properties of heterovalent and heterocrystalline α -Sn/CdTe(001) quantum wells (QWs) are studied in dependence on the thickness of α -Sn by means of ab initio calculations. We calculate the topological Z2 invariants of the respective bulk crystals, which identify α -Sn as strong three-dimensional (3D) topological insulators (TIs), whereas CdTe is a trivial insulator. We predict the existence of two-dimensional (2D) topological interface states between both materials and show that a topological phase transition from a trivial insulating phase into the quantum spin Hall (QSH) phase in the QW structures occurs at much higher thicknesses than in the HgTe case. The QSH effect is characterized by the localization, dispersion, and spin polarization of the topological interface states. We address the distinction of the 3D and 2D TI characters of the studied QW structures, which is inevitable for an understanding of the underlying quantum state of matter. The 3D TI nature is characterized by two-dimensional topological interface states, while the 2D phase exhibits one-dimensional edge states. The two different state characteristics are often intermixed in the discussion of the topology of 2D QW structures, especially, the comparison of ab initio calculations and experimental transport studies.
Half integer features in the quantum Hall Effect: experiment and theory
NASA Astrophysics Data System (ADS)
Kramer, Tobias; Heller, E. J.; Parrott, R. E.; Liang, C.-T.; Huang, C. F.; Chen, K. Y.; Lin, L.-H.; Wu, J.-Y.; Lin, S.-D.
2009-03-01
We discuss experimental data and a new model of the integer quantum Hall effect (IQHE), which explains an intriguing substructure within Landau levels observed at higher currents. The experiments show inflection points in the Hall resistivity around filling factors 5/2 and 7/2. The experiments require to revisit the foundations of the IQHE and to establish an injection model which incorporates the correct boundary conditions imposed by a real Hall device and the Lorentz force. We have to follow the electrons to their source: one corner of the Hall bar and its steep electric field gradients, rather than focusing on the middle of the Hall device. We find the entire Hall resistivity curve is calculable as a function of magnetic field, temperature, and current. In contrast to previous theories of the IQHE, disorder plays no fundamental role in our theory. Contrary to the standard picture of Landau levels in disorder system, we predict and observe gaps right in the middle of certain Landau levels. The Hall plateaus and half integer inflections are shown to result from the LDOS appropriate to the magnetic field and the strong electric field at the injection corner.
From Floquet to Dicke: Quantum Spin Hall Insulator Interacting with Quantum Light.
Gulácsi, Balázs; Dóra, Balázs
2015-10-16
Time-periodic perturbations due to classical electromagnetic fields are useful to engineer the topological properties of matter using the Floquet theory. Here we investigate the effect of quantized electromagnetic fields by focusing on the quantized light-matter interaction on the edge state of a quantum spin Hall insulator. A Dicke-type superradiant phase transition occurs at arbitrary weak coupling, the electronic spectrum acquires a finite gap, and the resulting ground-state manifold is topological with a Chern number of ±1. When the total number of excitations is conserved, a photocurrent is generated along the edge, being pseudoquantized as ωln(1/ω) in the low-frequency limit and decaying as 1/ω for high frequencies with ω the photon frequency. The photon spectral function exhibits a clean Goldstone mode, a Higgs-like collective mode at the optical gap and the polariton continuum. PMID:26550853
Even-denominator fractional quantum Hall effect in multi-terminal suspended bilayer graphene
NASA Astrophysics Data System (ADS)
Morpurgo, Alberto
2015-03-01
I will discuss magneto-transport experiments through multi-terminal suspended bilayer graphene devices of very high quality (mean-free path larger than the device size; density of charge inhomogeneity 109 cm-2) . The multi-terminal geometry enables independent measurements of the longitudinal and transverse magneto resistance, which are essential to properly measure quantum Hall states. At high magnetic field, different fractional states emerge on the hole side, including states at ν = -4/3 and ν = -1/2 that are fully developed (plateau in Rxy quantized with an accuracy better than 0.5%, and a concomitant minimum in Rxx) and other states (e.g., at -5/2, -2/3, -8/5), which manifest themselves through a clear minimum in Rxx occurring at a fixed value of filling factor. The more pronounced states are consistent with predictions of a recent theory by Papic and Abanin, that describes the mixing of the degenerate, zero-energy N =0 and N =1 Landau levels of graphene bilayers due to e-e interactions, and which indicates that the even denominator ν = -1/2 state is of the Moore-Read type. If time allows, I will also discuss our recent experiments of suspended multi-terminal 4-layer graphene, on which we made different interesting observations. One is an integer quantum Hall effect consistent with an even larger degeneracy of the E =0 Landau levels, for which it may be interesting to start exploring theoretically possible new physics in the fractional regime. The second is the occurrence of an unexpected gapped insulating state at zero magnetic field. Together with previous experiments on suspended mono, bi, and trilayers, this observation points to an even-odd effect of e-e interaction (at zero magnetic field) in graphene multilayers: even layers are gapped by e-e interactions while odd layers stay conducting, due to the presence of a Dirac-like band in their electronic structure. A comparison of the gapped state in bilayers and four-layers show that the magnitude of the
Beyond the Plasma Analogy: Collective Field Theory for Quantum Hall States
NASA Astrophysics Data System (ADS)
Can, Tankut; Laskin, Michael; Wiegmann, Paul
We develop a quantum field theory of collective coordinates describing fractional quantum Hall (FQH) states. We show that the familiar properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian theory arise from ultraviolet regularization, and go beyond the celebrated plasma analogy. They give rise to a gravitational anomaly described by the Liouville theory of 2D quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies. This talk is based on the preprint arXiv:1412.8716.
Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Gromov, Andrey; Cho, Gil Young; You, Yizhi; Abanov, Alexander G.; Fradkin, Eduardo
2015-01-01
We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.
Second Landau level fractional quantum Hall effects in the Corbino geometry
NASA Astrophysics Data System (ADS)
Schmidt, B. A.; Bennaceur, K.; Bilodeau, S.; Gervais, G.; Pfeiffer, L. N.; West, K. W.
2015-09-01
For certain measurements, the Corbino geometry has a distinct advantage over the Hall and van der Pauw geometries, in that it provides a direct probe of the bulk 2DEG without complications due to edge effects. This may be important in enabling detection of the non-Abelian entropy of the 5/2 fractional quantum Hall state via bulk thermodynamic measurements. We report the successful fabrication and measurement of a Corbino-geometry sample in an ultra-high mobility GaAs heterostructure, with a focus on transport in the second and higher Landau levels. In particular, we report activation energy gaps of fractional quantum Hall states, with all edge effects ruled out, and extrapolate σ0 from the Arrhenius fits. Our results show that activated transport in the second Landau level remains poorly understood. The development of this Corbino device opens the possibility to study the bulk of the 5/2 state using techniques not possible in other geometries.
Framing anomaly in the effective theory of the fractional quantum Hall effect.
Gromov, Andrey; Cho, Gil Young; You, Yizhi; Abanov, Alexander G; Fradkin, Eduardo
2015-01-01
We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states. PMID:25615495
Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice.
Zhu, W; Gong, Shou-Shu; Zeng, Tian-Sheng; Fu, Liang; Sheng, D N
2016-08-26
Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. Here, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry. We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Importantly, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Thus, we identify the liquid phase as a quantum Hall phase, which provides a "proof-of-principle" demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band. PMID:27610866
Operation of graphene quantum Hall resistance standard in a cryogen-free table-top system
NASA Astrophysics Data System (ADS)
Janssen, T. J. B. M.; Rozhko, S.; Antonov, I.; Tzalenchuk, A.; Williams, J. M.; Melhem, Z.; He, H.; Lara-Avila, S.; Kubatkin, S.; Yakimova, R.
2015-09-01
We demonstrate quantum Hall resistance measurements with metrological accuracy in a small cryogen-free system operating at a temperature of around 3.8 K and magnetic fields below 5 T. Operating this system requires little experimental knowledge or laboratory infrastructure, thereby greatly advancing the proliferation of primary quantum standards for precision electrical metrology. This significant advance in technology has come about as a result of the unique properties of epitaxial graphene on SiC.
Prediction of Near-Room-Temperature Quantum Anomalous Hall Effect on Honeycomb Materials
NASA Astrophysics Data System (ADS)
Yan, Binghai; Wu, Shu-Chun; Shan, Guangcun
2015-03-01
Recently, this long-sought quantum anomalous Hall effect was realized in the magnetic topological insulator. However, the requirement of an extremely low temperature (~ 30 mK) hinders realistic applications. Based on honeycomb lattices comprised of Sn and Ge, which are found to be 2D topological insulators, we propose a quantum anomalous Hall platform with large energy gap of 0.34 and 0.06 eV, respectively. The ferromagnetic order forms in one sublattice of the honeycomb structure by controlling the surface functionalization rather than dilute magnetic doping, which is expected to be visualized by spin polarized STM in experiment. Strong coupling between the inherent quantum spin Hall state and ferromagnetism results in considerable exchange splitting and consequently an ferromagnetic insulator with large energy gap. The estimated mean-field Curie temperature is 243 and 509 K for Sn and Ge lattices, respectively. The large energy gap and high Curie temperature indicate the feasibility of the quantum anomalous Hall effect in the near-room-temperature and even room-temperature regions. We thank the helpful discussions with C. Felser, S. Kanugo, C.-X. Liu, Z. Wang, Y. Xu, K. Wu, and Y. Zhou.
NASA Astrophysics Data System (ADS)
Deng, Nianpei
The two dimensional electron gas subjected to a magnetic field has been a model system in contemporary condensed matter physics which generated many beautiful experiments as well as novel fundamental concepts. These novel concepts are of broad interests and have benefited other fields of research. For example, the observations of conventional odd-denominator fractional quantum Hall states have enriched many-body physics with important concepts such as fractional statistics and composite fermions. The subsequent discovery of the enigmatic even-denominator nu=5/2 fractional quantum Hall state has led to more interesting concepts such as non-Abelian statistics and pairing of composite fermions which can be intimately connected to the electron pairing in superconductivity. Moreover, the observations of stripe phases and reentrant integer quantum Hall states have stimulated research on exotic electron solids which have more intricate structures than the Wigner Crystal. In contrast to fractional quantum Hall states and stripes phases, the reentrant integer quantum Hall states are very little studied and their ground states are the least understood. There is a lack of basic information such as exact filling factors, temperature dependence and energy scales for the reentrant integer quantum Hall states. A critical experimental condition in acquiring this information is a stable ultra-low temperature environment. In the first part of this dissertation, I will discuss our unique setup of 3He immersion cell in a state-of-art dilution refrigerator which achieves the required stability of ultra-low temperature. With this experimental setup, we are able to observe for the first time very sharp magnetotransport features of reentrant integer quantum Hall states across many Landau levels for the first time. I will firstly present our results in the second Landau level. The temperature dependence measurements reveal a surprisingly sharp peak signature that is unique to the reentrant
Varlet, Anastasia; Bischoff, Dominik; Simonet, Pauline; Watanabe, Kenji; Taniguchi, Takashi; Ihn, Thomas; Ensslin, Klaus; Mucha-Kruczyński, Marcin; Fal'ko, Vladimir I
2014-09-12
Bilayer graphene is a unique system where both the Fermi energy and the low-energy electron dispersion can be tuned. This is brought about by an interplay between trigonal warping and the band gap opened by a transverse electric field. Here, we drive the Lifshitz transition in bilayer graphene to experimentally controllable carrier densities by applying a large transverse electric field to a h-BN-encapsulated bilayer graphene structure. We perform magnetotransport measurements and investigate the different degeneracies in the Landau level spectrum. At low magnetic fields, the observation of filling factors -3 and -6 quantum Hall states reflects the existence of three maxima at the top of the valence-band dispersion. At high magnetic fields, all integer quantum Hall states are observed, indicating that deeper in the valence band the constant energy contours are singly connected. The fact that we observe ferromagnetic quantum Hall states at odd-integer filling factors testifies to the high quality of our sample. This enables us to identify several phase transitions between correlated quantum Hall states at intermediate magnetic fields, in agreement with the calculated evolution of the Landau level spectrum. The observed evolution of the degeneracies, therefore, reveals the presence of a Lifshitz transition in our system. PMID:25259994
Composite fermion model for entanglement spectrum of fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Davenport, Simon C.; Rodríguez, Iván D.; Slingerland, J. K.; Simon, Steven H.
