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
NASA Astrophysics Data System (ADS)
Firoz Islam, SK; Benjamin, Colin
2016-09-01
The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. In particular, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivitity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms.
Topologically induced fractional Hall steps in the integer quantum Hall regime of MoS 2.
Islam, S K Firoz; Benjamin, Colin
2016-09-23
The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. In particular, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivitity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms.
Topologically induced fractional Hall steps in the integer quantum Hall regime of MoS 2.
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
Coherent Superconductor-Semiconductor Coupling In The Quantum Hall Regime
NASA Astrophysics Data System (ADS)
Flexner, Soren; Eckstein, James N.
2004-03-01
We present experiments exploring the coherent coupling of the superconducting wave function in niobium nitride, a high critical magnetic field superconductor, to edge states in a two dimensional electron gas (2DEG) in the integer quantum hall regime. The 2DEG is created using molecular beam epitaxy (MBE) growth of AlGaAs/GaAs heterojunctions. Silicon doped InGaAs capping layers are used to facilitate ohmic connection between the 2DEG and niobium nitride superconducting contacts. Both in situ, and ex situ deposited niobium nitride contacts are investigated. The edge states associated with the quantum hall effect provide degenerate channels with very long coherence lengths (>um). The consequences of cooper pair transport through these channels, in the form of Andeev reflection and the Josephson effects, are considered.
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.
Imaging currents in HgTe quantum wells in the quantum spin Hall regime.
Nowack, Katja C; Spanton, Eric M; Baenninger, Matthias; König, Markus; Kirtley, John R; Kalisky, Beena; Ames, C; Leubner, Philipp; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W; Goldhaber-Gordon, David; Moler, Kathryn A
2013-09-01
The quantum spin Hall (QSH) state is a state of matter characterized by a non-trivial topology of its band structure, and associated conducting edge channels. The QSH state was predicted and experimentally demonstrated to be realized in HgTe quantum wells. The existence of the edge channels has been inferred from local and non-local transport measurements in sufficiently small devices. Here we directly confirm the existence of the edge channels by imaging the magnetic fields produced by current flowing in large Hall bars made from HgTe quantum wells. These images distinguish between current that passes through each edge and the bulk. On tuning the bulk conductivity by gating or raising the temperature, we observe a regime in which the edge channels clearly coexist with the conducting bulk, providing input to the question of how ballistic transport may be limited in the edge channels. Our results represent a versatile method for characterization of new QSH materials systems.
Scaling in the quantum Hall effect regime in n-InGaAs/GaAs nanostructures
Arapov, Yu. G.; Gudina, S. V.; Klepikova, A. S.; Neverov, V. N. Novokshonov, S. G.; Kharus, G. I.; Shelushinina, N. G.; Yakunin, M. V.
2013-07-15
The longitudinal {rho}{sub xx}(B) and Hall {rho}{sub xy}(B) magnetoresistances are investigated experimentally in the integer quantum Hall effect (QHE) regime in n-InGaAs/GaAs double quantum well nanostructures in the range of magnetic fields B = (0-16) T and temperatures T = (0.05-70) K before and after IR illumination. The results are evaluated within the scaling hypothesis with regard to electron-electron interaction.
Supercurrent in the quantum Hall regime: part I
NASA Astrophysics Data System (ADS)
Ke, Chung-Ting; Amet, Francois; Borzenets, Ivan; Wang, Jiyingmei; Watanabe, Keji; Taniguchi, Takashi; Deacon, Russell; Yamamoto, Michihisa; Bomze, Yuriy; Tarucha, Seigo; Finkelstein, Gleb
The remarkable electronic quality of graphene/boron nitride heterostructures makes them an ideal medium to study induced superconductivity. Our Josephson junctions are made of encapsulated graphene demonstrate ballistic superconducting transport at the micron scale. In the hole-doped regime, a Fabry-Perot resonator is formed by PN junctions close to superconducting contacts, which causes quantum interference of the critical current. We study variations of the Fraunhofer pattern (I_C vs. B) thought the gate voltage range. At higher magnetic fields, superconducting transport across the junctions becomes profoundly non-periodic. Despite demonstrating strong fluctuations as a function of density and magnetic field, we find that supercurrent persists in a wide range of parameters.
Electron Interferometry in the Quantum Hall Regime: Aharonov-Bohm Effect of Interacting Electrons
Lin, P.V.; Camino, F.; Goldman, V.J.
2009-09-01
An apparent h/fe Aharonov-Bohm flux period, where f is an integer, has been reported in coherent quantum Hall devices. Such subperiod is not expected for noninteracting electrons and thus is thought to result from interelectron Coulomb interaction. Here we report experiments in a Fabry-Perot interferometer comprised of two wide constrictions enclosing an electron island. By carefully tuning the constriction front gates, we find a regime where interference oscillations with period h/2e persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling. In a large quantum Hall sample, a transition between integer plateaus occurs near half-filling, where the bulk of the sample becomes delocalized and thus dissipative bulk current flows between the counterpropagating edges ('backscattering'). In a quantum Hall constriction, where conductance is due to electron tunneling, a transition between forward and backscattering is expected near the half-filling. In our experiment, neither period nor amplitude of the oscillations show a discontinuity at half-filling, indicating that only one interference path exists throughout the transition. We also present experiments and an analysis of the front-gate dependence of the phase of the oscillations. The results point to a single physical mechanism of the observed conductance oscillations: Aharonov-Bohm interference of interacting electrons in quantum Hall regime.
Selective equilibration among the current-carrying states in the quantum Hall regime
NASA Technical Reports Server (NTRS)
Alphenaar, B. W.; Mceuen, P. L.; Wheeler, R. G.; Sacks, R. N.
1990-01-01
The Hall resistance of a two-dimensional electron gas is measured with gated probes to determine the extent of equilibration among the N current-carrying states in the quantum Hall regime. After traveling macroscopic distances, current injected into the first state is equilibrated among the N - 1 lowest states but equilibration into the highest state varies strongly across the Hall plateau. This is attributed to a change in the Nth state from being localized within a magnetic length of the edge to substantially extending into the sample.
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 .
Accessing the quantum Hall regime in cold atom traps using circularly polarized light
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Yan, Bin; Greene, Chris H.
2016-05-01
There has been considerable interest in designing cold atom experiments to explore the quantum Hall effect with the extreme control allowed in such trapped atom systems. Many theoretical proposals and experimental attempts have been made in the effort to construct a cold atom fractional quantum Hall experiment, but so far, the fractional quantum Hall regime has proven difficult to achieve in experimental setups. One method for reaching the quantum Hall effect consists of rapidly rotating a cold atom system in a harmonic trap to near the centrifugal limit, where the system's Hamiltonian matches the two-dimensional magnetic field Hamiltonian. This condition could be reached in a few-body system through a scheme which increases the angular momentum of the particles in the trap through precision photon excitations. According to the hyperspherical framework from few-body theory, when particle interactions break the harmonic energy spectrum degeneracy, it becomes possible for circularly polarized light to excite the system selectively into the high angular momentum states required for the quantum Hall effect. We will discuss possible experimental systems where this technique could be applicable and challenges that these systems may face.
Coherent nonlinear optical response of graphene in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Avetissian, H. K.; Mkrtchian, G. F.
2016-07-01
We study the nonlinear optical response of graphene in the quantum Hall regime to an intense laser pulse. In particular, we consider the harmonic generation process. We demonstrate that the generalized magneto-optical conductivity of graphene on the harmonics of a strong pump laser radiation has a characteristic Hall plateau feature. The plateau heights depend on the laser intensity and broadening of the Landau levels so that they are not quantized exactly. This nonlinear effect remains robust against the significant broadening of the Landau levels. We predict realization of an experiment through the observation of the third-harmonic signal and nonlinear Faraday effect, which are within the experimental feasibility.
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.
Field effect in the quantum Hall regime of a high mobility graphene wire
NASA Astrophysics Data System (ADS)
Barraud, C.; Choi, T.; Butti, P.; Shorubalko, I.; Taniguchi, T.; Watanabe, K.; Ihn, T.; Ensslin, K.
2014-08-01
In graphene-based electronic devices like in transistors, the field effect applied thanks to a gate electrode allows tuning the charge density in the graphene layer and passing continuously from the electron to the hole doped regime across the Dirac point. Homogeneous doping is crucial to understand electrical measurements and for the operation of future graphene-based electronic devices. However, recently theoretical and experimental studies highlighted the role of the electrostatic edge due to fringing electrostatic field lines at the graphene edges [P. Silvestrov and K. Efetov, Phys. Rev. B 77, 155436 (2008); F. T. Vasko and I. V. Zozoulenko, Appl. Phys. Lett. 97, 092115 (2010)]. This effect originates from the particular geometric design of the samples. A direct consequence is a charge accumulation at the graphene edges giving a value for the density, which deviates from the simple picture of a plate capacitor and also varies along the width of the graphene sample. Entering the quantum Hall regime would, in principle, allow probing this accumulation thanks to the extreme sensitivity of this quantum effect to charge density and the charge distribution. Moreover, the presence of an additional and counter-propagating edge channel has been predicted [P. Silvestrov and K. Efetov, Phys. Rev. B 77, 155436 (2008)] giving a fundamental aspect to this technological issue. In this article, we investigate this effect by tuning a high mobility graphene wire into the quantum Hall regime in which charge carriers probe the electrostatic potential at high magnetic field close to the edges. We observe a slight deviation to the linear shift of the quantum Hall plateaus with magnetic field and we study its evolution for different filling factors, which correspond to different probed regions in real space. We discuss the possible origins of this effect including an increase of the charge density towards the edges.
Field effect in the quantum Hall regime of a high mobility graphene wire
Barraud, C. E-mail: clement.barraud@univ-paris-diderot.fr; Choi, T.; Ihn, T.; Ensslin, K.; Butti, P.; Shorubalko, I.; Taniguchi, T.; Watanabe, K.
2014-08-21
In graphene-based electronic devices like in transistors, the field effect applied thanks to a gate electrode allows tuning the charge density in the graphene layer and passing continuously from the electron to the hole doped regime across the Dirac point. Homogeneous doping is crucial to understand electrical measurements and for the operation of future graphene-based electronic devices. However, recently theoretical and experimental studies highlighted the role of the electrostatic edge due to fringing electrostatic field lines at the graphene edges [P. Silvestrov and K. Efetov, Phys. Rev. B 77, 155436 (2008); F. T. Vasko and I. V. Zozoulenko, Appl. Phys. Lett. 97, 092115 (2010)]. This effect originates from the particular geometric design of the samples. A direct consequence is a charge accumulation at the graphene edges giving a value for the density, which deviates from the simple picture of a plate capacitor and also varies along the width of the graphene sample. Entering the quantum Hall regime would, in principle, allow probing this accumulation thanks to the extreme sensitivity of this quantum effect to charge density and the charge distribution. Moreover, the presence of an additional and counter-propagating edge channel has been predicted [P. Silvestrov and K. Efetov, Phys. Rev. B 77, 155436 (2008)] giving a fundamental aspect to this technological issue. In this article, we investigate this effect by tuning a high mobility graphene wire into the quantum Hall regime in which charge carriers probe the electrostatic potential at high magnetic field close to the edges. We observe a slight deviation to the linear shift of the quantum Hall plateaus with magnetic field and we study its evolution for different filling factors, which correspond to different probed regions in real space. We discuss the possible origins of this effect including an increase of the charge density towards the edges.
AC-magnetotransport of a 2DEG in the quantum Hall regime
Hernández, C.; Chaubet, C.
2014-05-15
In this paper we present an ac-magneto-transport study of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime, for frequencies in the range [100Hz, 1MHz]. We present a new approach to understand admittance measurements based in the Landauer-Buttiker formalism for QHE edge channels and taking into account the capacitance and the topology of the cables connected to the contacts used in the measurements. Our model predicts an universal behavior with the a-dimensional parameter RCω where R is the 2 wires resistance of the 2DEG, C the capacitance cables and the angular frequency, in agreement with experiments.
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.
Voltage-controlled group velocity of edge magnetoplasmon in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Kamata, H.; Ota, T.; Muraki, K.; Fujisawa, T.
2010-02-01
We investigate the group velocity of edge magnetoplasmons (EMPs) in the quantum Hall regime by means of time-of-flight measurement. The EMPs are injected from an Ohmic contact by applying a voltage pulse, and detected at a quantum point contact by applying another voltage pulse to its gate. We find that the group velocity of the EMPs traveling along the edge channel defined by a metallic gate electrode strongly depends on the voltage applied to the gate. The observed variation of the velocity can be understood to reflect the degree of screening caused by the metallic gate, which damps the in-plane electric field and, hence, reduces the velocity. The degree of screening can be controlled by changing the distance between the gate and the edge channel with the gate voltage.
Edge magnetoplasmons in graphene: determination of carrier drift velocity in Quantum Hall regime
NASA Astrophysics Data System (ADS)
Petkovic, Ivana; Williams, F. I. B.; Bennaceur, Keyan; Portier, Fabien; Roche, Patrice; Glattli, D. C.
2013-03-01
Edge Magneto-Plasmons (EMP) are gapless quasi 1D elementary excitations which are split off from the bulk magneto-plasmon modes by the sample boundary, and are a tool of choice to investigate the structure of the edge of a 2D electron gas. We give a first experimental demonstration of their presence in graphene in the quantum Hall regime and use our results to evaluate the carrier drift velocity along the edge. The group velocity of these modes is a sum of the Hall conductivity contribution and the carrier drift velocity at the edge. In graphene, due to its particular dynamics and an abrupt edge, the drift velocity is expected to be of the order of the Fermi velocity, thus becoming experimentally accessible. We show EMP to exist by timing the travel of narrow wave-packets on picosecond time scales around exfoliated samples. They show chiral propagation with low attenuation at a velocity which is quantized on Hall plateaus. We extract the carrier drift contribution and find it to be slightly less than the Fermi velocity, as expected for an abrupt edge. We also extract the spatial spread of edge accumulated charge and find it to be narrower than for soft edge systems. We acknowledge ERC Grant # 228273 and RTRA ``Gamet'' Grant.
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).
TOPICAL REVIEW: Circuit type simulations of magneto-transport in the quantum Hall effect regime
NASA Astrophysics Data System (ADS)
Oswald, Josef; Oswald, Manfred
2006-02-01
Localization in the bulk is one of the most important ingredients for the theory of the quantum Hall effect and much attention has been paid to this topic for more than two decades. However, less effort has been made to model the current transport itself. Network models are frequently used in this context and an answer should be given as to whether these are also suitable for modelling the lateral distribution of experimentally excited currents and voltages in the quantum Hall effect (QHE) regime. The term 'network model' is of more general meaning and therefore the term 'circuit type simulations' should be used instead for expressing this kind of modelling. In preceding papers a Landauer-Büttiker type representation of bulk current transport has been successfully used for the numerical simulation of the magneto-transport of two-dimensional electron systems in the high magnetic field regime. This approach allows us to build up a network model, which describes correctly the effect of non-equilibrium currents injected via metallic contacts as in real experiments. In this context we suggest a network model, which serves as a circuit type representation of magneto-transport. It is demonstrated that it is in full agreement with a treatment of bulk current transport as a quantum tunnelling process between magnetic bound states, which exist in the high magnetic field regime. Additionally, we find a striking correspondence between our network representation and the bulk current picture in terms of mixed phases mapped on a chequerboard: at half filled Landau level (LL) coupled droplets of a quantum Hall (QH) liquid phase and coupled droplets of an insulator phase exist at the same time, with each of them occupying half of the bulk area. Removing a single electron from such a QH liquid droplet at half filling completes the QH plateau transition to the next higher QH plateau, while adding a single electron to such a droplet at half filling completes the QH plateau transition
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.
High-frequency hopping conductivity in the quantum Hall effect regime: Acoustical studies
NASA Astrophysics Data System (ADS)
Drichko, I. L.; Diakonov, A. M.; Smirnov, I. Yu.; Galperin, Yu. M.; Toropov, A. I.
2000-09-01
The high-frequency conductivity of Si δ-doped GaAs/AlGaAs heterostructures is studied in the integer quantum Hall effect (QHE) regime, using acoustic methods. Both the real and the imaginary parts of the complex conductivity are determined from the experimentally observed magnetic field and temperature dependencies of the velocity and the attenuation of a surface acoustic wave. It is demonstrated that in structures with carrier density (1.3-2.8)×1011 cm-2 and mobility (1-2)×105 cm2/V s the mechanism of low-temperature conductance near the QHE plateau centers is hopping. It is also shown that at magnetic fields corresponding to filling factors 2 and 4, the doped Si δ layer efficiently shunts the conductance in the two-dimensional electron gas (2DEG) channel. A method to separate the two contributions to the real part of the conductivity is developed, and the localization length in the 2DEG channel is estimated within the context of a nearest-neighbor hopping model.
Tsiper, E V
2006-08-18
The concept of fractional charge is central to the theory of the fractional quantum Hall effect. Here I use exact diagonalization as well as configuration space renormalization to study finite clusters which are large enough to contain two independent edges. I analyze the conditions of resonant tunneling between the two edges. The "computer experiment" reveals a periodic sequence of resonant tunneling events consistent with the experimentally observed fractional quantization of electric charge in units of e/3 and e/5.
Domain walls, fusion rules, and conformal field theory in the quantum Hall regime.
