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
Chida, K.; Yamauchi, Y.; Arakawa, T.; Kobayashi, K.; Ono, T.; Hashisaka, M.; Nakamura, S.; Machida, T.
2013-12-04
We performed the resistively-detected nuclear magnetic resonance (RDNMR) to study the electron spin polarization in the non-equilibrium quantum Hall regime. By measuring the Knight shift, we derive source-drain bias voltage dependence of the electron spin polarization in quantum wires. The electron spin polarization shows minimum value around the threshold voltage of the dynamic nuclear polarization.
NASA Astrophysics Data System (ADS)
Avdonin, A.; Skupiński, P.; Grasza, K.
2016-02-01
A simple description of the Hall effect in the hopping regime of conductivity in semiconductors is presented. Expressions for the Hall coefficient and Hall mobility are derived by considering averaged equilibrium electron transport in a single triangle of localization sites in a magnetic field. Dependence of the Hall coefficient is analyzed in a wide range of temperature and magnetic field values. Our theoretical result is applied to our experimental data on temperature dependence of Hall effect and Hall mobility in ZnO.
NASA Astrophysics Data System (ADS)
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.
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.
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.
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
NASA Astrophysics Data System (ADS)
Guterding, Daniel; Jeschke, Harald O.; Valentí, Roser
2016-05-01
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach to the natural mineral herbertsmithite. We prove the feasibility of the proposed modifications by performing ab-initio density functional theory calculations and demonstrate the occurrence of the predicted effects using realistic models. Our results herald a new family of quantum anomalous Hall and quantum spin Hall insulators at affordable energy/temperature scales based on kagome lattices of transition metal ions.
Guterding, Daniel; Jeschke, Harald O; Valentí, Roser
2016-01-01
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach to the natural mineral herbertsmithite. We prove the feasibility of the proposed modifications by performing ab-initio density functional theory calculations and demonstrate the occurrence of the predicted effects using realistic models. Our results herald a new family of quantum anomalous Hall and quantum spin Hall insulators at affordable energy/temperature scales based on kagome lattices of transition metal ions. PMID:27185665
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; 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
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
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.
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.
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.
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
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.
Supersymmetric Quantum-Hall Effect on a Fuzzy Supersphere
Hasebe, Kazuki
2005-05-27
Supersymmetric quantum-Hall liquids are constructed on a supersphere in a supermonopole background. We derive a supersymmetric generalization of the Laughlin wave function, which is a ground state of a hard-core OSp(1 vertical bar 2) invariant Hamiltonian. We also present excited topological objects, which are fractionally charged deficits made by super Hall currents. Several relations between quantum-Hall systems and their supersymmetric extensions are discussed.
Quantum Hall 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.
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
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 .
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
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.
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).
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.}
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
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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
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.
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
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.
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.
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.
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.
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
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.
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.
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].
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
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
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.
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 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.
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.
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.
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.
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.
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.
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
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.
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)
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.
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.
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.
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.
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.