2015-09-01
We show that the entanglement spectrum associated with a certain class of strongly correlated many-body states—the wave functions proposed by Laughlin and Jain to describe the fractional quantum Hall effect—can be very well described in terms of a simple model of noninteracting (or weakly interacting) composite fermions.
Superconducting quantum spin-Hall systems with giant orbital g-factors
NASA Astrophysics Data System (ADS)
Hankiewicz, Ewelina; Reinthaler, Rolf; Tkachov, Grigory
Topological aspects of superconductivity in quantum spin-Hall systems (QSHSs) such as thin layers of three-dimensional topological insulators (3D Tis) or two-dimensional Tis are in the focus of current research. Here, we describe a novel superconducting quantum spin-Hall effect (quantum spin Hall system in the proximity to the s-wave superconductor and in the orbital in-plane magnetic field), which is protected against elastic backscattering by combined time-reversal and particle-hole symmetry. This effect is characterized by spin-polarized edge states, which can be manipulated in weak magnetic fields due to a giant effective orbital g-factor, allowing the generation of spin currents. The phenomenon provides a novel solution to the outstanding challenge of detecting the spin-polarization of the edge states. Here we propose the detection of the edge polarization in the three-terminal junction using unusual transport properties of superconducting quantum Hall-effect: a non-monotonic excess current and a zero-bias conductance splitting. We thank for the financial support the German Science Foundation (DFG), Grants No HA 5893/4-1 within SPP 1666, HA5893/5-2 within FOR1162 and TK60/1-1 (G.T.), as well the ENB graduate school ``Topological insulators''.
Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations
Lapilli, Cintia M.; Wexler, Carlos
2006-02-15
A variety of recent experiments probing the low-temperature transport properties of quantum Hall systems have suggested an interpretation in terms of liquid crystalline mesophases dubbed quantum Hall liquid crystals. The single mode approximation (SMA) has been a useful tool for the determination of the excitation spectra of various systems such as phonons in {sup 4}He and in the fractional quantum Hall effect. In this paper we calculate (via the SMA) the spectrum of collective excitations in a quantum Hall liquid crystal by considering nematic, tetratic, and hexatic generalizations of Laughlin's trial wave function having twofold, fourfold, and sixfold broken rotational symmetry, respectively. In the limit of zero wave vector q the dispersion of these modes is singular, with a gap that is dependent on the direction along which q=0 is approached for nematic and tetratic liquid crystalline states, but remains regular in the hexatic state, as permitted by the fourth order wave-vector dependence of the (projected) oscillator strength and static structure factor.
Hamiltonians for the Quantum Hall Effect on Spaces with Non-Constant Metrics
NASA Astrophysics Data System (ADS)
Bracken, Paul Francis
2007-01-01
The problem of studying the quantum Hall effect on manifolds with non constant metric is addressed. The Hamiltonian on a space with hyperbolic metric is determined, and the spectrum and eigenfunctions are calculated in closed form. The hyperbolic disk is also considered and some other applications of this approach are discussed as well.
NASA Astrophysics Data System (ADS)
Varlet, Anastasia; Bischoff, Dominik; Simonet, Pauline; Watanabe, Kenji; Taniguchi, Takashi; Ihn, Thomas; Ensslin, Klaus; Mucha-Kruczyński, Marcin; Fal'ko, Vladimir I.
2014-09-01
Bilayer graphene is a unique system where both the Fermi energy and the low-energy electron dispersion can be tuned. This is brought about by an interplay between trigonal warping and the band gap opened by a transverse electric field. Here, we drive the Lifshitz transition in bilayer graphene to experimentally controllable carrier densities by applying a large transverse electric field to a h-BN-encapsulated bilayer graphene structure. We perform magnetotransport measurements and investigate the different degeneracies in the Landau level spectrum. At low magnetic fields, the observation of filling factors -3 and -6 quantum Hall states reflects the existence of three maxima at the top of the valence-band dispersion. At high magnetic fields, all integer quantum Hall states are observed, indicating that deeper in the valence band the constant energy contours are singly connected. The fact that we observe ferromagnetic quantum Hall states at odd-integer filling factors testifies to the high quality of our sample. This enables us to identify several phase transitions between correlated quantum Hall states at intermediate magnetic fields, in agreement with the calculated evolution of the Landau level spectrum. The observed evolution of the degeneracies, therefore, reveals the presence of a Lifshitz transition in our system.
Relativistic laser-plasma interactions in the quantum regime.
Eliasson, Bengt; Shukla, P K
2011-04-01
We consider nonlinear interactions between a relativistically strong laser beam and a plasma in the quantum regime. The collective behavior of electrons is modeled by a Klein-Gordon equation, which is nonlinearly coupled with the electromagnetic wave through the Maxwell and Poisson equations. This allows us to study nonlinear interactions between arbitrarily large-amplitude electromagnetic waves and a quantum plasma. We have used our system of nonlinear equations to study theoretically the parametric instabilities involving stimulated Raman scattering and modulational instabilities. A model for quasi-steady-state propagating electromagnetic wave packets is also derived, and which shows possibility of localized solitary structures in a quantum plasma. Numerical simulations demonstrate collapse and acceleration of electrons in the nonlinear stage of the modulational instability, as well as possibility of the wake-field acceleration of electrons to relativistic speeds by short laser pulses at nanometer length scales. Our study is relevant for understanding the localization of intense electromagnetic pulses in a quantum plasma with extremely high electron densities and relatively low temperature. PMID:21599316
Quantum Hall effect in an InAs /AlSb double quantum well
NASA Astrophysics Data System (ADS)
Yakunin, M. V.; Podgornykh, S. M.; Sadofyev, Yu. G.
2009-01-01
Double quantum wells (DQWs) were first implemented in the InAs /AlSb heterosystem, which is characterized by a large Landé g factor ∣g∣=15 of the InAs layers forming the well, much larger than the bulk g factor ∣g∣=0.4 of the GaAs in conventional GaAs /AlGaAs DQWs. The quality of the samples is good enough to permit observation of a clear picture of the quantum Hall effect (QHE). Despite the small tunneling gap, which is due to the large barrier height (1.4eV), features with odd filling factors ν =3,5,7,… are present in the QHE, due to collectivized interlayer states of the DQW. When the field is rotated relative to the normal to the layers, the ν =3 state is suppressed, confirming the collectivized nature of that state and denying that it could owe its existence to a strong asymmetry of the DQW. Previously the destruction of the collectivized QHE states by a parallel field had been observed only for the ν =1 state. The observation of a similar effect for ν =3 in an InAs /AlSb DQW may be due to the large bulk g factor of InAs.
THz photoresponse of quantum Hall devices based on HgTe-Quantum wells
NASA Astrophysics Data System (ADS)
Gouider, F.; Hein, G.; Brüne, C.; Buhmann, H.; Vasilyev, Yu. B.; Nachtwei, G.
2010-01-01
This study concerns the experimental investigation of the Terahertz -(THz-) photoresponse in systems under quantum-Hall-(QH-) conditions. These investigations are interesting regarding a potential application of QH-systems as fast and spectrally sensitive THz-detectors. The measurements of the THz-photoresponse (PR) of devices with HgTe quantum wells (QWs) embedded in CdHgTe barriers are aimed at obtaining photosignals at smaller magnetic fields in comparison to detectors made of GaAs/AlGaAs wafers. This can be realized by changing the electron density (application of a gate electrode). The QWs have a thickness of dQW between 7 nm and 12 nm, so that the material HgTe of the QW possesses a semimetallic band structure. We found a cyclotron mass of about mc = 0.026 m0 for our samples from cyclotron resonance measurements (also approximately determined from our PR). As this cyclotron mass is by about a factor 3 smaller than the one of electrons in GaAs, the same Landau level splitting is reached at about 1/3 of the magnetic field as in GaAs.
Zhou, Jian; Sun, Qiang; Wang, Qian; Kawazoe, Yoshiyuki; Jena, Puru
2016-06-01
Exploring a two-dimensional intrinsic quantum spin Hall state with a large band gap as well as an anomalous Hall state in realizable materials is one of the most fundamental and important goals for future applications in spintronics, valleytronics, and quantum computing. Here, by combining first-principles calculations with a tight-binding model, we predict that Sb or Bi can epitaxially grow on a stable and ferromagnetic MnO2 thin film substrate, forming a flat honeycomb sheet. The flatness of Sb or Bi provides an opportunity for the existence of Dirac points in the Brillouin zone, with its position effectively tuned by surface hydrogenation. The Dirac points in spin up and spin down channels split due to the proximity effects induced by MnO2. In the presence of both intrinsic and Rashba spin-orbit coupling, we find two band gaps exhibiting a large band gap quantum spin Hall state and a nearly quantized anomalous Hall state which can be tuned by adjusting the Fermi level. Our findings provide an efficient way to realize both quantized intrinsic spin Hall conductivity and anomalous Hall conductivity in a single material. PMID:27181160
Fractional Quantum Hall Effect and Wigner Crystal of Interacting Composite Fermions
NASA Astrophysics Data System (ADS)
Liu, Yang; Kamburov, Dobromir; Hasdemir, Sukret; Shayegan, Mansour; Pfeiffer, Loren; West, Ken; Baldwin, Kirk
2015-03-01
In two-dimensional electron systems confined to GaAs quantum wells, as a function of either tilting the sample in magnetic field or increasing density, we observe multiple transitions of the fractional quantum Hall states (FQHSs) near filling factors ν = 3/4 and 5/4. The data reveal that these are spin-polarization transitions of interacting two-flux composite Fermions, which form their own FQHSs at these fillings. The fact that the reentrant integer quantum Hall effect near ν = 4/5 always develops following the transition to full spin polarization of the ν = 4/5 FQHS strongly links the reentrant phase to a pinned ferromagnetic Wigner crystal of two-flux composite Fermions. We acknowledge support through the NSF (DMR-1305691) for measurements, and the Gordon and Betty Moore Foundation (Grant GBMF4420), Keck Foundation, the NSF MRSEC (DMR-0819860), and the DOE BES (DE-FG02-00-ER45841) for sample fabrication.