Ardonne, Eddy
2009-05-01
We provide a simple way to obtain the fusion rules associated with elementary quasiholes over quantum Hall wave functions, in terms of domain walls. The knowledge of the fusion rules is helpful in the identification of the underlying conformal field theory describing the wave functions. We show that, for a certain two-parameter family (k,r) of wave functions, the fusion rules are those of su(r)k. In addition, we give an explicit conformal field theory construction of these states, based on the Mk(k+1,k+r) "minimal" theories. For r=2, these states reduce to the Read-Rezayi states. The "Gaffnian" wave function is the prototypical example for r>2, in which case the conformal field theory is nonunitary.
Zero-bias anomalies in narrow tunnel junctions in the quantum Hall regime.
Jiang, P; Chien, C-C; Yang, I; Kang, W; Baldwin, K W; Pfeiffer, L N; West, K W
2010-12-10
We report on the study of cleaved-edge-overgrown line junctions with a serendipitously created narrow opening in an otherwise thin, precise line barrier. Two sets of zero-bias anomalies are observed with an enhanced conductance for filling factors ν>1 and a strongly suppressed conductance for ν<1. A transition between the two behaviors is found near ν≈1. The zero-bias anomaly (ZBA) line shapes find explanation in Luttinger liquid models of tunneling between quantum Hall edge states. The ZBA for ν<1 occurs from strong backscattering induced by suppression of quasiparticle tunneling between the edge channels for the n=0 Landau levels. The ZBA for ν>1 arises from weak tunneling of quasiparticles between the n=1 edge channels.
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
2006-03-17
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. The 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/4pi). 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.
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.
NASA Astrophysics Data System (ADS)
Arapov, Yu. G.; Gudina, S. V.; Neverov, V. N.; Novokshonov, S. G.; Klepikova, A. S.; Kharus, G. I.; Shelushinina, N. G.; Yakunin, M. V.
2013-01-01
Temperature and magnetic-field dependences of longitudinal ρxx(B,T) and Hall ρxy(B,T) resistivities of n-InxGa1-xAs/GaAs nanostructures with single and double quantum wells are investigated in the quantum Hall regime at B = 0-16 Т and T = 0.05-70 K, before and after IR illumination. The temperature dependence of the QHE plateau-plateau transition width is analyzed and information about temperature dependences of the bandwidth of delocalized states in the center of Landau subbands is obtained.
NASA Astrophysics Data System (ADS)
Dujovne, Irene
This dissertation presents inelastic light scattering results that probe low energy physics in quantum liquids and in materials with novel contemporary applications. Two areas are considered: (a) low-lying excitations in two dimensional structures under the extreme conditions that occur in the fractional quantum Hall regime (FQH), (b) low energy vibrational modes in relaxor ferroelectrics. In the FQH regime we concentrate in the region 1/2 ≥ nu ≥ 1/3. We discovered new spin-flip excitations that provide insight into composite fermions (CF) energy level spacings and interactions. In the filling factor region 2/5 ≥ nu ≥ 1/3 we uncover new excitations that extend to filling factors between the main fractions of the FQH effect and can be associated to transitions between different CF Landau levels. These results provide information on residual interactions between the CFs. We find that residual interactions are not negligible and could lead to novel behaviors. An analysis of the density dependence of CF energy levels at filling factors nu = 1/3 and nu = 2/5 based on simple energy level models is presented. The main assumptions are that the splitting between quasiparticle levels and spin reversal energies are proportional to the Coulomb energy. Energy level structures of CF quasiparticles are also probed by means of light scattering experiments with spin-flip excitations at nu = 3/7 and nu = 4/9. Measurements of spin excitations in the limit of nu → 1/2 uncover a delicate balance between spin reversal and Fermi energies. The interactions are exposed in low-lying spin-flip excitations that have marked sensitivity to the state of spin polarization of the system when nu → 1/2. We are able to determine the boundaries between full and partial spin polarization, these, together with the observation of spin-flip rotons reveal spin reversal energies much larger than the bare Zeeman splitting. Inelastic light scattering by optical phonons (Raman scattering) in
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.
NASA Astrophysics Data System (ADS)
Radzihovsky, Leo
2003-03-01
Liquid-crystals, defined as states of matter intermediate in their properties between fully disordered isotropic liquids and fully ordered crystals are ubiquitous in nature. Recent transport measurements on two-dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally-ordered, compressible liquid state. I will discuss electronic liquid-crystals interpretation of these experiments, focusing on a recently proposed quantum Hall nematic state that is predicted to exhibit a novel, highly anisotropic q^3 density-director mode and other interesting phenomenology.
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.
Hall viscosity of hierarchical quantum Hall states
NASA Astrophysics Data System (ADS)
Fremling, Mikael; Hansson, Thors Hans; Suorsa, Juha
2015-03-01
We construct model wave functions on a torus for all chiral states in the abelian quantum Hall hierarchy. These functions have no variational parameters, and they transform under the modular group in the same way as the multicomponent generalizations of the Laughlin wave functions. Assuming the absence of Berry phases upon adiabatic variations of the modular parameter τ, we calculate the quantum Hall viscosity and find it to be in agreement with the formula, given by Read, which relates the viscosity to the average orbital spin of the electrons. For the filling factor ν = 2 / 5 Jain state, which is at the second level in the hierarchy, we compare our model wave function with the numerically obtained ground state of the Coulomb interaction Hamiltonian in the lowest Landau level, and find very good agreement in a large region of the complex τ-plane. For the same example, we also numerically compute the Hall viscosity and find good agreement with the analytical result for both the model wave function and the numerically obtained Coulomb wave function. We argue that this supports the notion of a generalized plasma analogy that would ensure that wave functions obtained using conformal field theory methods do not acquire Berry phases upon adiabatic evolution.
Anomalous hydrodynamics of fractional quantum Hall states
Wiegmann, P.
2013-09-15
We propose a comprehensive framework for quantum hydrodynamics of the fractional quantum Hall (FQH) states. We suggest that the electronic fluid in the FQH regime can be phenomenologically described by the quantized hydrodynamics of vortices in an incompressible rotating liquid. We demonstrate that such hydrodynamics captures all major features of FQH states, including the subtle effect of the Lorentz shear stress. We present a consistent quantization of the hydrodynamics of an incompressible fluid, providing a powerful framework to study the FQH effect and superfluids. We obtain the quantum hydrodynamics of the vortex flow by quantizing the Kirchhoff equations for vortex dynamics.
Generalized quantum Hall projection Hamiltonians
NASA Astrophysics Data System (ADS)
Simon, Steven H.; Rezayi, E. H.; Cooper, Nigel R.
2007-02-01
Certain well known quantum Hall states—including the Laughlin states, the Moore-Read Pfaffian, and the Read-Rezayi Parafermion states—can be defined as the unique lowest degree symmetric analytic function that vanishes as at least p powers as some number (g+1) of particles approach the same point. Analogously, these same quantum Hall states can be generated as the exact highest density zero energy state of simple angular momentum projection operators. Following this theme we determine the highest density zero energy state for many other values of p and g .
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.
Nonlocal transport in the quantum spin Hall state.
Roth, Andreas; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W; Maciejko, Joseph; Qi, Xiao-Liang; Zhang, Shou-Cheng
2009-07-17
Nonlocal transport through edge channels holds great promise for low-power information processing. However, edge channels have so far only been demonstrated to occur in the quantum Hall regime, at high magnetic fields. We found that mercury telluride quantum wells in the quantum spin Hall regime exhibit nonlocal edge channel transport at zero external magnetic field. The data confirm that the quantum transport through the (helical) edge channels is dissipationless and that the contacts lead to equilibration between the counterpropagating spin states at the edge. The experimental data agree quantitatively with the theory of the quantum spin Hall effect. The edge channel transport paves the way for a new generation of spintronic devices for low-power information processing.
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.
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.
Quantum Hall states in strained InAs heterostructures
NASA Astrophysics Data System (ADS)
Kanter, Jesse; Arese Lucini, Francesca; Duboy, Alexandra; Mishima, T. D.; Santos, M. B.; Shabani, Javad
In a recent development it was realized that non-Abelian quasiparticles, parafermion zero-modes emerge at an interface between a superconductor and two dimensional electron system (2DES) in the quantum Hall regime.. Unlike widely used GaAs systems, surface level pinning in InAs could allow for fabrication of transparent contacts to superconductors. However, no fractional quantum Hall state has been observed in InAs quantum wells so far. Whether this is due to the type of disorder present in the quantum well is not clear. In this work, we study the transport and dingle mobility of 2DESs confined to strained InAs quantum wells as a function of electron density and spacer thickness to the surface. We compare our results to early observation of fractional quantum Hall states in GaAs. This material is based upon work supported by the NSF under Grant No. DMR-1207537.
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.
Theory of Quantum Hall Nematics
NASA Astrophysics Data System (ADS)
Radzihovsky, Leo; Dorsey, Alan T.
2002-05-01
Transport measurements on two-dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally ordered, compressible liquid state. We develop and analyze a microscopic theory of such a ``quantum Hall nematic'' (QHN) phase, predict the existence of a novel, highly anisotropic q3 density-director mode, find that the T = 0 long-range orientational order is unstable to weak disorder, and compute the tunneling into such a strongly correlated state. This microscopic approach is supported and complemented by a hydrodynamic model of the QHN, which, in the dissipationless limit, reproduces the modes of the microscopic model.
Theory of quantum Hall nematics.
Radzihovsky, Leo; Dorsey, Alan T
2002-05-27
Transport measurements on two-dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally ordered, compressible liquid state. We develop and analyze a microscopic theory of such a "quantum Hall nematic" (QHN) phase, predict the existence of a novel, highly anisotropic q(3) density-director mode, find that the T = 0 long-range orientational order is unstable to weak disorder, and compute the tunneling into such a strongly correlated state. This microscopic approach is supported and complemented by a hydrodynamic model of the QHN, which, in the dissipationless limit, reproduces the modes of the microscopic model. PMID:12059490
Critical currents of ideal quantum Hall superfluids
NASA Astrophysics Data System (ADS)
Abolfath, M.; MacDonald, A. H.; Radzihovsky, Leo
2003-10-01
Filling factor ν=1 bilayer electron systems in the quantum Hall regime have an excitonic-condensate superfluid ground state when the layer separation d is less than a critical value dc. On a quantum Hall plateau current injected and removed through one of the two layers drives a dissipationless edge current that carries parallel currents and a dissipationless bulk supercurrent that carries opposing currents in the two layers. In this paper we discuss the theory of finite supercurrent bilayer states, both in the presence and in the absence of symmetry breaking interlayer hybridization. Solutions to the microscopic mean-field equations exist at all condensate phase winding rates for zero and sufficiently weak hybridization strengths. We find, however, that collective instabilities occur when the supercurrent exceeds a critical value determined primarily by a competition between direct and exchange interlayer Coulomb interactions. The critical current is estimated using a local stability criterion and varies as (dc-d)1/2 when d approaches dc from below. For large interlayer hybridization, we find that the critical current is limited by a soliton instability of microscopic origin.
Theory of Quantum Hall Nematics
NASA Astrophysics Data System (ADS)
Radzihovsky, Leo; Dorsey, Alan
2002-03-01
Transport measurements on two dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally-ordered, compressible liquid state. We develop and analyze [1] a microscopic theory of such a ``quantum Hall nematic'' (QHN) phase, predict the existence of a novel, highly anisotropic q^3 density-director mode, find that the T=0 long-range orientational order is unstable to weak disorder, and compute the tunneling into such a strongly correlated state. This microscopic approach is supported and complemented by a hydrodynamic model of the QHN, which, in the dissipationless limit, reproduces the modes of the microscopic model. This research was supported by NSF DMR-9978547, DMR-9625111, and the Sloan and Packard Foundations. [1] L. Radzihovsky and A. T. Dorsey, cond-mat/0110083
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.
Generalized Clustered Quantum Hall States
NASA Astrophysics Data System (ADS)
Simon, Steven H.; Cooper, Nigel R.; Rezayi, Ed
2005-03-01
The Read-Rezayi (parafermion) quantum Hall states[1] for bosons can be defined as states where the wavefunction does not vanish when g bosons come together to the same point, but does vanish as z^2 as a g+1st particle approaches that point. These states can equivalently be defined as the unique ground state of a point contact g+1 particle interaction Hamiltonian. Interestingly, the series of Read-Rezayi states appears to describe well the groundstates of rotating Bose condensates with point-contact two body interactions at a series of filling fractions [2]. If one attaches a Jastrow factor to such bose wavefunctions, one obtains fermion wavefunctions that may occur in electronic quantum Hall systems including the (g=2) Pfaffian [3] and the (g=3) ν=13/5 Read-Rezayi state [1]. In this work, we consider generalized cluster wavefunctions defined by the algebraic manner in which a wavefunction vanishes as g+1 particles coalesce. We find Hamiltonians that generate these wavefunctions as their exact ground state. Among this series of states is the previously studied Haffnian wavefunction[4] and a host of states not previously discussed. We catalogue and study the new states and discuss whether any of them might occur in actual physical systems. [1] N. Read and E. Rezayi, PRB59, 8084 (1999). [2] N. R. Cooper, N. K. Wilkin, and J. M. F. Gunn, PRL87, 120405 (2001) [3] G. Moore and N. Read, Nuc. Phys. B360, 362 (1991). [4] D. Green, PhD Thesis.
Level statistics for quantum Hall systems
NASA Astrophysics Data System (ADS)
Kagalovsky, V.; Horovitz, B.; Avishai, Y.
2005-03-01
Level statistics for two classes of disordered systems at criticality are analyzed in terms of different realizations of the Chalker-Coddington network model. These include: 1) Re-examination of the standard U(1) model describing dynamics of electrons on the lowest Landau level in the quantum Hall effect, where it is shown that after proper local unfolding the nearest-neighbor spacing distribution (NNSD) at the critical energy follows the Wigner surmise for Gaussian unitary ensembles (GUE). 2) Quasi-particles in disordered superconductors with broken time reversal and spin rotation invariance (in the language of random matrix theory this system is a representative of symmetry class D in the classification scheme of Altland and Zirnbauer). Here again the NNSD obeys the Wigner surmise for GUE, reflecting therefore only "basic" discrete symmetries of the system (time reversal violation) and ignoring particle-hole symmetries and other finer details (criticality). In the localized regime level repulsion is suppressed.
Quantum Hall edge states in topological insulator nanoribbons
NASA Astrophysics Data System (ADS)
Pertsova, A.; Canali, C. M.; MacDonald, A. H.
2016-09-01
We present a microscopic theory of the chiral one-dimensional electron gas system localized on the sidewalls of magnetically doped Bi2Se3 -family topological insulator nanoribbons in the quantum anomalous Hall effect (QAHE) regime. Our theory is based on a simple continuum model of sidewall states whose parameters are extracted from detailed ribbon and film geometry tight-binding model calculations. In contrast to the familiar case of the quantum Hall effect in semiconductor quantum wells, the number of microscopic chiral channels depends simply and systematically on the ribbon thickness and on the position of the Fermi level within the surface state gap. We use our theory to interpret recent transport experiments that exhibit nonzero longitudinal resistance in samples with accurately quantized Hall conductances.
Chiral thermoelectrics with quantum Hall edge states.
Sánchez, Rafael; Sothmann, Björn; Jordan, Andrew N
2015-04-10
The thermoelectric properties of a three-terminal quantum Hall conductor are investigated. We identify a contribution to the thermoelectric response that relies on the chirality of the carrier motion rather than on spatial asymmetries. The Onsager matrix becomes maximally asymmetric with configurations where either the Seebeck or the Peltier coefficients are zero while the other one remains finite. Reversing the magnetic field direction exchanges these effects, which originate from the chiral nature of the quantum Hall edge states. The possibility to generate spin-polarized currents in quantum spin Hall samples is discussed. PMID:25910147
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.
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.
The microscopic nature of localization in the quantum Hall effect.
Ilani, S; Martin, J; Teitelbaum, E; Smet, J H; Mahalu, D; Umansky, V; Yacoby, A
2004-01-22
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the electronic transport properties owing to particle localization. In the conventional theory of the quantum Hall effect, strong-field localization is associated with a single-particle drift motion of electrons along contours of constant disorder potential. Transport experiments that probe the extended states in the transition regions between quantum Hall phases have been used to test both the theory and its implications for quantum Hall phase transitions. Although several experiments on highly disordered samples have affirmed the validity of the single-particle picture, other experiments and some recent theories have found deviations from the predicted universal behaviour. Here we use a scanning single-electron transistor to probe the individual localized states, which we find to be strikingly different from the predictions of single-particle theory. The states are mainly determined by Coulomb interactions, and appear only when quantization of kinetic energy limits the screening ability of electrons. We conclude that the quantum Hall effect has a greater diversity of regimes and phase transitions than predicted by the single-particle framework. Our experiments suggest a unified picture of localization in which the single-particle model is valid only in the limit of strong disorder.
Ezawa, Motohiko
2013-12-04
Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low energy dynamics is described by Dirac electrons, but they are massive due to relatively large spin-orbit interactions. I will explain the following properties of silicene: 1) The band structure is controllable by applying an electric field. 2) Silicene undergoes a phase transition from a topological insulator to a band insulator by applying external electric field. 3) The topological phase transition can be detected experimentally by way of diamagnetism. 4) There is a novel valley-spin selection rules revealed by way of photon absorption. 5) Silicene yields a remarkably many phases such as quantum anomalous Hall phase and valley polarized metal when the exchange field is additionally introduced. 6) A silicon nanotubes can be used to convey spin currents under an electric field.
Quantum Hall effect in momentum space
NASA Astrophysics Data System (ADS)
Ozawa, Tomoki; Price, Hannah M.; Carusotto, Iacopo
2016-05-01
We theoretically discuss a momentum-space analog of the quantum Hall effect, which could be observed in topologically nontrivial lattice models subject to an external harmonic trapping potential. In our proposal, the Niu-Thouless-Wu formulation of the quantum Hall effect on a torus is realized in the toroidally shaped Brillouin zone. In this analogy, the position of the trap center in real space controls the magnetic fluxes that are inserted through the holes of the torus in momentum space. We illustrate the momentum-space quantum Hall effect with the noninteracting trapped Harper-Hofstadter model, for which we numerically demonstrate how this effect manifests itself in experimental observables. Extension to the interacting trapped Harper-Hofstadter model is also briefly considered. We finally discuss possible experimental platforms where our proposal for the momentum-space quantum Hall effect could be realized.
Quantum hall effect at low magnetic fields
Huckestein
2000-04-01
The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of the quantum Hall effect, are in fact in agreement with the standard theory. The apparent low-field transition observed in the experiments is identified as a crossover due to weak localization and a strong reduction of the conductivity when Landau quantization becomes dominant.
Integer quantum Hall effect for bosons.
Senthil, T; Levin, Michael
2013-01-25
A simple physical realization of an integer quantum Hall state of interacting two dimensional bosons is provided. This is an example of a symmetry-protected topological (SPT) phase which is a generalization of the concept of topological insulators to systems of interacting bosons or fermions. Universal physical properties of the boson integer quantum Hall state are described and shown to correspond with those expected from general classifications of SPT phases.
Quantum depinning transition of quantum Hall stripes.
Li, M-R; Fertig, H A; Côté, R; Yi, Hangmo
2004-05-01
We examine the effect of disorder on the electromagnetic response of quantum Hall stripes using an effective elastic theory to describe their low-energy dynamics, and replicas and the Gaussian variational method to handle disorder effects. Within our model we demonstrate the existence of a depinning transition at a critical partial Landau level filling factor Deltanu(c). For Deltanu
Hierarchical nature of the quantum Hall effects.
Bonderson, Parsa
2012-02-10
I demonstrate that the wave function for a ν=n+ν[over ˜] quantum Hall state with Landau levels 0,1,…,n-1 filled and a filling fraction ν[over ˜] quantum Hall state with 0<ν[over ˜]≤1 in the nth Landau level can be obtained hierarchically from the ν=n state by introducing quasielectrons which are then projected into the (conjugate of the) ν[over ˜] state. In particular, the ν[over ˜]=1 case produces the filled Landau level wave functions hierarchically, thus establishing the hierarchical nature of the integer quantum Hall states. It follows that the composite fermion description of fractional quantum Hall states fits within the hierarchy theory of the fractional quantum Hall effect. I also demonstrate this directly by generating the composite fermion ground-state wave functions via application of the hierarchy construction to fractional quantum Hall states, starting from the ν=1/m Laughlin states.
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.
Charge fractionalization in the integer quantum Hall effect.
Inoue, Hiroyuki; Grivnin, Anna; Ofek, Nissim; Neder, Izhar; Heiblum, Moty; Umansky, Vladimir; Mahalu, Diana
2014-04-25
We report an observation, via sensitive shot noise measurements, of charge fractionalization of chiral edge electrons in the integer quantum Hall effect regime. Such fractionalization results solely from interchannel Coulomb interaction, leading electrons to decompose to excitations carrying fractional charges. The experiment was performed by guiding a partitioned current carrying edge channel in proximity to another unbiased edge channel, leading to shot noise in the unbiased edge channel without net current, which exhibited an unconventional dependence on the partitioning. The determination of the fractional excitations, as well as the relative velocities of the two original (prior to the interaction) channels, relied on a recent theory pertaining to this measurement. Our result exemplifies the correlated nature of multiple chiral edge channels in the integer quantum Hall effect regime.
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.
A highly sensitive scanning far-infrared microscope with quantum Hall detectors
NASA Astrophysics Data System (ADS)
Ikushima, Kenji; Sakuma, Hisato; Komiyama, Susumu
2003-09-01
We develop a highly sensitive scanning far-infrared (FIR) microscope, which consists of a silicon solid immersion lens that probes FIR and a condenser lens that focuses the FIR onto a small quantum Hall detector (400 μm×400 μm). The solid immersion lens is in contact with the backside of a Hall bar sample, which is moved with a mechanical XY stage. The quantum Hall detector, which function as a narrow band FIR detector (bandwidth of about 2%), is a Hall bar with a large length-to-width ratio in integer quantum Hall effect regimes. The microscope is successfully applied to image extremely weak cyclotron emissions from quantum Hall devices with a spatial resolution of about 50 μm and a signal-to-noise ratio improved by a factor 18 compared to a previous system.
Quantum anomalous Hall effect with higher plateaus.
Wang, Jing; Lian, Biao; Zhang, Haijun; Xu, Yong; Zhang, Shou-Cheng
2013-09-27
The quantum anomalous Hall (QAH) effect in magnetic topological insulators is driven by the combination of spontaneous magnetic moments and spin-orbit coupling. Its recent experimental discovery raises the question if higher plateaus can also be realized. Here, we present a general theory for a QAH effect with higher Chern numbers and show by first-principles calculations that a thin film magnetic topological insulator of Cr-doped Bi2(Se,Te)3 is a candidate for the C=2 QAH insulator. Remarkably, whereas a higher magnetic field leads to lower Hall conductance plateaus in the integer quantum Hall effect, a higher magnetic moment leads to higher Hall conductance plateaus in the QAH effect.
Galilean invariance at quantum Hall edge
NASA Astrophysics Data System (ADS)
Moroz, Sergej; Hoyos, Carlos; Radzihovsky, Leo
2015-05-01
We construct the theory of a chiral Luttinger liquid that lives on the boundary of a Galilean invariant quantum Hall fluid. In contrast to previous studies, Galilean invariance of the total (bulk plus edge) theory is guaranteed. We consider electromagnetic response at the edge and calculate momentum- and frequency-dependent electric conductivity and argue that its experimental measurement can provide a new means to determine the "shift" and bulk Hall viscosity.
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
Guterding, Daniel; Jeschke, Harald O; Valentí, Roser
2016-05-17
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach to the natural mineral herbertsmithite. We prove the feasibility of the proposed modifications by performing ab-initio density functional theory calculations and demonstrate the occurrence of the predicted effects using realistic models. Our results herald a new family of quantum anomalous Hall and quantum spin Hall insulators at affordable energy/temperature scales based on kagome lattices of transition metal ions.
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.
Unconventional integer quantum Hall effect in graphene.
Gusynin, V P; Sharapov, S G
2005-09-30
Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by (2+1)-dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity sigma(xy) = -(2e2/h)(2n+1) with n = 0, 1, ..., which notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the n=0 Landau level and was discovered in recent experiments on ultrathin graphite films.
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.
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.
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.
The Integer and Fractional Quantum Hall Effects.
NASA Astrophysics Data System (ADS)
Usher, Alan
Available from UMI in association with The British Library. Requires signed TDF. This thesis reports investigations of the electrical conductivity of two-dimensional electron systems in high magnetic fields. Studies of the activated longitudinal conductivity associated with the integer quantum Hall effect reveal a large enhancement of the electronic g-factor, caused by the electron-electron interaction. A similar enhancement is observed in the Landau level separation. The magnetic field dependences of both effects are influenced by sample disorder. The activation data are analysed using three models for the shape of the extended state regions of disorder -broadened Landau levels. Only a small fraction of the electrons are found to occupy extended states. Values of the minimum metallic conductivity of electrons in broadened Landau levels are sample- and electron concentration-dependent. The fractional quantum Hall effect is a property of electrons in an incompressible quantum fluid state. The highest quality samples with low electron concentrations exhibit the effect in the manner predicted by simple theories involving spinless electrons. However, the influence of spin becomes apparent at higher electron concentrations, and in tilted field experiments. The effects of disorder are evident in measurements of the quasiparticle energy gap associated with the fractional quantum Hall effect. The experimental gap energies reported in this thesis are considerably smaller than those of theoretical studies, and they tend to zero at a non-zero magnetic field threshold. Simple theories predict that the fractional quantum Hall effect occurs only at odd denominator fractional occupancies. This thesis reports the first observations of the even denominator fractional quantum Hall effect. Persistent photoconductivity is a useful tool for increasing the concentration of two-dimensional electrons in GaAs-AlGaAs heterojunctions. A new photodeexcitation effect is reported, and possible
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
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.
Contactless measurement of alternating current conductance in quantum Hall structures
NASA Astrophysics Data System (ADS)
Drichko, I. L.; Diakonov, A. M.; Malysh, V. A.; Smirnov, I. Yu.; Galperin, Y. M.; Ilyinskaya, N. D.; Usikova, A. A.; Kummer, M.; von Känel, H.
2014-10-01
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.
Contactless measurement of alternating current conductance in quantum Hall structures
Drichko, I. L.; Diakonov, A. M.; Malysh, V. A.; Smirnov, I. Yu.; Ilyinskaya, N. D.; Usikova, A. A.; Galperin, Y. M.; Kummer, M.; Känel, H. von
2014-10-21
We report a procedure to determine the frequency-dependent conductance of quantum Hall structures in a broad frequency domain. The procedure is based on the combination of two known probeless methods—acoustic spectroscopy and microwave spectroscopy. By using the acoustic spectroscopy, we study the low-frequency attenuation and phase shift of a surface acoustic wave in a piezoelectric crystal in the vicinity of the electron (hole) layer. The electronic contribution is resolved using its dependence on a transverse magnetic field. At high frequencies, we study the attenuation of an electromagnetic wave in a coplanar waveguide. To quantitatively calibrate these data, we use the fact that in the quantum-Hall-effect regime the conductance at the maxima of its magnetic field dependence is determined by extended states. Therefore, it should be frequency independent in a broad frequency domain. The procedure is verified by studies of a well-characterized p-SiGe/Ge/SiGe heterostructure.
Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator.
Feng, Yang; Feng, Xiao; Ou, Yunbo; Wang, Jing; Liu, Chang; Zhang, Liguo; Zhao, Dongyang; Jiang, Gaoyuan; Zhang, Shou-Cheng; He, Ke; Ma, Xucun; Xue, Qi-Kun; Wang, Yayu
2015-09-18
We report experimental investigations on the quantum phase transition between the two opposite Hall plateaus of a quantum anomalous Hall insulator. We observe a well-defined plateau with zero Hall conductivity over a range of magnetic field around coercivity when the magnetization reverses. The features of the zero Hall plateau are shown to be closely related to that of the quantum anomalous Hall effect, but its temperature evolution exhibits a significant difference from the network model for a conventional quantum Hall plateau transition. We propose that the chiral edge states residing at the magnetic domain boundaries, which are unique to a quantum anomalous Hall insulator, are responsible for the novel features of the zero Hall plateau. PMID:26431002
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 (Cr(0.12)Bi(0.26)Sb(0.62))2Te3 film, and demonstrate the metal-to-insulator switching between two opposite QAHE plateau states up to 0.3 K. Moreover, the universal QAHE phase diagram is confirmed through the angle-dependent measurements. Our results address that the quantum phase transitions in both QAHE and QHE regimes are in the same universality class, yet the microscopic details are different. In addition, the realization of the QAHE insulating state unveils new ways to explore quantum phase-related physics and applications.
Metal-to-insulator switching in quantum anomalous Hall states
Kou, Xufeng; Pan, Lei; Wang, Jing; 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; et al
2015-10-07
After decades of searching for the dissipationless transport in the absence of any external magnetic field, quantum anomalous Hall effect (QAHE) was recently achieved in magnetic topological insulator films. However, the universal phase diagram of QAHE and its relation with quantum Hall effect (QHE) remain to be investigated. Here, we report the experimental observation of the giant longitudinal resistance peak and zero Hall conductance plateau at the coercive field in the six quintuple-layer (Cr0.12Bi0.26Sb0.62)2Te3 film, and demonstrate the metal-to-insulator switching between two opposite QAHE plateau states up to 0.3 K. Moreover, the universal QAHE phase diagram is confirmed through themore » angle-dependent measurements. Our results address that the quantum phase transitions in both QAHE and QHE regimes are in the same universality class, yet the microscopic details are different. Additionally, the realization of the QAHE insulating state unveils new ways to explore quantum phase-related physics and applications.« less
Metal-to-insulator switching in quantum anomalous Hall states
Kou, Xufeng; Pan, Lei; Wang, Jing; Fan, Yabin; Choi, Eun Sang; Lee, Wei -Li; Nie, Tianxiao; Murata, Koichi; Shao, Qiming; Zhang, Shou -Cheng; Wang, Kang L.
2015-10-07
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.
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.
Induced Superconductivity in the Quantum Spin Hall Edge
NASA Astrophysics Data System (ADS)
Ren, Hechen; Hart, Sean; Wagner, Timo; Leubner, Philipp; Muehlbauer, Mathias; Bruene, Christoph; Buhmann, Hartmut; Molenkamp, Laurens; Yacoby, Amir
2014-03-01
Two-dimensional topological insulators have a gapped bulk and helical edge states, making it a quantum spin Hall insulator. Combining such edge states with superconductivity can be an excellent platform for observing and manipulating localized Majorana fermions. In the context of condensed matter, these are emergent electronic states that obey non-Abelian statistics and hence support fault-tolerant quantum computing. To realize such theoretical constructions, an essential step is to show these edge channels are capable of carrying coherent supercurrent. In our experiment, we fabricate Josephson junctions with HgTe/HgCdTe quantum wells, a two-dimensional material that becomes a quantum spin Hall insulator when the quantum well is thicker than 6.3 nm and the bulk density is depleted. In this regime, we observe supercurrents whose densities are confined to the edges of the junctions, with edge widths ranging from 180 nm to 408 nm. To verify the topological nature of these edges, we measure identical junctions with HgTe/HgCdTe quantum wells thinner than 6.3 nm and observe only uniform supercurrent density across the junctions. This research is supported by Microsoft Corporation Project Q, the NSF DMR-1206016, the DOE SCGF Program, the German Research Foundation, and EU ERC-AG program.
Tunnelling between the edges of two lateral quantum Hall systems
Kang; Stormer; Pfeiffer; Baldwin; West
2000-01-01
The edge of a two-dimensional electron system in a magnetic field consists of one-dimensional channels that arise from the confining electric field at the edge of the system. The crossed electric and magnetic fields cause electrons to drift parallel to the sample boundary, creating a chiral current that travels along the edge in only one direction. In an ideal two-dimensional electron system in the quantum Hall regime, all the current flows along the edge. Quantization of the Hall resistance arises from occupation of N one-dimensional edge channels, each contributing a conductance of e2/h. Here we report differential conductance measurements, in the integer quantum Hall regime, of tunnelling between the edges of a pair of two-dimensional electron systems that are separated by an atomically precise, high-quality, tunnel barrier. The resultant interaction between the edge states leads to the formation of new energy gaps and an intriguing dispersion relation for electrons travelling along the barrier: for example, we see a persistent conductance peak at zero bias voltage and an absence of tunnelling features due to electron spin. These features are unexpected and are not consistent with a model of weakly interacting edge states. Remnant disorder along the barrier and charge screening may each play a role, although detailed numerical studies will be required to elucidate these effects.
Quantum spin hall insulator state in HgTe quantum wells.
König, Markus; Wiedmann, Steffen; Brüne, Christoph; Roth, Andreas; Buhmann, Hartmut; Molenkamp, Laurens W; Qi, Xiao-Liang; Zhang, Shou-Cheng
2007-11-01
Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e(2)/h, where e is the electron charge and h is Planck's constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field-induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.
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.
Supersonic regime of the Hall-magnetohydrodynamics resistive tearing instability
Ahedo, Eduardo; Ramos, Jesus J.
2012-07-15
An earlier analysis of the Hall-magnetohydrodynamics (MHD) tearing instability [E. Ahedo and J. J. Ramos, Plasma Phys. Controlled Fusion 51, 055018 (2009)] is extended to cover the regime where the growth rate becomes comparable or exceeds the sound frequency. Like in the previous subsonic work, a resistive, two-fluid Hall-MHD model with massless electrons and zero-Larmor-radius ions is adopted and a linear stability analysis about a force-free equilibrium in slab geometry is carried out. A salient feature of this supersonic regime is that the mode eigenfunctions become intrinsically complex, but the growth rate remains purely real. Even more interestingly, the dispersion relation remains of the same form as in the subsonic regime for any value of the instability Mach number, provided only that the ion skin depth is sufficiently small for the mode ion inertial layer width to be smaller than the macroscopic lengths, a generous bound that scales like a positive power of the Lundquist number.
Vortex Physics in the Quantum Hall Bilayer
NASA Astrophysics Data System (ADS)
Fertig, H. A.; Murthy, Ganpathy
2013-06-01
There exists a strong analogy between the quantum Hall bilayer system at total filling factor ν = 1 and a thin film superfluid, in which the groundstate is described as a condensate of particle-hole pairs. The analogy draws support from experiments which display near dissipationless transport properties at low temperatures. However dissipation is always present at any accessible temperature, suggesting that in a proper description, unpaired vortex-like excitations must be present. The mechanism by which this happens remains poorly understood. A key difference between the quantum Hall bilayer and simpler thin-film superfluids is that the vortices, more properly called merons in the former context, are charged objects. We demonstrate that a model in which disorder induces merons in the groundstate, through coupling to this charge, can naturally explain many of the observed imperfect superfluid properties...