Confinement-deconfinement transition due to spontaneous symmetry breaking in quantum Hall bilayers.
Pikulin, D I; Silvestrov, P G; Hyart, T
2016-01-01
Band-inverted electron-hole bilayers support quantum spin Hall insulator and exciton condensate phases. Interest in quantum spin Hall effect in these systems has recently put them in the spotlight. We investigate such a bilayer in an external magnetic field. We show that the interlayer correlations lead to formation of a helical quantum Hall exciton condensate state. Existence of the counterpropagating edge modes in this system results in formation of a ground state spin-texture not supporting gapless single-particle excitations. The charged edge excitations in a sufficiently narrow Hall bar are confined: a charge on one of the edges always gives rise to an opposite charge on the other edge. Magnetic field and gate voltages allow the control of a confinement-deconfinement transition of charged edge excitations, which can be probed with nonlocal conductance. Confinement-deconfinement transitions are of great interest, not least because of their possible significance in shedding light on the confinement problem of quarks. PMID:26804790
Confinement-deconfinement transition due to spontaneous symmetry breaking in quantum Hall bilayers
Pikulin, D. I.; Silvestrov, P. G.; Hyart, T.
2016-01-01
Band-inverted electron-hole bilayers support quantum spin Hall insulator and exciton condensate phases. Interest in quantum spin Hall effect in these systems has recently put them in the spotlight. We investigate such a bilayer in an external magnetic field. We show that the interlayer correlations lead to formation of a helical quantum Hall exciton condensate state. Existence of the counterpropagating edge modes in this system results in formation of a ground state spin-texture not supporting gapless single-particle excitations. The charged edge excitations in a sufficiently narrow Hall bar are confined: a charge on one of the edges always gives rise to an opposite charge on the other edge. Magnetic field and gate voltages allow the control of a confinement-deconfinement transition of charged edge excitations, which can be probed with nonlocal conductance. Confinement-deconfinement transitions are of great interest, not least because of their possible significance in shedding light on the confinement problem of quarks. PMID:26804790
NASA Astrophysics Data System (ADS)
Sato, Masatoshi; Tobe, Daijiro; Kohmoto, Mahito
2008-12-01
We consider a tight-binding model with the nearest-neighbor hopping integrals on the honeycomb lattice in a magnetic field. Assuming one of the three hopping integrals, which we denote by ta , can take a different value from the two others, we study quantum phase structures controlled by the anisotropy of the honeycomb lattice. For weak and strong ta regions, the Hall conductances are calculated algebraically by using the Diophantine equation. Except for a few specific gaps, we completely determine the Hall conductances in these two regions including those for subband gaps. In a weak magnetic field, it is found that the weak ta region shows the unconventional quantization of the Hall conductance, σxy=-(e2/h)(2n+1) (n=0,±1,±2,…) , near the half filling, while the strong ta region shows only the conventional one, σxy=-(e2/h)n (n=0,±1,±2,…) . From the topological nature of the Hall conductance, the existence of gap closing points and quantum phase transitions in the intermediate ta region is concluded. We also study numerically the quantum phase structure in detail and find that even when ta=1 , namely, in graphene case, the system is in the weak ta phase except when the Fermi energy is located near the Van Hove singularity or the lower and upper edges of the spectrum.
Confinement-deconfinement transition due to spontaneous symmetry breaking in quantum Hall bilayers
NASA Astrophysics Data System (ADS)
Pikulin, D. I.; Silvestrov, P. G.; Hyart, T.
2016-01-01
Band-inverted electron-hole bilayers support quantum spin Hall insulator and exciton condensate phases. Interest in quantum spin Hall effect in these systems has recently put them in the spotlight. We investigate such a bilayer in an external magnetic field. We show that the interlayer correlations lead to formation of a helical quantum Hall exciton condensate state. Existence of the counterpropagating edge modes in this system results in formation of a ground state spin-texture not supporting gapless single-particle excitations. The charged edge excitations in a sufficiently narrow Hall bar are confined: a charge on one of the edges always gives rise to an opposite charge on the other edge. Magnetic field and gate voltages allow the control of a confinement-deconfinement transition of charged edge excitations, which can be probed with nonlocal conductance. Confinement-deconfinement transitions are of great interest, not least because of their possible significance in shedding light on the confinement problem of quarks.
Devil's Staircase Phase Diagram of the Fractional Quantum Hall Effect in the Thin-Torus Limit.
Rotondo, Pietro; Molinari, Luca Guido; Ratti, Piergiorgio; Gherardi, Marco
2016-06-24
After more than three decades, the fractional quantum Hall effect still poses challenges to contemporary physics. Recent experiments point toward a fractal scenario for the Hall resistivity as a function of the magnetic field. Here, we consider the so-called thin-torus limit of the Hamiltonian describing interacting electrons in a strong magnetic field, restricted to the lowest Landau level, and we show that it can be mapped onto a one-dimensional lattice gas with repulsive interactions, with the magnetic field playing the role of the chemical potential. The statistical mechanics of such models leads us to interpret the sequence of Hall plateaux as a fractal phase diagram whose landscape shows a qualitative agreement with experiments. PMID:27391740
Fractional quantum Hall effect at Landau level filling ν = 4/11
Pan, W.; Baldwin, K. W.; West, K. W.; Pfeiffer, L. N.; Tsui, D. C.
2015-01-09
In this study, we report low temperature electronic transport results on the fractional quantum Hall effect of composite fermions at Landau level filling ν = 4/11 in a very high mobility and low density sample. Measurements were carried out at temperatures down to 15mK, where an activated magnetoresistance Rxx and a quantized Hall resistance Rxy, within 1% of the expected value of h/(4/11)e2, were observed. The temperature dependence of the Rxx minimum at 4/11 yields an activation energy gap of ~ 7 mK. Developing Hall plateaus were also observed at the neighboring states at ν = 3/8 and 5/13.
Fractional quantum Hall effect at Landau level filling ν = 4/11
Pan, W.; Baldwin, K. W.; West, K. W.; Pfeiffer, L. N.; Tsui, D. C.
2015-01-09
In this study, we report low temperature electronic transport results on the fractional quantum Hall effect of composite fermions at Landau level filling ν = 4/11 in a very high mobility and low density sample. Measurements were carried out at temperatures down to 15mK, where an activated magnetoresistance R_{xx} and a quantized Hall resistance R_{xy}, within 1% of the expected value of h/(4/11)e^{2}, were observed. The temperature dependence of the R_{xx} minimum at 4/11 yields an activation energy gap of ~ 7 mK. Developing Hall plateaus were also observed at the neighboring states at ν = 3/8 and 5/13.
Devil's Staircase Phase Diagram of the Fractional Quantum Hall Effect in the Thin-Torus Limit
NASA Astrophysics Data System (ADS)
Rotondo, Pietro; Molinari, Luca Guido; Ratti, Piergiorgio; Gherardi, Marco
2016-06-01
After more than three decades, the fractional quantum Hall effect still poses challenges to contemporary physics. Recent experiments point toward a fractal scenario for the Hall resistivity as a function of the magnetic field. Here, we consider the so-called thin-torus limit of the Hamiltonian describing interacting electrons in a strong magnetic field, restricted to the lowest Landau level, and we show that it can be mapped onto a one-dimensional lattice gas with repulsive interactions, with the magnetic field playing the role of the chemical potential. The statistical mechanics of such models leads us to interpret the sequence of Hall plateaux as a fractal phase diagram whose landscape shows a qualitative agreement with experiments.
Space Charge Saturated Sheath Regime and Electron Temperature Saturation in Hall Thrusters
Y. Raitses; D. Staack; A. Smirnov; N.J. Fisch
2005-03-16
Secondary electron emission in Hall thrusters is predicted to lead to space charge saturated wall sheaths resulting in enhanced power losses in the thruster channel. Analysis of experimentally obtained electron-wall collision frequency suggests that the electron temperature saturation, which occurs at high discharge voltages, appears to be caused by a decrease of the Joule heating rather than by the enhancement of the electron energy loss at the walls due to a strong secondary electron emission.
Observation of the quantum Hall effect in δ-doped SrTiO3
Matsubara, Y.; Takahashi, K. S.; Bahramy, M. S.; Kozuka, Y.; Maryenko, D.; Falson, J.; Tsukazaki, A.; Tokura, Y.; Kawasaki, M.
2016-01-01
The quantum Hall effect is a macroscopic quantum phenomenon in a two-dimensional electron system. The two-dimensional electron system in SrTiO3 has sparked a great deal of interest, mainly because of the strong electron correlation effects expected from the 3d orbitals. Here we report the observation of the quantum Hall effect in a dilute La-doped SrTiO3-two-dimensional electron system, fabricated by metal organic molecular-beam epitaxy. The quantized Hall plateaus are found to be solely stemming from the low Landau levels with even integer-filling factors, ν=4 and 6 without any contribution from odd ν's. For ν=4, the corresponding plateau disappears on decreasing the carrier density. Such peculiar behaviours are proposed to be due to the crossing between the Landau levels originating from the two subbands composed of d orbitals with different effective masses. Our findings pave a way to explore unprecedented quantum phenomena in d-electron systems. PMID:27228903
Observation of the quantum Hall effect in δ-doped SrTiO3
NASA Astrophysics Data System (ADS)
Matsubara, Y.; Takahashi, K. S.; Bahramy, M. S.; Kozuka, Y.; Maryenko, D.; Falson, J.; Tsukazaki, A.; Tokura, Y.; Kawasaki, M.
2016-05-01
The quantum Hall effect is a macroscopic quantum phenomenon in a two-dimensional electron system. The two-dimensional electron system in SrTiO3 has sparked a great deal of interest, mainly because of the strong electron correlation effects expected from the 3d orbitals. Here we report the observation of the quantum Hall effect in a dilute La-doped SrTiO3-two-dimensional electron system, fabricated by metal organic molecular-beam epitaxy. The quantized Hall plateaus are found to be solely stemming from the low Landau levels with even integer-filling factors, ν=4 and 6 without any contribution from odd ν's. For ν=4, the corresponding plateau disappears on decreasing the carrier density. Such peculiar behaviours are proposed to be due to the crossing between the Landau levels originating from the two subbands composed of d orbitals with different effective masses. Our findings pave a way to explore unprecedented quantum phenomena in d-electron systems.
Influence of device geometry on tunneling in the ν=(5)/(2) quantum Hall liquid
NASA Astrophysics Data System (ADS)
Yang, Guang; Feldman, D. E.
2013-08-01
Two recent experiments [Radu , ScienceSCIEAS0036-807510.1126/science.1157560 320, 899 (2008); Lin , Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.85.165321 85, 165321 (2012)] measured the temperature and voltage dependence of the quasiparticle tunneling through a quantum point contact in the ν=5/2 quantum Hall liquid. The results led to conflicting conclusions about the nature of the quantum Hall state. In this paper, we show that the conflict can be resolved by recognizing different geometries of the devices in the experiments. We argue that in some of those geometries there is significant unscreened electrostatic interaction between the segments of the quantum Hall edge on the opposite sides of the point contact. Coulomb interaction affects the tunneling current. We compare experimental results with theoretical predictions for the Pfaffian, SU(2)2, 331, and K=8 states and their particle-hole conjugates. After Coulomb corrections are taken into account, measurements in all geometries agree with the spin-polarized and spin-unpolarized Halperin 331 states.