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.
Universal spin Hall conductance fluctuations in chaotic Dirac quantum dots
NASA Astrophysics Data System (ADS)
Vasconcelos, T. C.; Ramos, J. G. G. S.; Barbosa, A. L. R.
2016-03-01
We present complete analytical and numerical results that demonstrate the anomalous universal fluctuations of the spin Hall conductance in chiral materials such as graphene and topological insulators. We investigate both the corresponding fluctuations, the universal fractionated and the universal quantized, and also the open channel orbital number crossover between the two regimes. In particular, we show that the Wigner-Dyson symmetries do not properly describe such conductances and the preponderant role of the chiral classes on the Dirac quantum dots. The results are analytical and solve outstanding issues.
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.
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
Line defects and quantum Hall plateaus in graphene
NASA Astrophysics Data System (ADS)
Dal Lago, V.; Foa Torres, L. E. F.
2015-04-01
Line defects in graphene can be either tailored-growth or arise naturally and are at the center of many discussions. Here we study the multiterminal conductance of graphene with an extended line defect in the quantum Hall regime analyzing the effects of the geometry of the setup, disorder and strain on the quantum Hall plateaus. We show that the defect turns out to affect the local and non-local conductance in very different ways depending on the geometrical configuration. When the defect is parallel to the sample edges one gets an equivalent circuit formed by parallel resistors. In contrast, when the defect bridges opposite edges, the Hall conductance may remain unaltered depending on the geometry of the voltage/current probes. The role of disorder, strain and the microscopic details of the defect in our results is also discussed. We show that the defect provides a realization of the electrical analog of an optical beam splitter. Its peculiar energy dependent inter-edge transmission allows it to be turned on or off at will and it may be used for routing the chiral edge states.
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.
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.
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 pump in quantum spin Hall edge states
NASA Astrophysics Data System (ADS)
Cheng, Fang
2016-09-01
We present a theory for quantum pump in a quantum spin Hall bar with two quantum point contacts (QPCs). The pump currents can be generated by applying harmonically modulating gate voltages at QPCs. The phase difference between the gate voltages introduces an effective gauge field, which breaks the time-reversal symmetry and generates pump currents. The pump currents display very different pump frequency dependence for weak and strong e-e interaction. These unique properties are induced by the helical feature of the edge states, and therefore can be used to detect and control edge state transport.
Quantum inferring acausal structures and the Monty Hall problem
NASA Astrophysics Data System (ADS)
Kurzyk, Dariusz; Glos, Adam
2016-09-01
This paper presents a quantum version of the Monty Hall problem based upon the quantum inferring acausal structures, which can be identified with generalization of Bayesian networks. Considered structures are expressed in formalism of quantum information theory, where density operators are identified with quantum generalization of probability distributions. Conditional relations between quantum counterpart of random variables are described by quantum conditional operators. Presented quantum inferring structures are used to construct a model inspired by scenario of well-known Monty Hall game, where we show the differences between classical and quantum Bayesian reasoning.
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.
Matrix Product States and Fractional Quantum Hall
NASA Astrophysics Data System (ADS)
Bernevig, B. Andrei; Estienne, Benoit; Regnault, Nicolas; Papic, Zlatko
2013-03-01
We present an exact matrix product state expansion (MPS) for a large series of Jack polynomial wavefunctions which serve as Fractional Quantum Hall ground-states of pseudopotential Hamiltonians. Using the basis of descendants in Virasoro and W algebras we build MPS descriptions of the (k,2) Jacks which include the Moore-Read state and the Gaffnian state, as well as MPS representation of the Z3 Read-Rezayi state. We then give a general method for computing MPS representations for other non-abelian states and their quasiholes.
Disordered Interactions and Fractional Quantum Hall States
NASA Astrophysics Data System (ADS)
Degottardi, Wade; Hafezi, Mohammad
The possibility that topological ordered states may be realized in photonic systems has recently attracted a great deal of attention. Given the rich phenomenology of the fractional quantum Hall effect, the bosonic Laughlin states have been of particular focus in this context. These states are known to arise in strongly nonlinear photonic lattices with artificial gauge fields, where nonlinearities associated with the resonators mimic on-site interactions. These effective interaction strengths are not universal and are subject to spatial disorder. We present a detailed study of the stability of these states and what implications they have for experiments.
Integer quantum Hall effect and correlated disorder
Greshnov, A. A. Zegrya, G. G.
2007-11-15
The effect of the form of the random potential of impurities and defects on the longitudinal {sigma}{sub xx} and Hall {sigma}{sub xy} components of conductivity in the mode of the integer quantum Hall effect is theoretically investigated. It is shown that the width of the Hall conductivity plateau as well as the peak values of the longitudinal conductivity heavily depend on the ratio {lambda}/a{sub H} between the random potential correlation length and the magnetic length. For the first time, it is established that in the case of the short-wavelength potential {lambda} << a{sub H}, the peak values of {sigma}{sub xx}{sup (N)} are directly proportional to the Landau level number N {>=} 1, {sigma}{sub xx} = 0.5Ne{sup 2}/h, whereas the peak values of {sigma}{sub xx}{sup (N)} are independent of the Landau level number in the case of the long-wavelength potential {lambda} >> a{sub H}, and their magnitude is much lower than 0.5e{sup 2}/h. The obtained results are in good agreement with the available experimental data.
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.
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
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.
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.
Quantum anomalous Hall and quantum spin-Hall phases in flattened Bi and Sb bilayers
Jin, Kyung-Hwan; Jhi, Seung-Hoon
2015-01-01
Discovery of two-dimensional topological insulator such as Bi bilayer initiates challenges in exploring exotic quantum states in low dimensions. We demonstrate a promising way to realize the Kane-Mele-type quantum spin Hall (QSH) phase and the quantum anomalous Hall (QAH) phase in chemically-modified Bi and Sb bilayers using first-principles calculations. We show that single Bi and Sb bilayers exhibit topological phase transitions from the band-inverted QSH phase or the normal insulator phase to Kane-Mele-type QSH phase upon chemical functionalization. We also predict that the QAH effect can be induced in Bi or Sb bilayers upon nitrogen deposition as checked from calculated Berry curvature and the Chern number. We explicitly demonstrate the spin-chiral edge states to appear in nitrogenated Bi-bilayer nanoribbons. PMID:25672932
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.
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].
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 .
Electromagnetic interactions in quantum Hall ferromagnets
Ray, Rashmi
1998-11-10
The {nu}=1 quantum Hall ground state in materials like GaAs is known to be ferromagnetic in nature. The exchange part of the Coulomb interaction provides the required attractive force to align the electronic spins spontaneously. The gapless Goldstone modes are the angular deviations of the magnetization vector from its fixed ground state orientation. Furthermore, the system supports electrically charged spin skyrmion configurations. It has been claimed in the literature that these skyrmions have half-integral spin owing to the presence of a topological Hopf term in the effective action governing the spin excitations. However, it has also been claimed that the derivation leading to this term is somewhat flawed. In this article, we demonstrate the existence of this term unambiguously. Furthermore, we investigate the electromagnetic interactions of the spin excitations and obtain a compact expression for the leading nonminimal electromagnetic coupling of these degrees of freedom.
Layered quantum Hall insulators with ultracold atoms
Zamora, A.; Szirmai, G.; Lewenstein, M.
2011-11-15
We consider a generalization of the two-dimensional (2D) quantum Hall insulator to a noncompact, non-Abelian gauge group, the Heisenberg-Weyl group. We show that this kind of insulator is actually a layered three-dimensional (3D) insulator with nontrivial topology. We further show that nontrivial combinations of quantized transverse conductivities can be engineered with the help of a staggered potential. We investigate the robustness and topological nature of this conductivity and connect it to the surface modes of the system. We also propose a simple experimental realization with ultracold atoms in 3D confined to a 2D square lattice with the third dimension being mapped to a gauge coordinate.
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.
Crossed Andreev effects in two-dimensional quantum Hall systems
NASA Astrophysics Data System (ADS)
Hou, Zhe; Xing, Yanxia; Guo, Ai-Min; Sun, Qing-Feng
2016-08-01
We study the crossed Andreev effects in two-dimensional conductor/superconductor hybrid systems under a perpendicular magnetic field. Both a graphene/superconductor hybrid system and an electron gas/superconductor one are considered. It is shown that an exclusive crossed Andreev reflection, with other Andreev reflections being completely suppressed, is obtained in a high magnetic field because of the chiral edge states in the quantum Hall regime. Importantly, the exclusive crossed Andreev reflection not only holds for a wide range of system parameters, e.g., the size of system, the width of central superconductor, and the quality of coupling between the graphene and the superconductor, but also is very robust against disorder. When the applied bias is within the superconductor gap, a robust Cooper-pair splitting process with high-efficiency can be realized in this system.
Quantum Hall effect in black phosphorus two-dimensional electron system
NASA Astrophysics Data System (ADS)
Li, Likai; Yang, Fangyuan; Ye, Guo Jun; Zhang, Zuocheng; Zhu, Zengwei; Lou, Wenkai; Zhou, Xiaoying; Li, Liang; Watanabe, Kenji; Taniguchi, Takashi; Chang, Kai; Wang, Yayu; Chen, Xian Hui; Zhang, Yuanbo
2016-07-01
The development of new, high-quality functional materials has been at the forefront of condensed-matter research. The recent advent of two-dimensional black phosphorus has greatly enriched the materials base of two-dimensional electron systems (2DESs). Here, we report the observation of the integer quantum Hall effect in a high-quality black phosphorus 2DES. The high quality is achieved by embedding the black phosphorus 2DES in a van der Waals heterostructure close to a graphite back gate; the graphite gate screens the impurity potential in the 2DES and brings the carrier Hall mobility up to 6,000 cm2 V-1 s-1. The exceptional mobility enabled us to observe the quantum Hall effect and to gain important information on the energetics of the spin-split Landau levels in black phosphorus. Our results set the stage for further study on quantum transport and device application in the ultrahigh mobility regime.
NASA Astrophysics Data System (ADS)
Yang, Kun
2016-04-01
We show that an acoustic crystalline wave gives rise to an effect similar to that of a gravitational wave to an electron gas. Applying this idea to a two-dimensional electron gas in the fractional quantum Hall regime, this allows for experimental study of its intra-Landau level dynamical response in the long-wavelength limit. To study such response we generalize Haldane's geometrical description of fractional quantum Hall states to situations where the external metric is time dependent. We show that such time-dependent metric (generated by acoustic wave) couples to collective modes of the system, including a quadrapolar mode at long wavelength, and magnetoroton at finite wavelength. Energies of these modes can be revealed in spectroscopic measurements, controlled by strain-induced Fermi velocity anisotropy. We argue that such geometrical probe provides a potentially highly useful alternative probe of quantum Hall liquids, in addition to the usual electromagnetic response.
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.
The Theory of the Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Shrivastava, Keshav N.
2008-05-01
Laughlin's theory of fractional charges is worked out in detail for small charges from 1/3 till 1/101. There is a small deviation between computed values and those obtained from the closed form expression. The ground state energy crosses that of the charge-density waves. We develop a theory of fractional charges by using the quantum mechanics of angular momentum. We find that fractional charges can be expressed in terms of spin and the values of charges 0, 1, 1/3, 2/3, 2/5, 3/5, …, are produced. The angular momenta eigen values when subjected to flux quantization, yield plateaus of energies which are independent of the magnetic field. In this way we are able to predict that charges of ±2e, ±6e, ±10e, ±14e, …, are produced. The higher order term in the flux quantization also produces quasiparticles of charges of ±4e. These calculated values of the charges are the same as those found in the experimental data of quantum Hall effect in graphene, which is a mono-atomic layer of carbon. Since the charge of the quasiparticles appears in the resistivity and there is a strong need of the electron spin to predict these charges, spin-charge coupling occurs in a natural way.
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.
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.
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.
Fractional quantum Hall effect in the absence of Landau levels.
Sheng, D N; Gu, Zheng-Cheng; Sun, Kai; Sheng, L
2011-01-01
It is well known that the topological phenomena with fractional excitations, the fractional quantum Hall effect, will emerge when electrons move in Landau levels. Here we show the theoretical discovery of the fractional quantum Hall effect in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically non-trivial flat-band model on a checkerboard lattice. In the presence of nearest-neighbouring repulsion, we find that at 1/3 filling, the Fermi-liquid state is unstable towards the fractional quantum Hall effect. At 1/5 filling, however, a next-nearest-neighbouring repulsion is needed for the occurrence of the 1/5 fractional quantum Hall effect when nearest-neighbouring repulsion is not too strong. We demonstrate the characteristic features of these novel states and determine the corresponding phase diagram.
Revealing topological superconductivity in extended quantum spin Hall Josephson junctions.
Lee, Shu-Ping; Michaeli, Karen; Alicea, Jason; Yacoby, Amir
2014-11-01
Quantum spin Hall-superconductor hybrids are promising sources of topological superconductivity and Majorana modes, particularly given recent progress on HgTe and InAs/GaSb. We propose a new method of revealing topological superconductivity in extended quantum spin Hall Josephson junctions supporting "fractional Josephson currents." Specifically, we show that as one threads magnetic flux between the superconductors, the critical current traces an interference pattern featuring sharp fingerprints of topological superconductivity-even when noise spoils parity conservation.
Josephson inplane and tunneling currents in bilayer quantum Hall system
Ezawa, Z. F.; Tsitsishvili, G.; Sawada, A.
2013-12-04
A Bose-Einstein condensation is formed by composite bosons in the quantum Hall state. A composite boson carries the fundamental charge (–e). We investigate Josephson tunneling of such charges in the bilayer quantum Hall system at the total filling ν = 1. We show the existence of the critical current for the tunneling current to be coherent and dissipationless in tunneling experiments with various geometries.
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.
Exciton Transport in a Bilayer Quantum Hall Superfluid
NASA Astrophysics Data System (ADS)
Eisenstein, J. P.; Finck, A. D. K.; Nandi, D.; Pfeiffer, L. N.; West, K. W.
2013-08-01
Bilayer quantum Hall systems at vT = 1 support an excitonic ground state. In addition to the usual charged quasiparticles, this system possesses a condensate degree of freedom: exciton transport. Detection of this neutral transport mode is facilitated by the use of the Corbino multiply-connected geometry in which charge transport is suppressed. We here summarize our recent experiments on Corbino devices which directly demonstrate exciton transport across the bulk of the incompressible vT = 1 quantum Hall state.
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).
Quantum diagrammatic theory of the extrinsic spin Hall effect in graphene
NASA Astrophysics Data System (ADS)
Milletarı, Mirco; Ferreira, Aires
2016-10-01
We present a rigorous microscopic theory of the extrinsic spin Hall effect in disordered graphene based on a nonperturbative quantum diagrammatic treatment incorporating skew scattering and anomalous (impurity-concentration-independent) quantum corrections on equal footing. The leading skew-scattering contribution to the spin Hall conductivity is shown to quantitatively agree with Boltzmann transport theory over a wide range of parameters. Our self-consistent approach, where all topologically equivalent noncrossing diagrams are resummed, unveils that the skewness generated by spin-orbit-active impurities deeply influences the anomalous component of the spin Hall conductivity, even in the weak-scattering regime. This seemingly counterintuitive result is explained by the rich sublattice structure of scattering potentials in graphene, for which traditional Gaussian disorder approximations fail to capture the intricate correlations between skew scattering and side jumps generated through diffusion. Finally, we assess the role of quantum interference corrections by evaluating an important subclass of crossing diagrams recently considered in the context of the anomalous Hall effect, the X and Ψ diagrams [A. Ado et al., Europhys. Lett. 111, 37004 (2015), 10.1209/0295-5075/111/37004]. We show that Ψ diagrams, encoding quantum coherent skew scattering, display a strong Fermi energy dependence, dominating the anomalous spin Hall component away from the Dirac point. Our findings have direct implications for nonlocal transport experiments in spin-orbit-coupled graphene systems.
NASA Astrophysics Data System (ADS)
Kim, Joong Gyu; Kang, Haeyong; Park, Jeongmin; Yun, Yoojoo; Truong, Thuy Kieu; Kim, Jeong-Gyun; Park, Nahee; Lee, Yourack; Yun, Hoyeol; Lee, Sang Wook; Lee, Young Hee; Suh, Dongseok
2015-03-01
Quantum Hall effect (QHE) is one of the unique properties of two-dimensional electronic systems providing the universal standard of electrical resistance. Due to edge-state transport features in quantum Hall regime, the two-terminal graphene field-effect transistor (FET) is frequently examined for the study of the integer as well as the fractional QHEs of graphene. In this work, we present a simple method to identify the existence of quantum Hall state in the graphene FET especially at high temperatures. Using the monolayer graphene FET sample with fully broken degeneracy, we modified the equipotential line inside graphene FET by the addition of extra electrode for the clear identification of the quantum Hall state formation at given temperature and magnetic field. We suggest a simple model to explain the difference and similarity between two-terminal and multi-terminal configurations, including the discussion about the QHE devices connected in series.
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.