Quantum Hall conductance of graphene combined with charge-trap memory operation.
Kang, Haeyong; Yun, Yoojoo; Park, Jeongmin; Kim, Joonggyu; Truong, Thuy Kieu; Kim, Jeong-Gyun; Park, Nahee; Yun, Hoyeol; Lee, Sang Wook; Lee, Young Hee; Suh, Dongseok
2015-08-28
The combination of quantum Hall conductance and charge-trap memory operation was qualitatively examined using a graphene field-effect transistor. The characteristics of two terminal quantum Hall conductance appeared clearly on the background of a huge conductance hysteresis during a gate-voltage sweep for a device using monolayer graphene as a channel,hexagonal boron-nitride flakes as a tunneling dielectric and defective silicon oxide as the charge storage node. Even though there was a giant shift of the charge neutrality point, the deviation of quantized resistance value at the state of filling factor 2 was less than 1.6% from half of the von Klitzing constant. At high Landau level indices, the behaviors of quantum conductance oscillation between the increasing and the decreasing electron densities were identical in spite ofa huge memory window exceeding 100 V. Our results indicate that the two physical phenomena, two-terminal quantum Hall conductance and charge-trap memory operation, can be integrated into one device without affecting each other. PMID:26242388
Observation of the quantum Hall effect in δ-doped SrTiO3.
Matsubara, Y; Takahashi, K S; Bahramy, M S; Kozuka, Y; Maryenko, D; Falson, J; Tsukazaki, A; Tokura, Y; Kawasaki, M
2016-01-01
The quantum Hall effect is a macroscopic quantum phenomenon in a two-dimensional electron system. The two-dimensional electron system in SrTiO3 has sparked a great deal of interest, mainly because of the strong electron correlation effects expected from the 3d orbitals. Here we report the observation of the quantum Hall effect in a dilute La-doped SrTiO3-two-dimensional electron system, fabricated by metal organic molecular-beam epitaxy. The quantized Hall plateaus are found to be solely stemming from the low Landau levels with even integer-filling factors, ν=4 and 6 without any contribution from odd ν's. For ν=4, the corresponding plateau disappears on decreasing the carrier density. Such peculiar behaviours are proposed to be due to the crossing between the Landau levels originating from the two subbands composed of d orbitals with different effective masses. Our findings pave a way to explore unprecedented quantum phenomena in d-electron systems. PMID:27228903
Quantum Hall states of atomic Bose gases: Density profiles in single-layer and multilayer geometries
Cooper, N. R.; Lankvelt, F. J. M. van; Reijnders, J. W.; Schoutens, K.
2005-12-15
We describe the density profiles of confined atomic Bose gases in the high-rotation limit, in single-layer and multilayer geometries. We show that, in a local-density approximation, the density in a single layer shows a landscape of quantized steps due to the formation of incompressible liquids, which are analogous to fractional quantum Hall liquids for a two-dimensional electron gas in a strong magnetic field. In a multilayered setup we find different phases, depending on the strength of the interlayer tunneling t. We discuss the situation where a vortex lattice in the three-dimensional condensate (at large tunneling) undergoes quantum melting at a critical tunneling t{sub c{sub 1}}. For tunneling well below t{sub c{sub 1}} one expects weakly coupled or isolated layers, each exhibiting a landscape of quantum Hall liquids. After expansion, this gives a radial density distribution with characteristic features (cusps) that provide experimental signatures of the quantum Hall liquids.
NASA Astrophysics Data System (ADS)
Kharitonov, Maxim; Juergens, Stefan; Trauzettel, Björn
2016-07-01
We consider a class of quantum Hall topological insulators: topologically nontrivial states with zero Chern number at finite magnetic field, in which the counterpropagating edge states are protected by a symmetry (spatial or spin) other than time-reversal. HgTe-type heterostructures and graphene are among the relevant systems. We study the effect of electron interactions on the topological properties of the system. We particularly focus on the vicinity of the topological phase transition, marked by the crossing of two Landau levels, where the system is a strongly interacting quantum Hall ferromagnet. We analyze the edge properties using the formalism of the nonlinear σ -model. We establish the symmetry requirement for the topological protection in this interacting system: effective continuous U(1) symmetry with respect to uniaxial isospin rotations must be preserved. If U(1) symmetry is preserved, the topologically nontrivial phase persists; its edge is a helical Luttinger liquid with highly tunable effective interactions. We obtain explicit analytical expressions for the parameters of the Luttinger liquid in the quantum-Hall-ferromagnet regime. However, U(1) symmetry may be broken, either spontaneously or by U(1)-asymmetric interactions. In either case, interaction-induced transitions occur to the respective topologically trivial phases with gapped edge charge excitations.
``Perfect'' Coulomb Drag in a Bilayer Quantum Hall System
NASA Astrophysics Data System (ADS)
Nandi, D.; Finck, A. D. K.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2012-02-01
We report Coulomb drag measurements in Corbino geometry which reveal that equal but oppositely directed electrical currents can freely propagate across the insulating bulk of the bilayer quantized Hall state at νT=1 even when the two 2D layers are electrically isolated and interlayer tunneling has been heavily suppressed by an in-plane magnetic field. This effect, which we dub ``perfect'' Coulomb drag, reflects the transport of charge neutral excitons across the bulk of the 2D system. The equal magnitude of the drive and drag currents is lost at high current and when either the temperature or effective separation between the two 2D layers is increased. In each of these cases, ordinary quasiparticle charge transport across the annulus has grown to dominate over exciton transport.
Quantum Hall resistance standard in graphene devices under relaxed experimental conditions.
Ribeiro-Palau, R; Lafont, F; Brun-Picard, J; Kazazis, D; Michon, A; Cheynis, F; Couturaud, O; Consejo, C; Jouault, B; Poirier, W; Schopfer, F
2015-11-01
The quantum Hall effect provides a universal standard for electrical resistance that is theoretically based on only the Planck constant h and the electron charge e. Currently, this standard is implemented in GaAs/AlGaAs, but graphene's electronic properties have given hope for a more practical device. Here, we demonstrate that the experimental conditions necessary for the operation of devices made of high-quality graphene grown by chemical vapour deposition on silicon carbide can be extended and significantly relaxed compared with those for state-of-the-art GaAs/AlGaAs devices. In particular, the Hall resistance can be accurately quantized to within 1 × 10(-9) over a 10 T wide range of magnetic flux density, down to 3.5 T, at a temperature of up to 10 K or with a current of up to 0.5 mA. This experimental simplification highlights the great potential of graphene in the development of user-friendly and versatile quantum standards that are compatible with broader industrial uses beyond those in national metrology institutes. Furthermore, the measured agreement of the quantized Hall resistance in graphene and GaAs/AlGaAs, with an ultimate uncertainty of 8.2 × 10(-11), supports the universality of the quantum Hall effect. This also provides evidence of the relation of the quantized Hall resistance with h and e, which is crucial for the new Système International d'unités to be based on fixing such fundamental constants of nature. PMID:26344181
Quantum Hall resistance standard in graphene devices under relaxed experimental conditions
NASA Astrophysics Data System (ADS)
Ribeiro-Palau, R.; Lafont, F.; Brun-Picard, J.; Kazazis, D.; Michon, A.; Cheynis, F.; Couturaud, O.; Consejo, C.; Jouault, B.; Poirier, W.; Schopfer, F.
2015-11-01
The quantum Hall effect provides a universal standard for electrical resistance that is theoretically based on only the Planck constant h and the electron charge e. Currently, this standard is implemented in GaAs/AlGaAs, but graphene's electronic properties have given hope for a more practical device. Here, we demonstrate that the experimental conditions necessary for the operation of devices made of high-quality graphene grown by chemical vapour deposition on silicon carbide can be extended and significantly relaxed compared with those for state-of-the-art GaAs/AlGaAs devices. In particular, the Hall resistance can be accurately quantized to within 1 × 10-9 over a 10 T wide range of magnetic flux density, down to 3.5 T, at a temperature of up to 10 K or with a current of up to 0.5 mA. This experimental simplification highlights the great potential of graphene in the development of user-friendly and versatile quantum standards that are compatible with broader industrial uses beyond those in national metrology institutes. Furthermore, the measured agreement of the quantized Hall resistance in graphene and GaAs/AlGaAs, with an ultimate uncertainty of 8.2 × 10-11, supports the universality of the quantum Hall effect. This also provides evidence of the relation of the quantized Hall resistance with h and e, which is crucial for the new Système International d'unités to be based on fixing such fundamental constants of nature.
Domain wall in a quantum anomalous Hall insulator as a magnetoelectric piston
NASA Astrophysics Data System (ADS)
Upadhyaya, Pramey; Tserkovnyak, Yaroslav
2016-07-01
We theoretically study the magnetoelectric coupling in a quantum anomalous Hall insulator state induced by interfacing a dynamic magnetization texture to a topological insulator. In particular, we propose that the quantum anomalous Hall insulator with a magnetic configuration of a domain wall, when contacted by electrical reservoirs, acts as a magnetoelectric piston. A moving domain wall pumps charge current between electrical leads in a closed circuit, while applying an electrical bias induces reciprocal domain-wall motion. This pistonlike action is enabled by a finite reflection of charge carriers via chiral modes imprinted by the domain wall. Moreover, we find that, when compared with the recently discovered spin-orbit torque-induced domain-wall motion in heavy metals, the reflection coefficient plays the role of an effective spin-Hall angle governing the efficiency of the proposed electrical control of domain walls. Quantitatively, this effective spin-Hall angle is found to approach a universal value of 2, providing an efficient scheme to reconfigure the domain-wall chiral interconnects for possible memory and logic applications.
Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators.
Chang, Cui-Zu; Li, Mingda
2016-03-31
The quantum anomalous Hall effect (QAHE), the last member of Hall family, was predicted to exhibit quantized Hall conductivity σ(yx) = e2/h without any external magnetic field. The QAHE shares a similar physical phenomenon with the integer quantum Hall effect (QHE), whereas its physical origin relies on the intrinsic topological inverted band structure and ferromagnetism. Since the QAHE does not require external energy input in the form of magnetic field, it is believed that this effect has unique potential for applications in future electronic devices with low-power consumption. More recently, the QAHE has been experimentally observed in thin films of the time-reversal symmetry breaking ferromagnetic (FM) topological insulators (TI), Cr- and V- doped (Bi,Sb)2Te3. In this topical review, we review the history of TI based QAHE, the route to the experimental observation of the QAHE in the above two systems, the current status of the research of the QAHE, and finally the prospects for future studies. PMID:26934535
Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators
NASA Astrophysics Data System (ADS)
Chang, Cui-Zu; Li, Mingda
2016-03-01
The quantum anomalous Hall effect (QAHE), the last member of Hall family, was predicted to exhibit quantized Hall conductivity {σyx}=\\frac{{{e}2}}{h} without any external magnetic field. The QAHE shares a similar physical phenomenon with the integer quantum Hall effect (QHE), whereas its physical origin relies on the intrinsic topological inverted band structure and ferromagnetism. Since the QAHE does not require external energy input in the form of magnetic field, it is believed that this effect has unique potential for applications in future electronic devices with low-power consumption. More recently, the QAHE has been experimentally observed in thin films of the time-reversal symmetry breaking ferromagnetic (FM) topological insulators (TI), Cr- and V- doped (Bi,Sb)2Te3. In this topical review, we review the history of TI based QAHE, the route to the experimental observation of the QAHE in the above two systems, the current status of the research of the QAHE, and finally the prospects for future studies.