Anomalous spin Hall effects in Dresselhaus (110) quantum wells
NASA Astrophysics Data System (ADS)
Liu, Ming-Hao; Chang, Ching-Ray
2010-10-01
Anomalous spin Hall effects that belong to the intrinsic type in Dresselhaus (110) quantum wells are discussed. For the out-of-plane spin component, antisymmetric current-induced spin polarization induces opposite spin Hall accumulation, even though there is no spin-orbit force due to Dresselhaus (110) coupling. A surprising feature of this spin Hall induction is that the spin accumulation sign does not change upon bias reversal. Contribution to the spin Hall accumulation from the spin Hall induction and the spin deviation due to intrinsic spin-orbit force as well as extrinsic spin scattering can be straightforwardly distinguished simply by reversing the bias. For the in-plane component, inclusion of a weak Rashba coupling leads to a new type of Sy intrinsic spin Hall effect solely due to spin-orbit-force-driven spin separation.
Role of electrical field in quantum Hall effect of graphene
NASA Astrophysics Data System (ADS)
Luo, Ji
2013-01-01
The ballistic motion of carriers of graphene in an orthogonal electromagnetic field is investigated to explain quantum Hall effect of graphene under experimental conditions. With the electrical field, all electronic eigen-states have the same expectation value of the velocity operator, or classically, all carriers move in cycloid-like curves with the same average velocity. This velocity is the origin of the Hall conductance and its magnitude is just appropriate so that the quantized Hall conductance is exactly independent of the external field. Electrical field changes each Landau level into a bundle of energies. Hall conductance plateaus occur in small fields as bundle gaps exist and are destroyed in intermediate fields as bundles overlap. As the electrical field tends to the critical point, all bundles have the same width, and bundle gaps increase to infinity rapidly. As a result, saturation of the Hall conductance may be observed. Electrical field thus demonstrates nonlinear effects on the Hall conductance.
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.
Bilayer fractional quantum Hall states with dipoles
NASA Astrophysics Data System (ADS)
Yao, N. Y.; Bennett, S. D.; Laumann, C. R.; Lev, B. L.; Gorshkov, A. V.
2015-09-01
Using the example of dysprosium atoms in an optical lattice, we show how dipolar interactions between magnetic dipoles can be used to obtain fractional quantum Hall states. In our approach, dysprosium atoms are trapped one atom per site in a deep optical lattice with negligible tunneling. Microwave and spatially dependent optical dressing fields are used to define an effective spin-1/2 or spin-1 degree of freedom in each atom. Thinking of spin-1/2 particles as hard-core bosons, dipole-dipole interactions give rise to boson hopping, topological flat bands with Chern number 1, and the ν =1/2 Laughlin state. Thinking of spin-1 particles as two-component hard-core bosons, dipole-dipole interactions again give rise to boson hopping, topological flat bands with Chern number 2, and the bilayer Halperin (2,2,1) state. By adjusting the optical fields, we find a phase diagram, in which the (2,2,1) state competes with superfluidity. Generalizations to solid-state magnetic dipoles are discussed.
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 Spin Hall Effect in Ultrasonic Metamaterials
NASA Astrophysics Data System (ADS)
Mousavi, S. Hossein; Khanikaev, Alexander B.; Wang, Zheng
2015-03-01
The discovery of topological order without breaking time-reversal symmetry, such as that in Quantum Spin Hall (QSH) effect and Topological Insulators, is one of the most groundbreaking advancements of recent years in condensed matters physics. The approach to topological order without breaking time-reversal symmetry is particularly important in elastics because no natural elastic materials show linear nonreciprocal response. Here we illustrate the first elastic-wave system emulating QSH effect and demonstrate existence of topologically protected elastic edge states. The system represents an elastic metamaterial-based phononic crystal. In this crystal, we achieved degenerate linear dispersion for two sets of modes, classified by one of the system's symmetries. Then, by relaxing and removing that symmetry by deliberately engineering a gauge field emulating a strong spin-orbit coupling of QSH, we observe opening a complete topological bandgap. Finally, the hallmark of the topological order, namely the presence of one-way chiral edge waves insensitive to nonmagnetic defects and disorders, is demonstrated in such elastic metacrystals. We illustrate the unique property of these elastic edge waves to flow around sharp corners without back-reflection or localization.
Studies of exciton condensation and transport in quantum Hall bilayers
NASA Astrophysics Data System (ADS)
Finck, Aaron David Kiyoshi
This thesis is a report of the transport properties of bilayer two-dimensional electron systems found in GaAs/AlGaAs double quantum well semiconductor heterostructures. When a strong perpendicular magnetic field is applied so that the total Landau filling factor is equal to one and if the two layers are close enough together, a novel quantum Hall (QH) state with strong interlayer correlations can form. This QH state is often described as an excitonic condensate, in which electrons in one layer pair with holes in the other. As neutral particles, excitons feel no Lorentz force and are not confined to the edges of the bilayer system like charged quasiparticles are. Instead, excitons are expected to be able to move freely through the bulk and even flow without any dissipation under proper conditions (i.e.,~excitonic superfluidity). Counterflow studies that directly probe the bulk verify this exciton transport in the electrically insulating interior. We also report on studies of the phase boundary between the correlated and uncorrelated phases at total Landau filling factor one as the effective interlayer separation is tuned. When both phases are fully spin polarized at high Zeeman energy, the phase transition is much broader than when the uncorrelated phase is incompletely polarized at low Zeeman energy. This suggests a possible change in the nature of the phase transition in the regime of complete spin polarization.
Broken symmetry quantum Hall states in dual-gated ABA trilayer graphene.
Lee, Yongjin; Velasco, Jairo; Tran, David; Zhang, Fan; Bao, W; Jing, Lei; Myhro, Kevin; Smirnov, Dmitry; Lau, Chun Ning
2013-04-10
ABA-stacked trilayer graphene is a unique 2D electron system with mirror reflection symmetry and unconventional quantum Hall effect. We present low-temperature transport measurements on dual-gated suspended trilayer graphene in the quantum Hall (QH) regime. We observe QH plateaus at filling factors ν = -8, -2, 2, 6, and 10, which is in agreement with the full-parameter tight binding calculations. In high magnetic fields, odd-integer plateaus are also resolved, indicating almost complete lifting of the 12-fold degeneracy of the lowest Landau level (LL). Under an out-of-plane electric field E(perpendicular), we observe degeneracy breaking and transitions between QH plateaus. Interestingly, depending on its direction, E(perpendicular) selectively breaks the LL degeneracies in the electron-doped or hole-doped regimes. Our results underscore the rich interaction-induced phenomena in trilayer graphene.
Quantum simulation of conductivity plateaux and fractional quantum Hall effect using ultracold atoms
NASA Astrophysics Data System (ADS)
Barberán, Nuria; Dagnino, Daniel; García-March, Miguel Angel; Trombettoni, Andrea; Taron, Josep; Lewenstein, Maciej
2015-12-01
We analyze the role of impurities in the fractional quantum Hall effect using a highly controllable system of ultracold atoms. We investigate the mechanism responsible for the formation of plateaux in the resistivity/conductivity as a function of the applied magnetic field in the lowest Landau level regime. To this aim, we consider an impurity immersed in a small cloud of an ultracold quantum Bose gas subjected to an artificial magnetic field. We consider scenarios corresponding to experimentally realistic systems with gauge fields induced by rotation of the trapping parabolic potential. Systems of this kind are adequate to simulate quantum Hall effects in ultracold atom setups. We use exact diagonalization for few atoms and to emulate transport equations, we analyze the time evolution of the system under a periodic perturbation. We provide a theoretical proposal to detect the up-to-now elusive presence of strongly correlated states related to fractional filling factors in the context of ultracold atoms. We analyze the conditions under which these strongly correlated states are associated with the presence of the resistivity/conductivity plateaux. Our main result is the presence of a plateau in a region, where the transfer between localized and non-localized particles takes place, as a necessary condition to maintain a constant value of the resistivity/conductivity as the magnetic field increases.
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.
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).
Thermoelectric properties of a two-dimensional electron gas exhibiting the quantum Hall effect
Davidson, J.S.; Dahlberg, E.D.; Valois, A.J.; Robinson, G.Y.
1986-02-15
This Communication reports studies of the thermoelectric properties of a two-dimensional electron gas in the quantum Hall regime. The data are compared to theoretical predictions for the thermopower when the chemical potential lies either in the middle of a Landau level or midway between two levels. For the comparison a Gaussian broadening is assumed and a good fit to the data can be obtained with the width of the levels as the adjustable parameter.
Revealing the quantum regime in tunnelling plasmonics.
Savage, Kevin J; Hawkeye, Matthew M; Esteban, Rubén; Borisov, Andrei G; Aizpurua, Javier; Baumberg, Jeremy J
2012-11-22
When two metal nanostructures are placed nanometres apart, their optically driven free electrons couple electrically across the gap. The resulting plasmons have enhanced optical fields of a specific colour tightly confined inside the gap. Many emerging nanophotonic technologies depend on the careful control of this plasmonic coupling, including optical nanoantennas for high-sensitivity chemical and biological sensors, nanoscale control of active devices, and improved photovoltaic devices. But for subnanometre gaps, coherent quantum tunnelling becomes possible and the system enters a regime of extreme non-locality in which previous classical treatments fail. Electron correlations across the gap that are driven by quantum tunnelling require a new description of non-local transport, which is crucial in nanoscale optoelectronics and single-molecule electronics. Here, by simultaneously measuring both the electrical and optical properties of two gold nanostructures with controllable subnanometre separation, we reveal the quantum regime of tunnelling plasmonics in unprecedented detail. All observed phenomena are in good agreement with recent quantum-based models of plasmonic systems, which eliminate the singularities predicted by classical theories. These findings imply that tunnelling establishes a quantum limit for plasmonic field confinement of about 10(-8)λ(3) for visible light (of wavelength λ). Our work thus prompts new theoretical and experimental investigations into quantum-domain plasmonic systems, and will affect the future of nanoplasmonic device engineering and nanoscale photochemistry.
Theory of the thermal Hall effect in quantum magnets.
Katsura, Hosho; Nagaosa, Naoto; Lee, Patrick A
2010-02-12
We present a theory of the thermal Hall effect in insulating quantum magnets, where the heat current is totally carried by charge-neutral objects such as magnons and spinons. Two distinct types of thermal Hall responses are identified. For ordered magnets, the intrinsic thermal Hall effect for magnons arises when certain conditions are satisfied for the lattice geometry and the underlying magnetic order. The other type is allowed in a spin liquid which is a novel quantum state since there is no order even at zero temperature. For this case, the deconfined spinons contribute to the thermal Hall response due to Lorentz force. These results offer a clear experimental method to prove the existence of the deconfined spinons via a thermal transport phenomenon.
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
NASA Astrophysics Data System (ADS)
Barkeshli, Maissam; Wen, Xiao-Gang
2011-09-01
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 Z4 parafermion (Read-Rezayi) state is a special case. This provides an example in which Z2 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.
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.
Ising Quantum Hall Ferromagnetism in AlAs Quantum Wells.
NASA Astrophysics Data System (ADS)
de Poortere, Etienne
2002-03-01
Though quantum Hall ferromagnetic transitions in two-dimensional (2D) systems are observed in several materials, such transitions in AlAs 2D electrons offer a unique combination of two remarkable properties: (1) the resistance of the carrier system increases sharply at the transition, and (2) these resistance spikes are hysteretic at low temperatures [1]. We have been able to uncover these properties thanks to recent improvements in the quality of our AlAs samples [2], which now attain a mobility as high as 31 m^2/Vs at a density 5 × 10^11 cm-2. These transport phenomena at Ising transitions result in part from the electronic properties of AlAs, which favor a strong competition between exchange, cyclotron and Zeeman energies. Indeed, 2D electrons in AlAs have a high and anisotropic effective band mass comparable to that of Si, and a band g-factor close to 2. In addition, high-density AlAs 2D electrons occupy two X-point valleys of the Brillouin zone, allowing for inter-valley Ising transitions. In this talk we present results from our study of Ising transitions in AlAs 2D electrons. We observe that the hysteretic resistance of a given transition depends sensitively on the occupation of the two levels involved in the transition, increasing in amplitude as these levels are depleted. We also analyze the spike temperature dependence, which shows that unlike the nearby quantum Hall resistance minima, the resistance spikes themselves are not activated. Other parameters are also varied, such as total carrier density and transverse electric field in the AlAs quantum well. A Hartree-Fock picture of these Ising transitions has been drawn, involving magnetic domains and increased scattering at the domain boundaries [3]. Nevertheless, many of the measured dependencies of the Ising transition resistance spikes are not yet qualitatively understood, forming thus a jigsaw puzzle of many parts. [1] E. P. De Poortere et al., Science 290, 1546 (2000). [2] E. P. De Poortere et al
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.
Tuning the spin Hall effect of Pt from the moderately dirty to the superclean regime
NASA Astrophysics Data System (ADS)
Sagasta, Edurne; Omori, Yasutomo; Isasa, Miren; Gradhand, Martin; Hueso, Luis E.; Niimi, Yasuhiro; Otani, YoshiChika; Casanova, Fèlix
2016-08-01
We systematically measure and analyze the spin diffusion length and the spin Hall effect in Pt with a wide range of conductivities using the spin absorption method in lateral spin valve devices. We observe a linear relation between the spin diffusion length and the conductivity, evidencing that the spin relaxation in Pt is governed by the Elliott-Yafet mechanism. We find a single intrinsic spin Hall conductivity (σSHint=1600 ±150 Ω-1c m-1) for Pt in the full range studied which is in good agreement with theory. We have obtained the crossover between the moderately dirty and the superclean scaling regimes of the spin Hall effect by tuning the conductivity. This is equivalent to that obtained for the anomalous Hall effect. Our results explain the spread of the spin Hall angle values in the literature and find a route to maximize this important parameter.
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.
Quantized anomalous Hall effect in two-dimensional ferromagnets: quantum Hall effect in metals.
Onoda, Masaru; Nagaosa, Naoto
2003-05-23
We study the effect of disorder on the anomalous Hall effect (AHE) in two-dimensional ferromagnets. The topological nature of the AHE leads to the integer quantum Hall effect from a metal, i.e., the quantization of sigma(xy) induced by the localization except for the few extended states carrying Chern numbers. Extensive numerical study on a model reveals that Pruisken's two-parameter scaling theory holds even when the system has no gap with the overlapping multibands and without the uniform magnetic field. Therefore, the condition for the quantized AHE is given only by the Hall conductivity sigma(xy) without the quantum correction, i.e., /sigma(xy)/>e(2)/(2h).
An improved far-infrared microscope with quantum Hall detectors
NASA Astrophysics Data System (ADS)
Ikushima, Kenji; Sakuma, Hisato; Komiyama, Susumu
2003-05-01
A highly-sensitive scanning far-infrared (FIR) microscope is developed. The microscope consists of a silicon solid immersion lens that probes FIR and a condenser lens that focuses the FIR onto a small and highly-sensitive quantum Hall detector. The solid immersion lens is in contact with a sample, which is moved with a mechanical stage. The microscope is successfully applied to image extremely weak cyclotron emission from quantum Hall devices with a spatial resolution about 50 μm and a signal-to-noise ratio improved by a factor 18 compared to a previous system.
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.
Fractional quantum Hall states in the vicinity of Mott plateaus
Umucalilar, R. O.; Mueller, Erich J.
2010-05-15
We perform variational Monte Carlo calculations to show that bosons in a rotating optical lattice will form analogs of fractional quantum Hall states when the tunneling is sufficiently weak compared to the interactions, and the deviation of density from an integer is commensurate with the effective magnetic field. We compare the energies of superfluid and correlated states to one another and to the energies found in full configuration-interaction calculations on small systems. We look at overlaps between our variational states and the exact ground state, characterizing the ways in which fractional quantum Hall effect correlations manifest themselves near the Mott insulating state. We explore the experimental signatures of these states.
Collective modes and the periodicity of quantum Hall stripes.
Kukushkin, I V; Umansky, V; von Klitzing, K; Smet, J H
2011-05-20
We investigate the quantum Hall stripe phase at filling factor 9/2 at the microscopic level by probing the dispersion of its collective modes with the help of surface acoustic waves with wavelengths down to 60 nm. The dispersion is strongly anisotropic. It is highly dispersive and exhibits a roton minimum for wave vectors aligned along the easy transport direction. In the perpendicular direction, however, the dispersion is featureless, although not flat as predicted by theory. Oscillatory behavior in the absorption intensity of the collective mode with a wave vector perpendicular to the stripes is attributed to a commensurability effect. It allows us to extract the periodicity of the quantum Hall stripes.
Scrutinizing Hall Effect in Mn1 -xFex Si : Fermi Surface Evolution and Hidden Quantum Criticality
NASA Astrophysics Data System (ADS)
Glushkov, V. V.; Lobanova, I. I.; Ivanov, V. Yu.; Voronov, V. V.; Dyadkin, V. A.; Chubova, N. M.; Grigoriev, S. V.; Demishev, S. V.
2015-12-01
Separating between the ordinary Hall effect and anomalous Hall effect in the paramagnetic phase of Mn1 -xFex Si reveals an ordinary Hall effect sign inversion associated with the hidden quantum critical (QC) point x*˜0.11 . The effective hole doping at intermediate Fe content leads to verifiable predictions in the field of fermiology, magnetic interactions, and QC phenomena in Mn1 -xFex Si . The change of electron and hole concentrations is considered as a "driving force" for tuning the QC regime in Mn1 -xFex Si via modifying the Ruderman-Kittel-Kasuya-Yosida exchange interaction within the Heisenberg model of magnetism.
On the Quantum Spin Hall Gap of Monolayer 1T'-WTe2.