Lu Yuanming; Wang Ziqiang; Wen Xiaogang; Wang Zhenghan
2010-03-15
In the pattern-of-zeros approach to quantum Hall states, a set of data (n;m;S{sub a}|a=1,...,n;n,m,S{sub a} is n element of N) (called the pattern of zeros) is introduced to characterize a quantum Hall wave function. In this paper we find sufficient conditions on the pattern of zeros so that the data correspond to a valid wave function. Some times, a set of data (n;m;S{sub a}) corresponds to a unique quantum Hall state, while other times, a set of data corresponds to several different quantum Hall states. So in the latter cases, the pattern of zeros alone does not completely characterize the quantum Hall states. In this paper, we find that the following expanded set of data (n;m;S{sub a};c|a=1,...,n;n,m,S{sub a} is an element of N;c is an element of R) provides a more complete characterization of quantum Hall states. Each expanded set of data completely characterizes a unique quantum Hall state, at least for the examples discussed in this paper. The result is obtained by combining the pattern of zeros and Z{sub n} simple-current vertex algebra which describes a large class of Abelian and non-Abelian quantum Hall states PHI{sub Z{sub n}{sup sc}}. The more complete characterization in terms of (n;m;S{sub a};c) allows us to obtain more topological properties of those states, which include the central charge c of edge states, the scaling dimensions and the statistics of quasiparticle excitations.
Edge-channel interferometer at the graphene quantum Hall pn junction
Morikawa, Sei; Moriya, Rai; Masubuchi, Satoru Machida, Tomoki; Watanabe, Kenji; Taniguchi, Takashi
2015-05-04
We demonstrate a quantum Hall edge-channel interferometer in a high-quality graphene pn junction under a high magnetic field. The co-propagating p and n quantum Hall edge channels traveling along the pn interface functions as a built-in Aharonov-Bohm-type interferometer, the interferences in which are sensitive to both the external magnetic field and the carrier concentration. The trajectories of peak and dip in the observed resistance oscillation are well reproduced by our numerical calculation that assumes magnetic flux quantization in the area enclosed by the co-propagating edge channels. Coherent nature of the co-propagating edge channels is confirmed by the checkerboard-like pattern in the dc-bias and magnetic-field dependences of the resistance oscillations.
Spin-Hamiltonian for the Quantum Hall State in a Ladder Geometry
NASA Astrophysics Data System (ADS)
Kapit, Eliot
2005-03-01
The first calculation of the true ground state of the parent-Hamiltonian proposed by Laughlin [R. B. Laughlin, Ann. Phys. 191, 163 (1989)] for the m=2 Fractional Quantum Hall state on a torus is presented. Laughlin's model is generalized to the case of a system in a ladder geometry and rewritten in terms of familiar spin-spin interactions, demonstrating that the model corresponds to a long-range Heisenberg Hamiltonian with an additional four-site interaction. The exact diagonalization of the Hamiltonian is performed to extract the energy, correlation functions, sub-lattice magnetization, and overlap with the Quantum Hall state. Our results confirm the recent work showing that the model is not exact [D. F. Schroeter, Ann. Phys. 310, 155 (2004)] and also show it to be not without merit: the overlap between the QH state and exact ground state approaches the significant value of 0.83 in the limit that the ladder becomes infinitely long.
Simulation of the many-body dynamical quantum Hall effect in an optical lattice
NASA Astrophysics Data System (ADS)
Zhang, Dan-Wei; Yang, Xu-Chen
2016-05-01
We propose an experimental scheme to simulate the many-body dynamical quantum Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice. We first show that the required model Hamiltonian of a spin-1/2 Heisenberg chain with an effective magnetic field and tunable parameters can be realized in this system. For dynamical response to ramping the external fields, the quantized plateaus emerge in the Berry curvature of the interacting atomic spin chain as a function of the effective spin-exchange interaction. The quantization of this response in the parameter space with the interaction-induced topological transition characterizes the many-body dynamical quantum Hall effect. Furthermore, we demonstrate that this phenomenon can be observed in practical cold atom experiments with numerical simulations.
The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid
NASA Astrophysics Data System (ADS)
Parameswaran, S. A.; Kivelson, S. A.; Sondhi, S. L.; Spivak, B. Z.
2011-03-01
The Pfaffian phase of electrons in the proximity of a half-filled Landau level is understood to be a p + ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing scale is small, i.e. in the weak-coupling, BCS, limit, where the coherence length is much larger than the charge screening length. We find that, as in a Type I superconductor, the vortices attract so that, upon varying the magnetic field from its magic value at ν = 5 / 2 , the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffian states exemplify a general dichotomy between Type I and Type II quantum Hall fluids. This work was supported in part by NSF grants DMR-1006608 and PHY-1005429 (SAP, SLS), DMR-0758356 (SAK) and DMR-0704151 (BZS).
The weakly coupled Pfaffian as a type I quantum hall liquid
NASA Astrophysics Data System (ADS)
Parameswaran, S. A.; Kivelson, S. A.; Sondhi, S. L.; Spivak, B. Z.
2012-06-01
The Pfaffian phase of electrons in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing scale is small, i.e. in the weak coupling, BCS, limit, where the coherence length is much larger than the charge screening length. We find that, as in a Type I superconductor, vortices attract so that, upon varying the magnetic field from its magic value at ν=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffian states exemplify a general dichotomy between Type I and Type II quantum Hall fluids.
Phase diagram for bilayer quantum Hall effect at total filling νT=5
NASA Astrophysics Data System (ADS)
Shi, Chuntai; Jolad, Shivakumar; Regnault, Nicolas; Jain, Jainendra
2009-03-01
There has been much interest in bilayer quantum Hall systems at total filling νT=1, which exhibit excitonic superfluidity at small separations and two uncoupled composite fermion Fermi seas at large separations. We evaluate the phase diagram of the bilayer quantum Hall effect at total filling νT=5, neglecting interlayer tunneling and spin fluctuations, which is expected to be a bilayer excitonic superfluid at small separations and two uncoupled 5/2 FQHE states at large separations. Based on a combination of variational and exact diagonalization (for up to 20 electrons) studies, we estimate that the transition between these states occurs at a layer separation of approximately one magnetic length,independent of the individual layer thickness. The composite fermion Fermi sea is not found to be relevant for any parameters.
Spin-singlet quantum Hall states and Jack polynomials with a prescribed symmetry
NASA Astrophysics Data System (ADS)
Estienne, Benoit; Bernevig, B. Andrei
2012-04-01
We show that a large class of bosonic spin-singlet Fractional Quantum Hall model wavefunctions and their quasihole excitations can be written in terms of Jack polynomials with a prescribed symmetry. Our approach describes new spin-singlet quantum Hall states at filling fraction ν=2k/2r-1 and generalizes the (k,r) spin-polarized Jack polynomial states. The NASS and Halperin spin-singlet states emerge as specific cases of our construction. The polynomials express many-body states which contain configurations obtained from a root partition through a generalized squeezing procedure involving spin and orbital degrees of freedom. The corresponding generalized Pauli principle for root partitions is obtained, allowing for counting of the quasihole states. We also extract the central charge and quasihole scaling dimension, and propose a conjecture for the underlying CFT of the (k,r) spin-singlet Jack states.
Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures
Xiao, Di; Zhu, Wenguang; Ran, Ying; Nagaosa, Naoto; Okamoto, Satoshi
2011-01-01
Topological insulators (TIs) are characterized by a non-trivial band topology driven by the spin-orbit coupling. To fully explore the fundamental science and application of TIs, material realization is indispensable. Here we predict, based on tight-binding modeling and first-principles calculations, that bilayers of perovskite-type transition-metal oxides grown along the [111] crystallographic axis are potential candidates for two-dimensional TIs. The topological band structure of these materials can be fine-tuned by changing dopant ions, substrates and external gate voltages. We predict that LaAuO$_3$ bilayers have a topologically non-trivial energy gap of about 0.15~eV, which is sufficiently large to realize the quantum spin Hall effect at room temperature. Intriguing phenomena, such as fractional quantum Hall effect, associated with the nearly flat topologically non-trivial bands found in $e_g$ systems are also discussed.
Fragile Fractional Quantum Hall States in the Lowest and the Second Landau Level
NASA Astrophysics Data System (ADS)
Csathy, Gabor; Kleinbaum, Ethan; Kumar, Ashwani; Samkharadze, Nodar; Pfeiffer, Loren; West, Ken
Ultra-low temperature measurements of the two-dimensional electron gas have revealed some of the most fragile fractional quantum Hall states. In these experiments electron thermalization was achieved using a He-3 immersion cell and the temperature of the bath is monitored using a quartz tuning fork viscometer. We will review the recently discovered fractional quantum Hall state at filling factor ν = 3 + 1 / 3 observed in the second Landau level and those at the filling factor ν = 4 / 11 and 5 / 13 in the lowest Landau level. The work at Purdue was supported by NSF DMR 1207375 and 1505866 grants. The work at Princeton University was funded by the Gordon and Betty Moore Foundation through the EPiQS initiative Grant GBMF4420, and by the National Science Foundation MRSEC Grant DMR-1420541.
Observation of new fractional quantum Hall states in the first Landau level in graphene
NASA Astrophysics Data System (ADS)
Amet, Francois; Bestwick, Andrew; Williams, James; Watanabe, Kenji; Taniguchi, Takahashi; Goldhaber-Gordon, David
2014-03-01
We report on transport studies of the fractional quantum Hall effect in the n=0 and n=1 Landau level of monolayer graphene. The quality of the devices studied here -with mobilities up to 400 000cm2/Vs, and magnetic fields up to 45T- allows us to observe a variety of fractional quantum hall states following the composite fermion sequence, with denominators up to 9. The presence of odd numerator fractions between nu=1 and nu=2 is attributed to the breaking of the valley symmetry and correlates with a zero field insulating state observed at charge neutrality. We discuss the in-plane field dependence of the gaps, which is not trivial and shows dramatic differences between the n=0 and the n=1 Landau levels.
Interplay between snake and quantum edge states in a graphene Hall bar with a pn-junction
Milovanović, S. P. Peeters, F. M.; Ramezani Masir, M.
2014-09-22
The magneto- and Hall resistance of a locally gated cross shaped graphene Hall bar is calculated. The edge of the top gate is placed diagonally across the center of the Hall cross. Four-probe resistance is calculated using the Landauer-Büttiker formalism, while the transmission coefficients are obtained using the non-equilibrium Green's function approach. The interplay between transport due to edge channels and snake states is investigated. When two edge channels are occupied, we predict oscillations in the Hall and the bend resistance as function of the magnetic field, which are a consequence of quantum interference between the occupied snake states.
Operating Spin Echo in the Quantum Regime for an Atomic-Ensemble Quantum Memory.
Rui, Jun; Jiang, Yan; Yang, Sheng-Jun; Zhao, Bo; Bao, Xiao-Hui; Pan, Jian-Wei
2015-09-25
Spin echo is a powerful technique to extend atomic or nuclear coherence times by overcoming the dephasing due to inhomogeneous broadenings. However, there are disputes about the feasibility of applying this technique to an ensemble-based quantum memory at the single-quanta level. In this experimental study, we find that noise due to imperfections of the rephasing pulses has both intense superradiant and weak isotropic parts. By properly arranging the beam directions and optimizing the pulse fidelities, we successfully manage to operate the spin echo technique in the quantum regime by observing nonclassical photon-photon correlations as well as the quantum behavior of retrieved photons. Our work for the first time demonstrates the feasibility of harnessing the spin echo method to extend the lifetime of ensemble-based quantum memories at the single-quanta level. PMID:26451551
A spin-filter made of quantum anomalous Hall insulator nanowires
Wu, Jiansheng
2014-07-28
Topological end states (TES) in quantum anomalous Hall insulator nanowires can induce tunneling within the gap. Such TES are spin polarized, thus the induced current is spin polarized as well, which can be used to construct a spin-filter applied in spintronics. An interferometry device is designed to control the polarized current as well. The advantage and finite size effect on this system are discussed.
Collective nature of the reentrant integer quantum Hall states in the second Landau level.
Deng, N; Kumar, A; Manfra, M J; Pfeiffer, L N; West, K W; Csáthy, G A
2012-02-24
We report an unexpected sharp peak in the temperature dependence of the magnetoresistance of the reentrant integer quantum Hall states in the second Landau level. This peak defines the onset temperature of these states. We find that in different spin branches the onset temperatures of the reentrant states scale with the Coulomb energy. This scaling provides direct evidence that Coulomb interactions play an important role in the formation of these reentrant states evincing their collective nature. PMID:22463555
Collective Nature of the Reentrant Integer Quantum Hall States in the Second Landau Level
NASA Astrophysics Data System (ADS)
Deng, N.; Kumar, A.; Manfra, M. J.; Pfeiffer, L. N.; West, K. W.; Csáthy, G. A.
2012-02-01
We report an unexpected sharp peak in the temperature dependence of the magnetoresistance of the reentrant integer quantum Hall states in the second Landau level. This peak defines the onset temperature of these states. We find that in different spin branches the onset temperatures of the reentrant states scale with the Coulomb energy. This scaling provides direct evidence that Coulomb interactions play an important role in the formation of these reentrant states evincing their collective nature.
Effective-field-theory model for the fractional quantum Hall effect
NASA Technical Reports Server (NTRS)
Zhang, S. C.; Hansson, T. H.; Kivelson, S.
1989-01-01
Starting directly from the microscopic Hamiltonian, a field-theory model is derived for the fractional quantum Hall effect. By considering an approximate coarse-grained version of the same model, a Landau-Ginzburg theory similar to that of Girvin (1986) is constructed. The partition function of the model exhibits cusps as a function of density. It is shown that the collective density fluctuations are massive.
Evidence for a finite-temperature phase transition in a bilayer quantum Hall system.
Champagne, A R; Eisenstein, J P; Pfeiffer, L N; West, K W
2008-03-01
We study the Josephson-like interlayer tunneling signature of the strongly correlated nuT=1 quantum Hall phase in bilayer two-dimensional electron systems as a function of the layer separation, temperature, and interlayer charge imbalance. Our results offer strong evidence that a finite temperature phase transition separates the interlayer coherent phase from incoherent phases which lack strong interlayer correlations. The transition temperature is dependent on both the layer spacing and charge imbalance between the layers. PMID:18352740
Phase diagram for bilayer quantum Hall effect at total filling νT=5
NASA Astrophysics Data System (ADS)
Shi, Chuntai; Jolad, Shivakumar; Regnault, Nicolas; Jain, Jainendra K.
2008-04-01
We evaluate the phase diagram of the bilayer quantum Hall effect at total filling νT=5 , which is a bilayer phase coherent state at small separations and two uncoupled 5/2 states at large separations. Based on a combination of variational and exact calculations, we estimate that the transition between these states occurs at a layer separation of approximately one magnetic length. The composite fermion Fermi sea is not found to be relevant for any parameters.
Evidence for a Finite-Temperature Phase Transition in a Bilayer Quantum Hall System
NASA Astrophysics Data System (ADS)
Champagne, A. R.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2008-03-01
We study the Josephson-like interlayer tunneling signature of the strongly correlated νT=1 quantum Hall phase in bilayer two-dimensional electron systems as a function of the layer separation, temperature, and interlayer charge imbalance. Our results offer strong evidence that a finite temperature phase transition separates the interlayer coherent phase from incoherent phases which lack strong interlayer correlations. The transition temperature is dependent on both the layer spacing and charge imbalance between the layers.
Spin Polarization of the ν=1 Quantum Hall State Via Optical Spectroscopy
NASA Astrophysics Data System (ADS)
Goldberg, B. B.
1996-03-01
excitations where exchange energy dominates Zeeman energy in the integer quantum Hall regime at ν=1.
NASA Astrophysics Data System (ADS)
Xu, Yang; Miotkowski, Ireneusz; Chen, Yong; Yong P. Chen's Group in Purdue Team; Chih-Kang Shih's Group in UT-Austin Collaboration; M. Zahid Hasan's Group in Princeton Collaboration
2015-03-01
A three-dimensional (3D) topological insulator (TI) is a novel quantum matter with a gapped insulating bulk yet a conducting surface hosting topologically-protected gapless surface states of Dirac fermions. One of the most distinct electronic transport signatures predicted for such topological surface states (TSS) is a half-integer quantum Hall effect (QHE) in a magnetic field. We have observed well-developed QHE arising from TSS in an intrinsic TI of BiSbTeSe2. Our samples can exhibit surface dominated conduction even close to room temperature, while the bulk conduction is negligible. At low temperatures and high perpendicular magnetic fields, the Hall conductance shows well quantized integer plateaux in exfoliated flake devices on SiO2 / Si substrates, where the top and bottom surface each contributing a half integer e2 / h Hall conductance, accompanied by vanishing longitudinal resistance. We have also studied dual-gated devices where both the top and bottom surfaces can be independently gated. Such intrinsic 3D TI materials exhibiting no measurable bulk conduction and well-developed surface state QHE pave the way for further applications of topological quantum electronics. DARPA MESO program (Grant N66001-11-1-4107).
NASA Astrophysics Data System (ADS)
Balram, Ajit C.; Jain, J. K.
2016-02-01
The microscopic wave functions of the composite fermion theory can incorporate electron mass anisotropy by a trivial rescaling of the coordinates. These wave functions are very likely adiabatically connected to the actual wave functions of the anisotropic fractional quantum Hall states. We show in this paper that they possess the nice property that their energies can be analytically related to the previously calculated energies for the isotropic states through a universal scale factor, thus allowing an estimation of several observables in the thermodynamic limit for all fractional quantum Hall states as well as the composite fermion Fermi sea. The rather weak dependence of the scale factor on the anisotropy provides insight into why fractional quantum Hall effect and composite fermions are quite robust to electron mass anisotropy. We discuss how better, though still approximate, wave functions can be obtained by introducing a variational parameter, following Haldane [F. D. M. Haldane, Phys. Rev. Lett. 107, 116801 (2011), 10.1103/PhysRevLett.107.116801], but the resulting wave functions are not readily amenable to calculations. Our considerations are also applicable, with minimal modification, to the case where the dielectric function of the background material is anisotropic.
Kiyama, H. Fujita, T.; Teraoka, S.; Oiwa, A.; Tarucha, S.
2014-06-30
Spin filtering with electrically tunable efficiency is achieved for electron tunneling between a quantum dot and spin-resolved quantum Hall edge states by locally gating the two-dimensional electron gas (2DEG) leads near the tunnel junction to the dot. The local gating can change the potential gradient in the 2DEG and consequently the edge state separation. We use this technique to electrically control the ratio of the dot–edge state tunnel coupling between opposite spins and finally increase spin filtering efficiency up to 91%, the highest ever reported, by optimizing the local gating.
Interlayer transport of nuclear spin polarization in Î½ = 2/3 quantum Hall states
NASA Astrophysics Data System (ADS)
Tsuda, S.; Nguyen, M. H.; Terasawa, D.; Fukuda, A.; Zheng, Y. D.; Arai, T.; Sawada, A.
2013-12-01
We investigated the interlayer diffusion of nuclear spin polarization (NSP) by using the phase transition point of quantum Hall states at a Landau level filling factor of ν ν 2/3 in a double quantum well sample. When the NSP is current-pumped in one layer, the magnetoresistance in the other layer is enhanced after a delay of 150 s and the raising speed of this layer is lower than that of the pumped layer. The delay and lower value of the raising speed are explained by the diffusion of NSP.
Interlayer transport of nuclear spin polarization in ν = 2/3 quantum Hall states
Tsuda, S.; Nguyen, M. H.; Terasawa, D.; Fukuda, A.; Zheng, Y. D.; Arai, T.; Sawada, A.
2013-12-04
We investigated the interlayer diffusion of nuclear spin polarization (NSP) by using the phase transition point of quantum Hall states at a Landau level filling factor of ν ν 2/3 in a double quantum well sample. When the NSP is current-pumped in one layer, the magnetoresistance in the other layer is enhanced after a delay of 150 s and the raising speed of this layer is lower than that of the pumped layer. The delay and lower value of the raising speed are explained by the diffusion of NSP.
Impact of disorder on the 5/2 fractional quantum Hall state.
Pan, W; Masuhara, N; Sullivan, N S; Baldwin, K W; West, K W; Pfeiffer, L N; Tsui, D C
2011-05-20
We compare the energy gap of the ν = 5/2 fractional quantum Hall effect state obtained in conventional high mobility modulation-doped quantum-well samples with those obtained in high quality GaAs transistors (heterojunction insulated gate field-effect transistors). We are able to identify the different roles that long-range and short-range disorders play in the 5/2 state and observe that the long-range potential fluctuations are more detrimental to the strength of the 5/2 state than short-range potential disorder. PMID:21668256
Nanoscale Mach-Zehnder interferometer with spin-resolved quantum Hall edge states
NASA Astrophysics Data System (ADS)
Karmakar, Biswajit; Venturelli, Davide; Chirolli, Luca; Giovannetti, Vittorio; Fazio, Rosario; Roddaro, Stefano; Pfeiffer, Loren N.; West, Ken W.; Taddei, Fabio; Pellegrini, Vittorio
2015-11-01
We realize a nanoscale-area Mach-Zehnder interferometer with co-propagating quantum Hall spin-resolved edge states and demonstrate the persistence of gate-controlled quantum interference oscillations, as a function of an applied magnetic field, at relatively large temperatures. Arrays of top-gate magnetic nanofingers are used to induce a resonant charge transfer between the pair of spin-resolved edge states. To account for the pattern of oscillations measured as a function of magnetic field and gate voltage, we have developed a simple theoretical model which satisfactorily reproduces the data.