Zheng, Feipeng; Cai, Chaoyi; Ge, Shaofeng; Zhang, Xuefeng; Liu, Xin; Lu, Hong; Zhang, Yudao; Qiu, Jun; Taniguchi, Takashi; Watanabe, Kenji; Jia, Shuang; Qi, Jingshan; Chen, Jian-Hao; Sun, Dong; Feng, Ji
2016-06-01
Positive quantum spin Hall gap in mono-layer 1T'-WTe2 is consistently supported by density-functional theory calculations, ultrafast pump-probe, and electrical transport measurements. It is argued that monolayer 1T'-WTe2 , which was predicted to be a semimetallic quantum spin Hall material, is likely a truly 2D quantum spin Hall insulator with a positive quantum spin Hall gap.
On the Quantum Spin Hall Gap of Monolayer 1T'-WTe2.
Zheng, Feipeng; Cai, Chaoyi; Ge, Shaofeng; Zhang, Xuefeng; Liu, Xin; Lu, Hong; Zhang, Yudao; Qiu, Jun; Taniguchi, Takashi; Watanabe, Kenji; Jia, Shuang; Qi, Jingshan; Chen, Jian-Hao; Sun, Dong; Feng, Ji
2016-06-01
Positive quantum spin Hall gap in mono-layer 1T'-WTe2 is consistently supported by density-functional theory calculations, ultrafast pump-probe, and electrical transport measurements. It is argued that monolayer 1T'-WTe2 , which was predicted to be a semimetallic quantum spin Hall material, is likely a truly 2D quantum spin Hall insulator with a positive quantum spin Hall gap. PMID:27115098
A 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.
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.
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.
Information causality in the quantum and post-quantum regime.
Ringbauer, Martin; Fedrizzi, Alessandro; Berry, Dominic W; White, Andrew G
2014-01-01
Quantum correlations can be stronger than anything achieved by classical systems, yet they are not reaching the limit imposed by relativity. The principle of information causality offers a possible explanation for why the world is quantum and why there appear to be no even stronger correlations. Generalizing the no-signaling condition it suggests that the amount of accessible information must not be larger than the amount of transmitted information. Here we study this principle experimentally in the classical, quantum and post-quantum regimes. We simulate correlations that are stronger than allowed by quantum mechanics by exploiting the effect of polarization-dependent loss in a photonic Bell-test experiment. Our method also applies to other fundamental principles and our results highlight the special importance of anisotropic regions of the no-signalling polytope in the study of fundamental principles. PMID:25378182
Information causality in the quantum and post-quantum regime.
Ringbauer, Martin; Fedrizzi, Alessandro; Berry, Dominic W; White, Andrew G
2014-11-07
Quantum correlations can be stronger than anything achieved by classical systems, yet they are not reaching the limit imposed by relativity. The principle of information causality offers a possible explanation for why the world is quantum and why there appear to be no even stronger correlations. Generalizing the no-signaling condition it suggests that the amount of accessible information must not be larger than the amount of transmitted information. Here we study this principle experimentally in the classical, quantum and post-quantum regimes. We simulate correlations that are stronger than allowed by quantum mechanics by exploiting the effect of polarization-dependent loss in a photonic Bell-test experiment. Our method also applies to other fundamental principles and our results highlight the special importance of anisotropic regions of the no-signalling polytope in the study of fundamental principles.
Hall effect in quantum critical charge-cluster glass
NASA Astrophysics Data System (ADS)
Wu, Jie; Bollinger, Anthony T.; Sun, Yujie
2016-04-01
Upon doping, cuprates undergo a quantum phase transition from an insulator to a d-wave superconductor. The nature of this transition and of the insulating state is vividly debated. Here, we study the Hall effect in La2-xSrxCuO4 (LSCO) samples doped near the quantum critical point at x ˜ 0.06. Dramatic fluctuations in the Hall resistance appear below TCG ˜ 1.5 K and increase as the sample is cooled down further, signaling quantum critical behavior. We explore the doping dependence of this effect in detail, by studying a combinatorial LSCO library in which the Sr content is varied in extremely fine steps, Δx ˜ 0.00008. We observe that quantum charge fluctuations wash out when superconductivity emerges but can be restored when the latter is suppressed by applying a magnetic field, showing that the two instabilities compete for the ground state.
Hall effect in quantum critical charge-cluster glass.
Wu, Jie; Bollinger, Anthony T; Sun, Yujie; Božović, Ivan
2016-04-19
Upon doping, cuprates undergo a quantum phase transition from an insulator to a d-wave superconductor. The nature of this transition and of the insulating state is vividly debated. Here, we study the Hall effect in La2-xSrxCuO4(LSCO) samples doped near the quantum critical point atx∼ 0.06. Dramatic fluctuations in the Hall resistance appear belowTCG∼ 1.5 K and increase as the sample is cooled down further, signaling quantum critical behavior. We explore the doping dependence of this effect in detail, by studying a combinatorial LSCO library in which the Sr content is varied in extremely fine steps,Δx∼ 0.00008. We observe that quantum charge fluctuations wash out when superconductivity emerges but can be restored when the latter is suppressed by applying a magnetic field, showing that the two instabilities compete for the ground state. PMID:27044081
Hall effect in quantum critical charge-cluster glass
Wu, Jie; Bollinger, Anthony T.; Sun, Yujie; Božović, Ivan
2016-01-01
Upon doping, cuprates undergo a quantum phase transition from an insulator to a d-wave superconductor. The nature of this transition and of the insulating state is vividly debated. Here, we study the Hall effect in La2-xSrxCuO4 (LSCO) samples doped near the quantum critical point at x ∼ 0.06. Dramatic fluctuations in the Hall resistance appear below TCG ∼ 1.5 K and increase as the sample is cooled down further, signaling quantum critical behavior. We explore the doping dependence of this effect in detail, by studying a combinatorial LSCO library in which the Sr content is varied in extremely fine steps, Δx ∼ 0.00008. We observe that quantum charge fluctuations wash out when superconductivity emerges but can be restored when the latter is suppressed by applying a magnetic field, showing that the two instabilities compete for the ground state. PMID:27044081
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.
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.
Intrinsic gap of the nu=5/2 fractional quantum Hall state.
Dean, C R; Piot, B A; Hayden, P; Das Sarma, S; Gervais, G; Pfeiffer, L N; West, K W
2008-04-11
The fractional quantum Hall effect is observed at low magnetic field where the cyclotron energy is smaller than the Coulomb interaction energy. The nu=5/2 excitation gap at 2.63 T is measured to be 262+/-15 mK, similar to values obtained in samples with twice the electronic density. Examining the role of disorder on the 5/2 state, we find that a large discrepancy remains between theory and experiment for the intrinsic gap extrapolated from the infinite mobility limit. The observation of a 5/2 state in the low-field regime suggests that inclusion of nonperturbative Landau level mixing may be necessary to fully understand the energetics of half-filled fractional quantum Hall liquids.
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
Bulk excitonic currents in a bilayer quantum Hall system and Andreev reflection
NASA Astrophysics Data System (ADS)
Finck, A. D. K.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2011-03-01
Bilayer 2D electron systems in the quantum Hall regime can support a novel interlayer coherent phase which may be viewed as a Bose condensate of interlayer excitons. While numerous experiments over the past decade have revealed a host of remarkable properties of this strongly correlated quantum fluid, heretofore none have directly demonstrated the transport of excitons across the electrically insulating bulk of the system. We report here just such an observation. Our experimental results show that excitons may be launched into the bulk of the 2D system via a process analogous to Andreev reflection. Excitons are emitted into the bulk of the bilayer when electrons are injected into one 2D layer and withdrawn from the other along a common edge of the system. Similarly, we demonstrate that excitons arriving at the edge of the Hall droplet can drive current through external circuitry connected to contacts along that edge.
A toy model for quantum spin Hall effect
NASA Astrophysics Data System (ADS)
Owerre, S. A.; Nsofini, J.
2015-09-01
In this communication, we investigate a toy model of three-dimensional topological insulator surface, coupled homogeneously to a fictitious pseudospin-1/2 particle. We show that this toy model captures the interesting features of topological insulator surface states, which include topological quantum phase transition and quantum spin Hall effect. We further incorporate an out-of-plane magnetic field and obtain the Landau levels.
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.
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.
Band Collapse and the Quantum Hall Effect in Graphene
Bernevig, B.Andrei; Hughes, Taylor L.; Zhang, Shou-Cheng; Chen, Han-Dong; Wu, Congjun; /Santa Barbara, KITP
2010-03-16
The recent Quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall (QH) conductance in fermion systems with continuum Dirac spectrum. In this paper we take into account the lattice, and perform an exact diagonalization of the Landau problem on the hexagonal lattice. At very large magnetic fields the Dirac argument fails completely and the Hall conductance, given by the number of edge states present in the gaps of the spectrum, is dominated by lattice effects. As the field is lowered, the experimentally observed situation is recovered through a phenomenon which we call band collapse. As a corollary, for low magnetic field, graphene will exhibit two qualitatively different QHE's: at low filling, the QHE will be dominated by the 'relativistic' Dirac spectrum and the Hall conductance will be odd-integer; above a certain filling, the QHE will be dominated by a non-relativistic spectrum, and the Hall conductance will span all integers, even and odd.
Emergence of integer quantum Hall effect from chaos
NASA Astrophysics Data System (ADS)
Tian, Chushun; Chen, Yu; Wang, Jiao
2016-02-01
We present an analytic microscopic theory showing that in a large class of spin-1/2 quasiperiodic quantum kicked rotors, a dynamical analog of the integer quantum Hall effect (IQHE) emerges from an intrinsic chaotic structure. Specifically, the inverse of the Planck's quantum (he) and the rotor's energy growth rate mimic the "filling fraction" and the "longitudinal conductivity" in conventional IQHE, respectively, and a hidden quantum number is found to mimic the "quantized Hall conductivity." We show that for an infinite discrete set of critical values of he, the long-time energy growth rate is universal and of order of unity ("metallic" phase), but otherwise vanishes ("insulating" phase). Moreover, the rotor insulating phases are topological, each of which is characterized by a hidden quantum number. This number exhibits universal behavior for small he, i.e., it jumps by unity whenever he decreases, passing through each critical value. This intriguing phenomenon is not triggered by the likes of Landau band filling, well known to be the mechanism for conventional IQHE, and far beyond the canonical Thouless-Kohmoto-Nightingale-Nijs paradigm for quantum Hall transitions. Instead, this dynamical phenomenon is of strong chaos origin; it does not occur when the dynamics is (partially) regular. More precisely, we find that a topological object, similar to the topological theta angle in quantum chromodynamics, emerges from strongly chaotic motion at microscopic scales, and its renormalization gives the hidden quantum number. Our analytic results are confirmed by numerical simulations. Our findings indicate that rich topological quantum phenomena can emerge from chaos and might point to a new direction of study in the interdisciplinary area straddling chaotic dynamics and condensed matter physics. This work is a substantial extension of a short paper published earlier by two of us [Y. Chen and C. Tian, Phys. Rev. Lett. 113, 216802 (2014), 10.1103/PhysRevLett.113.216802].
Nonlocal Polarization Feedback in a Fractional Quantum Hall Ferromagnet.
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
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.
Quantum spin Hall insulators with interactions and lattice anisotropy
NASA Astrophysics Data System (ADS)
Wu, Wei; Rachel, Stephan; Liu, Wu-Ming; Le Hur, Karyn
2012-05-01
We investigate the interplay between spin-orbit coupling and electron-electron interactions on the honeycomb lattice, combining the cellular dynamical mean-field theory and its real-space extension with analytical approaches. We provide a thorough analysis of the phase diagram and temperature effects at weak spin-orbit coupling. We systematically discuss the stability of the quantum spin Hall phase toward interactions and lattice anisotropy, resulting in the plaquette-honeycomb model. We also show the evolution of the helical edge states characteristic of quantum spin Hall insulators as a function of Hubbard interaction and anisotropy. At very weak spin-orbit coupling and intermediate electron-electron interactions, we substantiate the existence of a quantum spin liquid phase.
Mini array of quantum Hall devices based on epitaxial graphene
NASA Astrophysics Data System (ADS)
Novikov, S.; Lebedeva, N.; Hämäläinen, J.; Iisakka, I.; Immonen, P.; Manninen, A. J.; Satrapinski, A.
2016-05-01
Series connection of four quantum Hall effect (QHE) devices based on epitaxial graphene films was studied for realization of a quantum resistance standard with an up-scaled value. The tested devices showed quantum Hall plateaux RH,2 at a filling factor v = 2 starting from a relatively low magnetic field (between 4 T and 5 T) when the temperature was 1.5 K. The precision measurements of quantized Hall resistance of four QHE devices connected by triple series connections and external bonding wires were done at B = 7 T and T = 1.5 K using a commercial precision resistance bridge with 50 μA current through the QHE device. The results showed that the deviation of the quantized Hall resistance of the series connection of four graphene-based QHE devices from the expected value of 4×RH,2 = 2 h/e2 was smaller than the relative standard uncertainty of the measurement (<1 × 10-7) limited by the used resistance bridge.
Quantum anomalous Hall effect in topological insulator memory
Jalil, Mansoor B. A.; Tan, S. G.; Siu, Z. B.
2015-05-07
We theoretically investigate the quantum anomalous Hall effect (QAHE) in a magnetically coupled three-dimensional-topological insulator (3D-TI) system. We apply the generalized spin-orbit coupling Hamiltonian to obtain the Hall conductivity σ{sup xy} of the system. The underlying topology of the QAHE phenomenon is then analyzed to show the quantization of σ{sup xy} and its relation to the Berry phase of the system. Finally, we analyze the feasibility of utilizing σ{sup xy} as a memory read-out in a 3D-TI based memory at finite temperatures, with comparison to known magnetically doped 3D-TIs.
Partition noise and statistics in the fractional quantum hall effect.
Safi, I; Devillard, P; Martin, T
2001-05-14
A microscopic theory of current partition in fractional quantum Hall liquids, described by chiral Luttinger liquids, is developed to compute the noise correlations, using the Keldysh technique. In this Hanbury-Brown and Twiss geometry, at Laughlin filling factors nu = 1/3, the real time noise correlator exhibits oscillations which persist over larger time scales than that of an uncorrelated Hall fluid. The zero frequency noise correlations are negative at filling factor 1/3 as for bare electrons (antibunching), but are strongly reduced in amplitude. These correlations become positive (bunching) for nu < or = 1/5, suggesting a tendency towards bosonic behavior.
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.
Chiral partition functions of quantum Hall droplets
Cappelli, Andrea Viola, Giovanni; Zemba, Guillermo R.
2010-02-15
Chiral partition functions of conformal field theory describe the edge excitations of isolated Hall droplets. They are characterized by an index specifying the quasiparticle sector and transform among themselves by a finite-dimensional representation of the modular group. The partition functions are derived and used to describe electron transitions leading to Coulomb blockade conductance peaks. We find the peak patterns for Abelian hierarchical states and non-Abelian Read-Rezayi states, and compare them. Experimental observation of these features can check the qualitative properties of the conformal field theory description, such as the decomposition of the Hilbert space into sectors, involving charged and neutral parts, and the fusion rules.
Intrinsic Spin Hall Effect Induced by Quantum Phase Transition in HgCdTe Quantum Wells
Yang, Wen; Chang, Kai; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
Spin Hall effect can be induced both by the extrinsic impurity scattering and by the intrinsic spin-orbit coupling in the electronic structure. The HgTe/CdTe quantum well has a quantum phase transition where the electronic structure changes from normal to inverted. We show that the intrinsic spin Hall effect of the conduction band vanishes on the normal side, while it is finite on the inverted side. This difference gives a direct mechanism to experimentally distinguish the intrinsic spin Hall effect from the extrinsic one.
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 States in Rotating Spin-1 Bose Systems
NASA Astrophysics Data System (ADS)
Read, Nicholas
2003-03-01
It has been pointed out that when cold atoms in a trap are rotated rapidly, the system can be mapped onto the quantum Hall effect situation of charged particles in a magnetic field, by passing to the rotating frame. For spinless bosons, as the rotation rate increases, the Bose condensate first develops a vortex lattice, then at high rotation rate this is replaced by a sequence of quantum liquids, which are quantum Hall states of bosons. Numerical work [1] has indicated that there is a sequence of these that are well-described by the parafermion states of Read-Rezayi [2]. For spin-1 bosons, we describe here two sequences of spin-singlet quantum Hall states, with applications to the ground states of a standard model Hamiltonian for this system [3]. We also describe the states at low rotation rates, where various spin textures occur. [1] N.R. Cooper, N.K. Wilkin, and J.M.F. Gunn, Phys. Rev. Lett. 87, 120405 (2001). [2] N. Read and E. Rezayi, Phys. Rev. B 59, 8084 (1999). [3] J.W. Reijnders, F.J.M. Lankvelt, K. Schoutens, and N. Read, Phys. Rev. Lett. 89, 120401 (2002).
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.
Spin Superfluidity in the ν=0 Quantum Hall State of Graphene.
Takei, So; Yacoby, Amir; Halperin, Bertrand I; Tserkovnyak, Yaroslav
2016-05-27
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. PMID:27284667
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.
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
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
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)
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.}
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
2015-11-26
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.
Fractionally charged skyrmions in fractional quantum Hall effect
Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; Pinczuk, A.; Jain, J. K.
2015-11-26
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.
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
Hopping conductivity in the quantum Hall effect: revival of universal scaling.