DC resistance comparison between a current comparator bridge and the quantum Hall system at Inmetro
NASA Astrophysics Data System (ADS)
da Silva, M. C.; Carvalho, H. R.; Vasconcellos, R. T. B.
2016-07-01
This paper presents a comparison results between the Quantum Hall System (QHS) under development at the Quantum Electrical Metrology Laboratory (Lameq) and the current comparator calibration system, traceable to the Bureau International des Poids et Mesures (BIPM), at the Electrical Standardization Metrology Laboratory (Lampe), both part of the Electrical Metrology Division, at Inmetro. Comparisons were performed with 1 Ω, 10 Ω, 100 Ω, 1 kΩ and 10 kΩ resistors. The results obtained over two years of work are presented here, showing that the comparison contributed to improve the calibration systems of both Lampe and Lameq.
Inmetro's Quantum Hall System verification on the basis of BIPM calibration results
NASA Astrophysics Data System (ADS)
Carvalho, H. R.; Briones, R. E. M.; Silva, J. R. B.
2015-01-01
This article presents the analysis generated by the primary resistance measurement system based on the Quantum Hall Effect, currently being implemented in the Quantum Electrical Metrology Laboratory (Lameq) of the National Institute of Metrology, Quality and Technology (Inmetro). It has as reference the calibration results emitted by the Bureau International des Poids et Mesures (BIPM) for the reference resistors maintained by the Electrical Standardization Metrology Laboratory (Lampe), also of Inmetro, thus offering a preliminary parameter of the compatibility status between the primary systems of these two institutions.
Persistent quantum resonance transition in spin Hall transport
NASA Astrophysics Data System (ADS)
Chen, Kuo-Chin; Lee, Hsin-Han; Chang, Ching-Ray
2016-01-01
We propose an H-shaped two-dimensional topological insulator (2DTI) as a persistent quantum resonance device. The helical edge states of 2DTI are robust against a nonmagnetic field. However, the helical edge states interfere with bound states created by a nonmagnetic impurity. Transmissions between leads shows two kinds of quantum resonance in this device, the Breit-Wigner resonance and a Fano-like resonance. These resonances can be realized in the device through modulating the on-site impurity potential. Resonances in 2DTI are persistent because the helical state has no backscattering that is protected by time-reversal-symmetry conservation. The finite-size effect in 2DTI leads to the phase transition between the Fano and the Breit-Wigner resonances through modulating the thickness of the 2DTI leads.
Interference-induced thermoelectric switching and heat rectification in quantum Hall junctions
NASA Astrophysics Data System (ADS)
Vannucci, Luca; Ronetti, Flavio; Dolcetto, Giacomo; Carrega, Matteo; Sassetti, Maura
2015-08-01
Interference represents one of the most striking manifestations of quantum physics in low-dimensional systems. Despite evidence of quantum interference in charge transport having been known for a long time, signatures of interference-induced thermal properties have been reported only recently, paving the way for the phase-coherent manipulation of heat in mesoscopic devices. In this work we show that anomalous thermoelectric properties and efficient heat rectification can be achieved by exploiting the phase-coherent edge states of quantum Hall systems. By considering a tunneling geometry with multiple quantum point contacts, we demonstrate that the interference paths effectively break the electron-hole symmetry, allowing for a thermoelectric charge current flowing either from hot to cold or vice versa, depending on the details of the tunnel junction. Correspondingly, an interference-induced heat current is predicted, and we are able to explain these results in terms of an intuitive physical picture. Moreover, we show that heat rectification can be achieved by coupling two quantum Hall systems with different filling factors, and that this effect can be enhanced by exploiting the interference properties of the tunnel junction.
Long-distance entanglement of spin qubits via quantum Hall edge states
NASA Astrophysics Data System (ADS)
Yang, Guang; Hsu, Chen-Hsuan; Stano, Peter; Klinovaja, Jelena; Loss, Daniel
2016-02-01
The implementation of a functional quantum computer involves entangling and coherent manipulation of a large number of qubits. For qubits based on electron spins confined in quantum dots, which are among the most investigated solid-state qubits at present, architectural challenges are often encountered in the design of quantum circuits attempting to assemble the qubits within the very limited space available. Here, we provide a solution to such challenges based on an approach to realizing entanglement of spin qubits over long distances. We show that long-range Ruderman-Kittel-Kasuya-Yosida interaction of confined electron spins can be established by quantum Hall edge states, leading to an exchange coupling of spin qubits. The coupling is anisotropic and can be either Ising type or XY type, depending on the spin polarization of the edge state. Such a property, combined with the dependence of the electron spin susceptibility on the chirality of the edge state, can be utilized to gain valuable insights into the topological nature of various quantum Hall states.
Long-distance entanglement of spin qubits via quantum Hall edge states
NASA Astrophysics Data System (ADS)
Yang, Guang; Hsu, Chen-Hsuan; Stano, Peter; Klinovaja, Jelena; Loss, Daniel
The implementation of a functional quantum computer involves entangling and coherent manipulation of a large number of qubits. For qubits based on electron spins confined in quantum dots, which are among the most investigated solid-state qubits at present, architectural challenges are often encountered in the design of quantum circuits attempting to assemble the qubits within the very limited space available. Here, we provide a solution to such challenges based on an approach to realizing entanglement of spin qubits over long distances. We show that long-range Ruderman-Kittel-Kasuya-Yosida interaction of confined electron spins can be established by quantum Hall edge states, leading to an exchange coupling of spin qubits. The coupling is anisotropic and can be either Ising-type or XY-type, depending on the spin polarization of the edge state. Such a property, combined with the dependence of the electron-spin susceptibility on the chirality of the edge state, can be utilized to gain valuable insights into the topological nature of various quantum Hall states.
Fractional Quantum Hall Effect of Rydberg-Polaritons
NASA Astrophysics Data System (ADS)
Grusdt, Fabian; Fleischhauer, Michael; Otterbach, Johannes
2012-02-01
Dark-state-polaritons (DSP) are bosonic quasiparticles arising in the interaction of light with 3-level atoms under conditions of electromagnetically induced transparency (EIT). They can be exposed to artificial magnetic fields, strong enough to enter the lowest Landau level regime [Otterbach et. al., Phys. Rev. Lett. 104 (2010)]. We take into account interactions between the DSPs via Rydberg dipole-dipole interactions and discuss the realization of the ν=1/2-Laughlin state and its anyonic excitations (quasiholes) in such systems. The DSPs can be prepared in the correct total angular-momentum subspace by using orbital angular momentum light beams. A numerical and semi-analytical evaluation of the quasihole-gap is presented.
Characterization of partially ordered GaInP/GaAs heterointerfaces by the quantum Hall effect
NASA Astrophysics Data System (ADS)
Uchida, Kazuo; Satoh, Kiwamu; Asano, Keita; Koizumi, Atsushi; Nozaki, Shinji
2013-05-01
The new approach to the characterization of semiconductor interfacial properties by the quantum Hall effect (QHE) and the scanning near field optical microscopy (SNOM) is demonstrated to the heterointerfaces of partially ordered GaInP/GaAs grown by low-pressure Metal Organic Vapor Phase Epitaxy. The Shubnikov de-Haas (SdH) oscillations and the Hall plateaus are observed in the heterointerfaces of both the less-ordered and more-ordered GaInP/GaAs samples with a large clover-shape, but these samples exhibit both 2D and 3D electron behaviors. In contrast to large clover-shaped samples, the distinct SdH oscillations and the Hall plateaus in the less-ordered sample, while the single SdH oscillation and the corresponding large plateau in the more-ordered small Hall-bar sample are observed. These results suggest that there may be many domains, each having a different carrier density and sizes in the less-ordered sample, while one or few large domains with uniform carrier concentration and sizes in the more-ordered sample. In SNOM measurements, PL intensity varies in the mapping of the more-ordered sample and it is concluded that the variation of the PL intensity may result from an inhomogeneous distribution of non-radiative recombination centers in the more-ordered sample.
Proposal for realizing the quantum spin Hall phase in a gapped graphene bilayer
NASA Astrophysics Data System (ADS)
Zhai, Xuechao; Jin, Guojun
2016-05-01
Quantum spin Hall (QSH) insulators with gapless edge states have potential applications in designing low-dissipation devices. In spite of many predictions, to verify the QSH phase in graphene layered materials experimentally is still difficult due to the obstacle in achieving spin-orbit coupling strong enough. We propose a Rashba system of graphene bilayer gapped by dielectric layers and show it can host a valley-polarized QSH phase even when the Rashba interaction approached zero. Such a system exhibits asymmetric topological quantum phase transitions under opposite interlayer biases, due to the dielectric-potential induced inversion asymmetry in the absence of interlayer bias. Specifically, the quantum valley Hall phase exists in zigzag-edged nanoribbons under the bias in one direction but is absent under the reverse bias. These topological phenomena can be well understood by the competition among the dielectric-induced potential, Rashba interaction, and interlayer bias in modulating the bulk band gap. Moreover, the phase diagram is given and the corresponding phase boundaries are derived analytically. Our findings provide a possible way to detect the QSH-related asymmetric topological quantum phenomena in graphene bilayer based on the current experimental technology.
Correlating scattering times with the strength of the ν=5/2 fractional quantum Hall state
NASA Astrophysics Data System (ADS)
Mondal, Sumit; Watson, John; Gardner, Geoffrey; Samkharadze, Nodar; Csathy, Gabor; Manfra, Michael
2012-02-01
There is widespread interest in the fractional quantum Hall effect at ν=5/2. Theory predicts that the state at ν=5/2 may possess non-Abelian braiding statistics. Experimental interrogation remains difficult due to the fragility of the excitation gaps requiring both high quality samples and examination at low temperatures. Mounting evidence suggests that the strength of the most fragile fractional quantum Hall states in the 2^nd Landau level including ν=5/2 are poorly correlated with the scattering time extracted from zero-field mobility measurements at higher temperatures. It is also unclear if the quantum scattering time derived from analysis of the low-field Shubnikov de-Haas oscillations provides any additional information relevant to prediction of the strengths of the observed fractional states. We report on a systematic attempt to correlate the T=0.3K behavior of the mobility lifetime, quantum scattering time, and an effective high field mobility lifetime evaluated at ν=5/2 with the measured activation gap. We will present results from a number of heterostructure designs over a wide span of zero-field mobility ranging from ˜10x10^6cm^2/Vs to greater than 20x10^6cm^2/Vs.
Lafont, F.; Ribeiro-Palau, R.; Kazazis, D.; Michon, A.; Couturaud, O.; Consejo, C.; Chassagne, T.; Zielinski, M.; Portail, M.; Jouault, B.; Schopfer, F.; Poirier, W.