Hohls, F; Zeitler, U; Haug, R J
2002-01-21
We have measured the temperature dependence of the conductivity sigma(xx) of a two-dimensional electron system deep into the localized regime of the quantum Hall plateau transition. Using variable-range hopping theory we extract directly the localization length xi from this experiment. We use our results to study the scaling behavior of xi as a function of the filling factor distance /deltanu/ to the critical point of the transition. We find for all samples a power-law behavior xi equivalent to /deltanu/(-gamma) in agreement with the theoretically proposed universal exponent gamma = 2.35.
Integer quantum Hall effect on a six-valley hydrogen-passivated silicon (111) surface.
Eng, K; McFarland, R N; Kane, B E
2007-07-01
We report magnetotransport studies of a two-dimensional electron system formed in an inversion layer at the interface between a hydrogen-passivated Si(111) surface and vacuum. Measurements in the integer quantum Hall regime demonstrate that the expected sixfold valley degeneracy for these surfaces is broken, resulting in an unequal occupation of the six valleys and anisotropy in the resistance. We hypothesize the misorientation of Si surface breaks the valley states into three unequally spaced pairs, but the observation of odd filling factors is difficult to reconcile with noninteracting electron theory.
Gauge fields and composite fermions in bilayer quantum Hall systems
NASA Astrophysics Data System (ADS)
Cipri, Robert
When placed in a strong magnetic field, a two-dimensional electron gas can exhibit the quantum Hall effect in which a step like pattern forms in the Hall resistance, RH, which is defined to be the voltage drop perpendicular to the current driven through the plane of the sample divided by the magnitude of the current. The filling fraction nu = p/q defines the quantization condition where p and q are relatively prime integers and q is odd, with RH =h/(nu e2) where h is Planck's constant and e is the charge of the electron. At the same time the Hall resistance becomes quantized the longitudinal resistance vanishes indicating dissipationless current flow. The integer quantum Hall effect (nu = 1, 2, 3...) is simply modeled using single-particle energy levels while the many-body fractional quantum Hall effect can be understood in terms of new particles known as composite fermions, electrons bound to an even number of statistical flux quanta. In this approach, the fractional quantum Hall effect for electrons is viewed as an effective integer quantum Hall effect for composite fermions. It was pointed out by Halperin, Lee and Read that for filling fraction nu = 1/2 the external magnetic field is exactly canceled by the average of the statistical flux quanta attached to the composite fermions. As a result, the composite fermions move in zero effective magnetic field with a well-defined Fermi surface at zero temperature. This "metallic" state is compressible and does not have a quantized Hall resistance. However, when two nu = 1/2 layers are brought close together, interactions between the layers lead to a new incompressible bilayer quantum Hall state in which electrons form a exciton condensate with total filling fraction nuT = 1/2 + 1/2 = 1. Recently it has been proposed that an interesting new transition may occur in this system in which interlayer Coulomb repulsion leads to excitonic condensation not of electrons but of composite fermions which are then free to tunnel
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.
Global phase diagram of bilayer quantum Hall ferromagnets
NASA Astrophysics Data System (ADS)
Abolfath, M.; Radzihovsky, L.; MacDonald, A. H.
2002-06-01
We present a microscopic study of the interlayer spacing d versus in-plane magnetic field B|| phase diagram for bilayer quantum Hall (QH) pseudoferromagnets. In addition to the interlayer charge balanced commensurate and incommensurate states analyzed previously, we address the corresponding interlayer charge unbalanced ``canted'' QH states. We predict a large anomaly in the bilayer capacitance at the canting transition and the formation of dipole stripe domains with periods exceeding 1 micron in the canted state.
Persistent currents and dissipation in narrow bilayer quantum Hall bars
NASA Astrophysics Data System (ADS)
Kyriakidis, Jordan; Radzihovsky, Leo
2001-11-01
Bilayer quantum Hall states support a flow of nearly dissipationless staggered current which can only decay through collective channels. We study the dominant finite-temperature dissipation mechanism which in narrow bars is driven by thermal nucleation of pseudospin solitons. We find the finite-temperature resistivity, predict the resulting staggered current-voltage characteristics, and calculate the associated zero-temperature critical staggered current and gate voltage.
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.
Anomalous Hall effect in ferromagnetic semiconductors in the hopping transport regime.
Burkov, A A; Balents, Leon
2003-08-01
We present a theory of the anomalous Hall effect in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity sigma(AH)(xy). We show that sigma(AH)(xy) is proportional to the first derivative of the density of states varrho(epsilon) and thus can be expected to change sign as a function of impurity band filling. We also show that sigma(AH)(xy) depends on temperature as the longitudinal conductivity sigma(xx) within logarithmic accuracy.
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}.
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.
Wave-function description of conductance mapping for a quantum Hall electron interferometer
NASA Astrophysics Data System (ADS)
Kolasiński, K.; Szafran, B.
2014-04-01
Scanning gate microscopy of quantum point contacts (QPC) in the integer quantum Hall regime is considered in terms of the scattering wave functions with a finite-difference implementation of the quantum transmitting boundary approach. Conductance (G) maps for a clean QPC as well as for a system including an antidot within the QPC constriction are evaluated. The steplike locally flat G maps for clean QPCs turn into circular resonances that are reentrant in an external magnetic field when the antidot is introduced to the constriction. The current circulation around the antidot and the spacing of the resonances at the magnetic field scale react to the probe approaching the QPC. The calculated G maps with a rigid but soft antidot potential reproduce the features detected recently in the electron interferometer [F. Martins et al., Sci. Rep. 3, 1416 (2013), 10.1038/srep01416].
Real-space imaging of fractional quantum Hall liquids.
Hayakawa, Junichiro; Muraki, Koji; Yusa, Go
2013-01-01
Electrons in semiconductors usually behave like a gas--as independent particles. However, when confined to two dimensions under a perpendicular magnetic field at low temperatures, they condense into an incompressible quantum liquid. This phenomenon, known as the fractional quantum Hall (FQH) effect, is a quantum-mechanical manifestation of the macroscopic behaviour of correlated electrons that arises when the Landau-level filling factor is a rational fraction. However, the diverse microscopic interactions responsible for its emergence have been hidden by its universality and macroscopic nature. Here, we report real-space imaging of FQH liquids, achieved with polarization-sensitive scanning optical microscopy using trions (charged excitons) as a local probe for electron spin polarization. When the FQH ground state is spin-polarized, the triplet/singlet intensity map exhibits a spatial pattern that mirrors the intrinsic disorder potential, which is interpreted as a mapping of compressible and incompressible electron liquids. In contrast, when FQH ground states with different spin polarization coexist, domain structures with spontaneous quasi-long-range order emerge, which can be reproduced remarkably well from the disorder patterns using a two-dimensional random-field Ising model. Our results constitute the first reported real-space observation of quantum liquids in a class of broken symmetry state known as the quantum Hall ferromagnet.
Isotropic to anisotropic transition in a fractional quantum Hall state
NASA Astrophysics Data System (ADS)
Mulligan, Michael; Nayak, Chetan; Kachru, Shamit
2010-08-01
We study an Abelian gauge theory in 2+1 dimensions which has surprising theoretical and phenomenological features. The theory has a vanishing coefficient for the square of the electric field ei2 , characteristic of a quantum critical point with dynamical critical exponent z=2 , and a level- k Chern-Simons coupling, which is marginal at this critical point. For k=0 , this theory is dual to a free z=2 scalar field theory describing a quantum Lifshitz transition, but k≠0 renders the scalar description nonlocal. The k≠0 theory exhibits properties intermediate between the (topological) pure Chern-Simons theory and the scalar theory. For instance, the Chern-Simons term does not make the gauge field massive. Nevertheless, there are chiral edge modes when the theory is placed on a space with boundary and a nontrivial ground-state degeneracy kg when it is placed on a finite-size Riemann surface of genus g . The coefficient of ei2 is the only relevant coupling; it tunes the system through a quantum phase transition between an isotropic fractional quantum Hall state and an anisotropic fractional quantum Hall state. We compute zero-temperature transport coefficients in both phases and at the critical point and comment briefly on the relevance of our results to recent experiments.
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.
Zhou, Tong; Zhang, Jiayong; Zhao, Bao; Zhang, Huisheng; Yang, Zhongqin
2015-08-12
Electronic and topological behaviors of Sb(111) monolayers decorated with H and certain magnetic atoms are investigated by using ab initio methods. The drastic exchange field induced by the magnetic atoms, together with strong spin-orbit coupling (SOC) of Sb atoms, generates one new category of valley polarized topological insulators, called quantum spin-quantum anomalous Hall (QSQAH) insulators in the monolayer, with a band gap up to 53 meV. The strong SOC is closely related to Sb px and py orbitals, instead of pz orbitals in usual two-dimensional (2D) materials. Topological transitions from quantum anomalous Hall states to QSQAH states and then to time-reversal-symmetry-broken quantum spin Hall states are achieved by tuning the SOC strength. The behind mechanism is revealed. Our work is helpful for future valleytronic and spintronic applications in 2D materials.
Quantum spin Hall effect in nanostructures based on cadmium fluoride
Bagraev, N. T.; Guimbitskaya, O. N.; Klyachkin, L. E.; Koudryavtsev, A. A.; Malyarenko, A. M.; Romanov, V. V.; Ryskin, A. I.; Shcheulin, A. S.
2010-10-15
Tunneling current-voltage (I-V) characteristics and temperature dependences of static magnetic susceptibility and specific heat of the CdB{sub x}F{sub 2-x}/p-CdF{sub 2}-QW/CdB{sub x}F{sub 2-x} planar sandwich structures formed on the surface of an n-CdF{sub 2} crystal have been studied in order to identify superconducting properties of the CdB{sub x}F{sub 2-x} {delta} barriers confining the p-type CdF{sub 2} ultranarrow quantum well. Comparative analysis of current-voltage (I-V) characteristics and conductance-voltage dependences (measured at the temperatures, respectively, below and above the critical temperature of superconducting transition) indicates that there is an interrelation between quantization of supercurrent and dimensional quantization of holes in the p-CdF{sub 2} ultranarrow quantum well. It is noteworthy that detection of the Josephson peak of current in each hole subband is accompanied by the appearance of the spectrum of the multiple Andreev reflection (MAR). A high degree of spin polarization of holes in the edge channels along the perimeter of the p-CdF{sub 2} ultranarrow quantum well appears as a result of MAR and makes it possible to identify the quantum spin Hall effect I-V characteristics; this effect becomes pronounced in the case of detection of nonzero conductance at the zero voltage applied to the vertical gate in the Hall geometry of the experiment. Within the energy range of superconducting gap, the I-V characteristics of the spin transistor and quantum spin Hall effect are controlled by the MAR spectrum appearing as the voltage applied to the vertical gate is varied. Beyond the range of the superconducting gap, the observed I-V characteristic of the quantum spin Hall effect is represented by a quantum conductance staircase with a height of the steps equal to e{sub 2}/h; this height is interrelated with the Aharonov-Casher oscillations of longitudinal and depends on the voltage applied to the vertical gate.
Hall effect in quantum critical charge-cluster glass
Bozovic, Ivan; Wu, Jie; Bollinger, Anthony T.; Sun, Yujie
2016-04-04
Upon doping, cuprates undergo a quantum phase transition from an insulator to a d-wave superconductor. The nature of this transition and of the insulating state is vividly debated. Here, we study the Hall effect in La2-xSrxCuO4 (LSCO) samples doped near the quantum critical point at x ≈ 0.06. Dramatic fluctuations in the Hall resistance appear below TCG ≈ 1.5 K and increase as the sample is cooled down further, signaling quantum critical behavior. We explore the doping dependence of this effect in detail, by studying a combinatorial LSCO library in which the Sr content is varied in extremely fine steps,more » Δx ≈ 0.00008. Furthermore, we observe that quantum charge fluctuations wash out when superconductivity emerges but can be restored when the latter is suppressed by applying a magnetic field, showing that the two instabilities compete for the ground state.« less
Application of the quantum Hall effect to resistance metrology
NASA Astrophysics Data System (ADS)
Poirier, Wilfrid; Schopfer, Félicien; Guignard, Jérémie; Thévenot, Olivier; Gournay, Pierre
2011-05-01
The quantum Hall effect (QHE) discovery has revolutionized metrology by providing with a representation of the unit of resistance, R, that can be reproduced within a relative uncertainty of one part in 10 9 and is theoretically only linked to Planck's constant h and the electron charge e. This breakthrough also results from the development of resistance comparison bridges using cryogenic current comparator (CCC). The QHE experimental know-how now allows the realization of perfectly quantized Quantum Hall Array Resistance Standards (QHARS) by combining a large number of single Hall bars. In the context of an evolution of the Système International (SI) of units by fixing some fundamental constants of physics, the determination of the von Klitzing constant R through the use of the so-called Thompson-Lampard calculable capacitor and the realization of refined universality tests of the QHE are of prime importance. Finally, the fascinating graphene material might be a new turning point in resistance metrology.
Function principle of a relaxation oscillator based on a bistable quantum Hall device
NASA Astrophysics Data System (ADS)
Nachtwei, G.; Kalugin, N. G.; Saǧol, B. E.; Stellmach, Ch.; Hein, G.
2003-03-01
We present a simple relaxation oscillator based on a quantum Hall device with Corbino geometry near the breakdown of the quantum Hall effect. In the hysteresis region of the breakdown, the quantum Hall device exhibits bistable behavior. If a resistance is connected in series and a capacitor in parallel to the quantum Hall device, the bistable switching leads to subsequent charging and discharging of the capacitor, detectable as relaxation oscillations. We explain the observed oscillations by solving Kirchhoff's equations and obtain a good quantitative description of the experiment. From this, we deduce some dynamical parameters of the Corbino device and discuss the performance limits of the oscillator.
NASA Astrophysics Data System (ADS)
Gu, Yingfei; Lee, Ching Hua; Wen, Xueda; Cho, Gil Young; Ryu, Shinsei; Qi, Xiao-Liang
2016-09-01
In this paper, we study (2 +1 ) -dimensional quantum anomalous Hall states, i.e., band insulators with quantized Hall conductance, using exact holographic mapping. Exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in (3 +1 ) -dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a (3 +1 ) -dimensional topological insulator. The dual description enables a characterization of topological properties of a system by the quantum entanglement between degrees of freedom at different length scales.
Superconducting analogue of the parafermion fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Vaezi, Abolhassan
2014-03-01
Read and Rezayi Zk parafermion wavefunctions describe ν = 2 + k /(kM + 2) fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this talk, we discuss the ν = 2 / k FQH-superconductor heterostructure and through analytical and numerical calculations we argue that it can yield the superconducting analogue of the Zk parafermion FQH state. The resulting topological state has a gapless chiral edge state with Zk parafermion conformal field theory description. For instance, we find that a ν = 2 / 3 FQH in proximity to a superconductor produces a Z3 parafermion superconducting state. This state can host Fibonacci anyons capable of performing universal quantum computation through braiding operations. We finally discuss our experimental proposal for realizing parafermion superconductors. Reference: arXiv:1307.8069
Quantum Hall physics with cold atoms in cylindrical optical lattices
NASA Astrophysics Data System (ADS)
Łåcki, Mateusz; Pichler, Hannes; Sterdyniak, Antoine; Lyras, Andreas; Lembessis, Vassilis E.; Al-Dossary, Omar; Budich, Jan Carl; Zoller, Peter
2016-01-01
We propose and study various realizations of a Hofstadter-Hubbard model on a cylinder geometry with fermionic cold atoms in optical lattices. The cylindrical optical lattice is created by copropagating Laguerre-Gauss beams, i.e., light beams carrying orbital angular momentum. By strong focusing of the light beams we create a real-space optical lattice in the form of rings, which are offset in energy. A second set of Laguerre-Gauss beams then induces a Raman-hopping between these rings, imprinting phases corresponding to a synthetic magnetic field (artificial gauge field). In addition, by rotating the lattice potential, we achieve a slowly varying flux through the hole of the cylinder, which allows us to probe the Hall response of the system as a realization of Laughlin's thought experiment. We study how in the presence of interactions fractional quantum Hall physics could be observed in this setup.
Interlayer tunneling in double-layer quantum hall pseudoferromagnets.
Balents, L; Radzihovsky, L
2001-02-26
We show that the interlayer tunneling I-V in double-layer quantum Hall states displays a rich behavior which depends on the relative magnitude of sample size, voltage length scale, current screening, disorder, and thermal lengths. For weak tunneling, we predict a negative differential conductance of a power-law shape crossing over to a sharp zero-bias peak. An in-plane magnetic field splits this zero-bias peak, leading instead to a "derivative" feature at V(B)(B(parallel)) = 2 pi Planck's over 2 pi upsilon B(parallel)d/e phi(0), which gives a direct measurement of the dispersion of the Goldstone mode corresponding to the spontaneous symmetry breaking of the double-layer Hall state. PMID:11290258
Tunneling at νT=1 in quantum Hall bilayers
NASA Astrophysics Data System (ADS)
Nandi, D.; Khaire, T.; Finck, A. D. K.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2013-10-01
Interlayer tunneling measurements in the strongly correlated bilayer quantized Hall phase at νT=1 are reported. The maximum, or critical, current for tunneling at νT=1 is shown to be a well-defined global property of the coherent phase, insensitive to extrinsic circuit effects and the precise configuration used to measure it, but also exhibiting a surprising scaling behavior with temperature. Comparisons between the experimentally observed tunneling characteristics and a recent theory are favorable at high temperatures, but not at low temperatures where the tunneling closely resembles the dc Josephson effect. The zero-bias tunneling resistance becomes extremely small at low temperatures, vastly less than that observed at zero magnetic field, but nonetheless remains finite. The temperature dependence of this tunneling resistance is similar to that of the ordinary in-plane resistivity of the quantum Hall phase.