2015-01-01
Replacing GaAs by graphene to realize more practical quantum Hall resistance standards (QHRS), accurate to within 10−9 in relative value, but operating at lower magnetic fields than 10 T, is an ongoing goal in metrology. To date, the required accuracy has been reported, only few times, in graphene grown on SiC by Si sublimation, under higher magnetic fields. Here, we report on a graphene device grown by chemical vapour deposition on SiC, which demonstrates such accuracies of the Hall resistance from 10 T up to 19 T at 1.4 K. This is explained by a quantum Hall effect with low dissipation, resulting from strongly localized bulk states at the magnetic length scale, over a wide magnetic field range. Our results show that graphene-based QHRS can replace their GaAs counterparts by operating in as-convenient cryomagnetic conditions, but over an extended magnetic field range. They rely on a promising hybrid and scalable growth method and a fabrication process achieving low-electron-density devices. PMID:25891533
Tunable insulator-quantum Hall transition in a weakly interacting two-dimensional electron system
2013-01-01
We have performed low-temperature measurements on a gated two-dimensional electron system in which electron–electron (e-e) interactions are insignificant. At low magnetic fields, disorder-driven movement of the crossing of longitudinal and Hall resistivities (ρxx and ρxy) can be observed. Interestingly, by applying different gate voltages, we demonstrate that such a crossing at ρxx ~ ρxy can occur at a magnetic field higher, lower, or equal to the temperature-independent point in ρxx which corresponds to the direct insulator-quantum Hall transition. We explicitly show that ρxx ~ ρxy occurs at the inverse of the classical Drude mobility 1/μD rather than the crossing field corresponding to the insulator-quantum Hall transition. Moreover, we show that the background magnetoresistance can affect the transport properties of our device significantly. Thus, we suggest that great care must be taken when calculating the renormalized mobility caused by e-e interactions. PMID:23819745
Proximity semiconducting nanowire junctions from Josephson to quantum dot regimes
NASA Astrophysics Data System (ADS)
Gharavi, Kaveh; Holloway, Gregory; Baugh, Jonathan
Experimental low-temperature transport results are presented on proximity-effect Josephson junctions made from low bandgap III-V semiconductor nanowires contacted with Nb. Two regimes are explored in terms of the Nb/nanowire interface transparency t. (i) High t allows a supercurrent to flow across the junction with magnitude Ic, which can be modulated using the voltage Vg on a global back gate or a local gate. Relatively high values are obtained for the figure-of-merit parameter IcRN / (eΔ) ~ 0 . 5 , and t ~ 0 . 75 , where RN is the normal state resistance and Δ the superconducting gap of the Nb leads. With the application of an axial magnetic field, Ic decays but exhibits oscillations before being fully suppressed. The period and amplitude of the oscillations depend on Vg. Possible explanations for this behaviour are presented, including Josephson interference of the orbital subbands in the nanowire. (ii) Lower transparency correlates with a spontaneous quantum dot (QD) formed in the nanowire channel. Pairs of Andreev Bound States (ABS) appear at energies | E | < Δ , with one pair unexpectedly pinned at E = 0 for a wide range of Vg. A description of the QD-ABS system beyond the Anderson model is presented to explain the latter results.
Bosonic integer quantum Hall states in topological bands with Chern number two
NASA Astrophysics Data System (ADS)
Zeng, Tian-Sheng; Zhu, W.; Sheng, D. N.
2016-05-01
We study the interacting bosons in topological Hofstadter bands with Chern number two. Using exact diagonalization, we demonstrate that the bosonic integer quantum Hall (BIQH) state emerges at integer boson filling factor ν =1 of the lowest Chern band with evidence including a robust spectrum gap and quantized topological Hall conductance two. Moreover, the robustness of BIQH state against different interactions and next-nearest-neighbor hopping is investigated. The strong nearest-neighbor interaction would favor a charge density wave. When the on-site interaction decreases, the BIQH state undergoes a continuous transition into a superfluid state. Without next-nearest-neighbor hopping, the ground state is possibly in a metallic Fermi-liquid-like phase.
Landau-level dispersion and the quantum Hall plateaus in bilayer graphene
Zarenia, M.; Peeters, F. M.; Vasilopoulos, P.; Pourtolami, N.
2013-12-04
We study the quantum Hall effect (QHE) in bilayer graphene using the Kubo-Greenwood formula. At zero temperature the Hall conductivity σ{sub yx} is given by σ{sub yx} = 4(N+1)e{sup 2}/h with N the index of the highest occupied Landau level (LL). Including the dispersion of the LLs and their width, due to e.g. scattering by impurities, produces the plateau of the n = 0 LL in agreement with experimental results on doped samples and similar theoretical results on single-layer graphene plateaus widen with impurity concentration. Further, the evaluated resistivity ρ{sub xx} exhibits a strong, oscillatory dependence on the electron concentration. Explicit results are obtained for δ-function impurities.
Hwang, Kyusung; Kim, Yong Baek
2016-01-01
We theoretically investigate emergent quantum phases in the thin film geometries of the pyrochore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases as well as novel quantum states that may arise only in the thin film platforms, are studied via a theoretical model that allows layer-dependent magnetic structures. It is found that the magnetic order develop in inhomogeneous fashions in the thin film geometries. This leads to a variety of magnetic metal phases with modulated magnetic ordering patterns across different layers. Both the bulk and boundary electronic states in these phases conspire to promote unusual electronic properties. In particular, such phases are akin to the Weyl semimetal phase in the bulk system and they would exhibit an unusually large anomalous Hall effect. PMID:27418293
Hwang, Kyusung; Kim, Yong Baek
2016-01-01
We theoretically investigate emergent quantum phases in the thin film geometries of the pyrochore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases as well as novel quantum states that may arise only in the thin film platforms, are studied via a theoretical model that allows layer-dependent magnetic structures. It is found that the magnetic order develop in inhomogeneous fashions in the thin film geometries. This leads to a variety of magnetic metal phases with modulated magnetic ordering patterns across different layers. Both the bulk and boundary electronic states in these phases conspire to promote unusual electronic properties. In particular, such phases are akin to the Weyl semimetal phase in the bulk system and they would exhibit an unusually large anomalous Hall effect. PMID:27418293
NASA Astrophysics Data System (ADS)
Hwang, Kyusung; Kim, Yong Baek
2016-07-01
We theoretically investigate emergent quantum phases in the thin film geometries of the pyrochore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases as well as novel quantum states that may arise only in the thin film platforms, are studied via a theoretical model that allows layer-dependent magnetic structures. It is found that the magnetic order develop in inhomogeneous fashions in the thin film geometries. This leads to a variety of magnetic metal phases with modulated magnetic ordering patterns across different layers. Both the bulk and boundary electronic states in these phases conspire to promote unusual electronic properties. In particular, such phases are akin to the Weyl semimetal phase in the bulk system and they would exhibit an unusually large anomalous Hall effect.
Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
Claassen, Martin; Lee, Ching-Hua; Thomale, Ronny; Qi, Xiao-Liang; Devereaux, Thomas P
2015-06-11
We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as dualsmore » of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.« less
Circuit models and SPICE macro-models for quantum Hall effect devices
NASA Astrophysics Data System (ADS)
Ortolano, Massimo; Callegaro, Luca
2015-08-01
Precise electrical measurement technology based on the quantum Hall effect is one of the pillars of modern quantum electrical metrology. Electrical networks including one or more QHE elements can be used as quantum resistance and impedance standards. The analysis of these networks allows metrologists to evaluate the effect of the inevitable parasitic parameters on their performance as standards. This paper presents a concise review of the various circuit models for QHE elements proposed in the literature, and the development of a new model. This last model is particularly suited to be employed with the analogue electronic circuit simulator SPICE. The SPICE macro-model and examples of SPICE simulations, validated by comparison with the corresponding analytical solution and/or experimental data, are provided.
Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
Claassen, Martin; Lee, Ching-Hua; Thomale, Ronny; Qi, Xiao-Liang; Devereaux, Thomas P
2015-06-11
We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as duals of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.
Quantum Hall effect in field-induced spin density wave systems
NASA Astrophysics Data System (ADS)
Tevosyan, Kahren
The research work described in this thesis is motivated by recent theoretical and experimental studies of the Quantum Hall Effect (QHE) in the quasi-one-dimensional conductors such as organic metals of the (TMTSF)sb2X family. These materials consist of weakly coupled parallel conducting chains that lie in the same plane. They exhibit very interesting behavior in the presence of a strong magnetic field which is perpendicular to the plane. At low temperatures a series of phase transitions from the metallic state to spin density wave states occur with increasing magnetic field. The latter are called the Field-Induced Spin Density Wave (FISDW) states. Within each FISDW phase, the value of the Hall resistance is quantized, signalling the presence of the Quantum Hall Effect. In contrast with the conventional QHE in isotropic two-dimensional systems, finite-width Landau bands appear naturally in the disorder-free (TMTSF)sb2X materials. In fact, the theory of the QHE in quasi-one-dimensiona1 organic conductors has so far been developed without any consideration of the effect of the disorder required to broaden Landau bands in isotropic systems. Here we address for the first time the localization properties of the quantum states in FISDW Landau bands. We employ the Thouless approach which uses the sensitivity of the eigenvalues to the choice of boundary conditions to study localization. Our results show that the localization properties of the states are very different from those of the conventional QHE systems. We find that the Thouless numbers do not decrease exponentially with the system size, indicating that states are not localized on the scales we can study. Another aspect of the dissertation deals with the edge state picture of the QHE which states that gapless excitations localized at the system edge are present whenever the quantum Hall effect occurs. We examine these properties of edge states for the FISDW systems by performing computer simulations to model the
Glorieux, Quentin; Guidoni, Luca; Guibal, Samuel; Likforman, Jean-Pierre; Coudreau, Thomas
2011-11-15
We study the generation of intensity quantum correlations using four-wave mixing in a rubidium vapor. The absence of cavities in these experiments allows to deal with several spatial modes simultaneously. In the standard amplifying configuration, we measure relative intensity squeezing up to 9.2 dB below the standard quantum limit. We also theoretically identify and experimentally demonstrate an original regime where, despite no overall amplification, quantum correlations are generated. In this regime, a four-wave mixing setup can play the role of a photonic beam splitter with nonclassical properties, that is, a device that splits a coherent state input into two quantum-correlated beams.
NASA Astrophysics Data System (ADS)
Greshnov, A. A.; Kolesnikova, E. N.; Utesov, O. I.; Zegrya, G. G.
2010-02-01
The divergent at ω=0 quantum correction to conductivity δσ2(ω) of the leading order in (kFl)-1 has been calculated neglecting Cooperon-type contributions suppressed by moderate or strong magnetic field. In the so-called diffusion approximation this quantity is equal to zero up to the second order in (kFl)-1. More subtle treatment of the problem shows that δσ2(ω) is non-zero due to ballistic contributions neglected previously. Knowledge of δσ2(ω) allows to estimate value of the so-called unitary localization length as ξu≈lexp(1.6g2) where Drude conductivity is given by σ0=ge2/h. This estimation underpins the statement of the linear growth of σxx peaks with Landau level number n in the integer quantum Hall effect regime [1] (Greshnov and Zegrya, 2008; Greshnov et al., 2008) at least for n≤2 and calls Pruisken-Khmelnitskii hypothesis of universality [2] (Levine et al., 1983; Khmelnitskii, 1983) in question.