Lin, P.V.; Camino, F.; Goldman, V.J.
2009-12-01
We report experiments in a large, 2.5 {mu}m diameter Fabry-Perot quantum Hall interferometer with two tunneling constrictions. Interference fringes are observed as conductance oscillations as a function of applied magnetic field (the Aharonov-Bohm flux through the electron island) or a global backgate voltage (electronic charge in the island). Depletion is such that in the fractional quantum Hall regime, filling 1/3 current-carrying chiral edge channels pass through constrictions when the island filling is 2/5. The interferometer device is calibrated with fermionic electrons in the integer quantum Hall regime. In the fractional regime, we observe magnetic flux and charge periods 5h/e and 2e, respectively, corresponding to creation of ten e/5 Laughlin quasiparticles in the island. These results agree with our prior report of the superperiods in a much smaller interferometer device. The observed experimental periods are interpreted as imposed by anyonic statistical interaction of fractionally charged quasiparticles.
Anyons and the quantum Hall effect-A pedagogical review
Stern, Ady
2008-01-15
The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined 'anyons', may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to non-abelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation.
Kondo effect in the helical edge liquid of the quantum spin Hall state.
Maciejko, Joseph; Liu, Chaoxing; Oreg, Yuval; Qi, Xiao-Liang; Wu, Congjun; Zhang, Shou-Cheng
2009-06-26
Following the recent observation of the quantum spin Hall (QSH) effect in HgTe quantum wells, an important issue is to understand the effect of impurities on transport in the QSH regime. Using linear response and renormalization group methods, we calculate the edge conductance of a QSH insulator as a function of temperature in the presence of a magnetic impurity. At high temperatures, Kondo and/or two-particle scattering give rise to a logarithmic temperature dependence. At low temperatures, for weak Coulomb interactions in the edge liquid, the conductance is restored to unitarity with unusual power laws characteristic of a "local helical liquid," while for strong interactions, transport proceeds by weak tunneling through the impurity where only half an electron charge is transferred in each tunneling event. PMID:19659109
Quantum Hall effect in a gate-controlled p-n junction of graphene.
Williams, J R; Dicarlo, L; Marcus, C M
2007-08-01
The unique band structure of graphene allows reconfigurable electric-field control of carrier type and density, making graphene an ideal candidate for bipolar nanoelectronics. We report the realization of a single-layer graphene p-n junction in which carrier type and density in two adjacent regions are locally controlled by electrostatic gating. Transport measurements in the quantum Hall regime reveal new plateaus of two-terminal conductance across the junction at 1 and 32 times the quantum of conductance, e(2)/h, consistent with recent theory. Beyond enabling investigations in condensed-matter physics, the demonstrated local-gating technique sets the foundation for a future graphene-based bipolar technology.
Observation of interaction-induced modulations of a quantum Hall liquid's area
Sivan, I.; Choi, H. K.; Park, Jinhong; Rosenblatt, A.; Gefen, Yuval; Mahalu, D.; Umansky, V.
2016-01-01
Studies of electronic interferometers, based on edge-channel transport in the quantum Hall effect regime, have been stimulated by the search for evidence of abelian and non-abelian anyonic statistics of fractional charges. In particular, the electronic Fabry–Pérot interferometer has been found to be Coulomb dominated, thus masking coherent Aharonov–Bohm interference patterns: the flux trapped within the interferometer remains unchanged as the applied magnetic field is varied, barring unobservable modulations of the interference area. Here we report on conductance measurements indicative of the interferometer's area ‘breathing' with the variation of the magnetic field, associated with observable (a fraction of a flux quantum) variations of the trapped flux. This is the result of partial (controlled) screening of Coulomb interactions. Our results introduce a novel experimental tool for probing anyonic statistics. PMID:27396234
Observation of interaction-induced modulations of a quantum Hall liquid's area
NASA Astrophysics Data System (ADS)
Sivan, I.; Choi, H. K.; Park, Jinhong; Rosenblatt, A.; Gefen, Yuval; Mahalu, D.; Umansky, V.
2016-07-01
Studies of electronic interferometers, based on edge-channel transport in the quantum Hall effect regime, have been stimulated by the search for evidence of abelian and non-abelian anyonic statistics of fractional charges. In particular, the electronic Fabry-Pérot interferometer has been found to be Coulomb dominated, thus masking coherent Aharonov-Bohm interference patterns: the flux trapped within the interferometer remains unchanged as the applied magnetic field is varied, barring unobservable modulations of the interference area. Here we report on conductance measurements indicative of the interferometer's area `breathing' with the variation of the magnetic field, associated with observable (a fraction of a flux quantum) variations of the trapped flux. This is the result of partial (controlled) screening of Coulomb interactions. Our results introduce a novel experimental tool for probing anyonic statistics.
Composite Fermion Theory for Bosonic Quantum Hall States on Lattices
NASA Astrophysics Data System (ADS)
Möller, G.; Cooper, N. R.
2009-09-01
We study the ground states of the Bose-Hubbard model in a uniform magnetic field, motivated by the physics of cold atomic gases on lattices at high vortex density. Mapping the bosons to composite fermions (CF) leads to the prediction of quantum Hall fluids that have no counterpart in the continuum. We construct trial states for these phases and test numerically the predictions of the CF model. We establish the existence of strongly correlated phases beyond those in the continuum limit and provide evidence for a wider scope of the composite fermion approach beyond its application to the lowest Landau level.
Quantum anomalous Hall effect in stable dumbbell stanene
NASA Astrophysics Data System (ADS)
Zhang, Huisheng; Zhang, Jiayong; Zhao, Bao; Zhou, Tong; Yang, Zhongqin
2016-02-01
Topological property of the dumbbell (DB) stanene, more stable than the stanene with a honeycomb lattice, is investigated by using ab initio methods. The magnetic DB stanene demonstrates an exotic quantum anomalous Hall (QAH) effect due to inversion of the Sn spin-up px,y and spin-down pz states. The QAH gap is found to be opened at Γ point rather than the usual K and K' points, beneficial to observe the effect in experiments. When a 3% tensile strain is applied, a large nontrivial gap (˜50 meV) is achieved. Our results provide another lighthouse for realizing QAH effects in two-dimensional systems.
Topological polaritons in a quantum spin Hall cavity
NASA Astrophysics Data System (ADS)
Janot, Alexander; Rosenow, Bernd; Refael, Gil
2016-04-01
We study the topological structure of matter-light excitations, so-called polaritons, in a quantum spin Hall insulator coupled to photonic cavity modes. We identify a topological invariant in the presence of time reversal (TR) symmetry, and demonstrate the existence of a TR-invariant topological phase. We find protected helical edge states with energies below the lower polariton branch and characteristic uncoupled excitonic states, both detectable by optical techniques. Applying a Zeeman field allows us to relate the topological index to the double coverage of the Bloch sphere by the polaritonic pseudospin.
Vortex equations governing the fractional quantum Hall effect
Medina, Luciano
2015-09-15
An existence theory is established for a coupled non-linear elliptic system, known as “vortex equations,” describing the fractional quantum Hall effect in 2-dimensional double-layered electron systems. Via variational methods, we prove the existence and uniqueness of multiple vortices over a doubly periodic domain and the full plane. In the doubly periodic situation, explicit sufficient and necessary conditions are obtained that relate the size of the domain and the vortex numbers. For the full plane case, existence is established for all finite-energy solutions and exponential decay estimates are proved. Quantization phenomena of the magnetic flux are found in both cases.
Topological superconductivity in quantum Hall-superconductor hybrid systems
NASA Astrophysics Data System (ADS)
Zocher, Björn; Rosenow, Bernd
2016-06-01
We develop a scenario to engineer a topological phase with Majorana edge states based on an integer quantum Hall (QH) system proximity coupled to a superconductor (SC). Due to the vortices in the SC order parameter, the SC-QH hybrid system is described by a Bloch problem with ten unpaired momenta, corresponding to the maxima and saddle points of the SC order parameter. For external potentials respecting the symmetry of the vortex lattice, the states with unpaired momenta have degeneracies such that the system always is in a trivial phase. However, an incommensurate potential can lift the degeneracies and drive the system into a topologically nontrivial phase.
Heat diode and engine based on quantum Hall edge states
NASA Astrophysics Data System (ADS)
Sánchez, Rafael; Sothmann, Björn; Jordan, Andrew N.
2015-07-01
We investigate charge and energy transport in a three-terminal quantum Hall conductor. The peculiar properties of chiral propagation along the edges of the sample have important consequences on the response to thermal biases. Based on the separation of charge and heat flows, thermoelectric conversion and heat rectification can be manipulated by tuning the scattering at gate-modulated constrictions. Chiral motion in a magnetic field allows for a different behavior of left- and right-moving carriers giving rise to thermal rectification by redirecting the heat flows. We propose our system both as an efficient heat-to-work converter and as a heat diode.
Global phase diagram of bilayer quantum Hall ferromagnets
NASA Astrophysics Data System (ADS)
Abolfath, Ramin; Radzihovsky, Leo; MacDonald, Allan
2002-03-01
We present a microscopic study of the interlayer spacing d versus in-plane magnetic field B_allel phase diagram for bilayer quantum Hall (QH) pseudo-ferromagnets [1]. In addition to the interlayer charge balanced commensurate and incommensurate states studied previously [2], we nalyze microscopically the corresponding interlayer charge unbalanced canted QH states, predicted in Ref. [3]. We predict a large anomaly in the bilayer capacitance at the canting transition and the formation of dipole stripe domains with periods exceeding 1 micron in the canted state. [1] M. Abolfath et al. cond-mat/0110049. [2] Yang et al. PRL 72, 732 (1994). [3] Leo Radzihovsky PRL 87, 236802 (2001).
Theory of interlayer tunneling in bilayer quantum Hall ferromagnets.
Stern, A; Girvin, S M; MacDonald, A H; Ma, N
2001-02-26
Spielman et al. [Phys. Rev. Lett. 84, 5808 (2000] recently observed a large and sharp Josephson-like zero-bias peak in the tunnel conductance of a bilayer system in a quantum Hall ferromagnet state. We argue that disorder-induced topological defects in the pseudospin order parameter limit the peak size and destroy the predicted Josephson effect. We predict that the peak would be split and shifted by an in-plane magnetic field in a way that maps the dispersion relation of the ferromagnet's Goldstone mode. We also predict resonant structures in the dc I-V characteristic under bias by an ac electric field.
Covariant effective action for a Galilean invariant quantum Hall system
NASA Astrophysics Data System (ADS)
Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.
2016-09-01
We construct effective field theories for gapped quantum Hall systems coupled to background geometries with local Galilean invariance i.e. Bargmann spacetimes. Along with an electromagnetic field, these backgrounds include the effects of curved Galilean spacetimes, including torsion and a gravitational field, allowing us to study charge, energy, stress and mass currents within a unified framework. A shift symmetry specific to single constituent theories constraints the effective action to couple to an effective background gauge field and spin connection that is solved for by a self-consistent equation, providing a manifestly covariant extension of Hoyos and Son's improvement terms to arbitrary order in m.
Spectral Gaps of Quantum Hall Systems with Interactions
NASA Astrophysics Data System (ADS)
Koma, Tohru
2000-04-01
A two-dimensional quantum Hall system without disorder for a wide class of interactions including any two-body interaction with finite range is studied by using the Lieb-Schultz-Mattis method [ Ann. Phys. (N.Y.) 16:407 (1961)]. The model is defined on an infinitely long strip with a fixed, large width, and the Hilbert space is restricted to the lowest ( n max+1) Landau levels with a large integer n max. We prove that, for a noninteger filling ν of the Landau levels, either (i) there is a symmetry breaking at zero temperature or (ii) there is only one infinite-volume ground state with a gapless excitation. We also prove the following two theorems: (a) If a pure infinite-volume ground state has a nonzero excitation gap for a noninteger filling ν, then a translational symmetry breaking occurs at zero temperature. (b) Suppose that there is no non-translationally invariant infinite-volume ground state. Then, if a pure infinite-volume ground state has a nonzero excitation gap, the filling factor ν must be equal to a rational number. Here the ground state is allowed to have a periodic structure which is a consequence of the translational symmetry breaking. We also discuss the relation between our results and the quantized Hall conductance, and phenomenologically explain why odd denominators of filling fractions ν giving the quantized Hall conductance are favored exclusively.
Anomalous Edge Transport in the Quantum Anomalous Hall State
NASA Astrophysics Data System (ADS)
Zhang, Shou-Cheng; Wang, Jing; Lian, Biao; Zhang, Haijun
2014-03-01
We predict by first-principles calculations that thin films of a Cr-doped (Bi,Sb)2Te3 magnetic topological insulator have gapless nonchiral edge states coexisting with the chiral edge state. Such gapless nonchiral states are not immune to backscattering, which would explain dissipative transport in the quantum anomalous Hall (QAH) state observed in this system experimentally. Here, we study the edge transport with both chiral and nonchiral states by the Landauer-Buttiker formalism and find that the longitudinal resistance is nonzero, whereas Hall resistance is quantized to h/e2. In particular, the longitudinal resistance can be greatly reduced by adding an extra floating probe even if it is not used, while the Hall resistance remains at the quantized value. We propose several transport experiments to detect the dissipative nonchiral edge channels. These results will facilitate the realization of pure dissipationless transport of QAH states in magnetic topological insulators. This work is supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract No. DE-AC02-76SF00515.
Edge physics of the quantum spin Hall insulator from a quantum dot excited by optical absorption.
Vasseur, Romain; Moore, Joel E
2014-04-11
The gapless edge modes of the quantum spin Hall insulator form a helical liquid in which the direction of motion along the edge is determined by the spin orientation of the electrons. In order to probe the Luttinger liquid physics of these edge states and their interaction with a magnetic (Kondo) impurity, we consider a setup where the helical liquid is tunnel coupled to a semiconductor quantum dot that is excited by optical absorption, thereby inducing an effective quantum quench of the tunneling. At low energy, the absorption spectrum is dominated by a power-law singularity. The corresponding exponent is directly related to the interaction strength (Luttinger parameter) and can be computed exactly using boundary conformal field theory thanks to the unique nature of the quantum spin Hall edge.
Matrix model for non-Abelian quantum Hall states
NASA Astrophysics Data System (ADS)
Dorey, Nick; Tong, David; Turner, Carl
2016-08-01
We propose a matrix quantum mechanics for a class of non-Abelian quantum Hall states. The model describes electrons which carry an internal SU(p ) spin. The ground states of the matrix model include spin-singlet generalizations of the Moore-Read and Read-Rezayi states and, in general, lie in a class previously introduced by Blok and Wen. The effective action for these states is a U(p ) Chern-Simons theory. We show how the matrix model can be derived from quantization of the vortices in this Chern-Simons theory and how the matrix model ground states can be reconstructed as correlation functions in the boundary WZW model.
Orbital Magnetization of Quantum Spin Hall Insulator Nanoparticles.
Potasz, P; Fernández-Rossier, J
2015-09-01
Both spin and orbital degrees of freedom contribute to the magnetic moment of isolated atoms. However, when inserted in crystals, atomic orbital moments are quenched because of the lack of rotational symmetry that protects them when isolated. Thus, the dominant contribution to the magnetization of magnetic materials comes from electronic spin. Here we show that nanoislands of quantum spin Hall insulators can host robust orbital edge magnetism whenever their highest occupied Kramers doublet is singly occupied, upgrading the spin edge current into a charge current. The resulting orbital magnetization scales linearly with size, outweighing the spin contribution for islands of a few nm in size. This linear scaling is specific of the Dirac edge states and very different from Schrodinger electrons in quantum rings. By modeling Bi(111) flakes, whose edge states have been recently observed, we show that orbital magnetization is robust with respect to disorder, thermal agitation, shape of the island, and crystallographic direction of the edges, reflecting its topological protection.
Matrix method analysis of quantum Hall effect device connections
NASA Astrophysics Data System (ADS)
Ortolano, M.; Callegaro, L.
2012-02-01
The modelling of electrical connections of single, or several, multiterminal quantum Hall effect (QHE) devices is relevant for electrical metrology: it is known, in fact, that certain particular connections allow (i) the realization of multiples or fractions of the quantized resistance, or (ii) the rejection of stray impedances, so that the configuration maintains the status of quantum standard. Ricketts-Kemeny and Delahaye equivalent circuits are known to be accurate models of the QHE: however, the numerical or analytical solution of electrical networks including these equivalent circuits can be difficult. In this paper, we introduce a method of analysis based on the representation of a QHE device by means of the indefinite admittance matrix: external connections are then represented with another matrix, easily written by inspection. Some examples, including the solution of double- and triple-series connections, are shown.
Quantum Hall effect in a system with an electron reservoir
NASA Astrophysics Data System (ADS)
Dorozhkin, S. I.
2016-04-01
Precise measurements of the magnetic-field and gate-voltage dependences of the capacitance of a field-effect transistor with an electron system in a wide GaAs quantum well have been carried out. It has been found that the capacitance minima caused by the gaps in the Landau spectrum of the electron system become anomalously wide when two size-quantization subbands are occupied. The effect is explained by retention of the chemical potential in the gap between the Landau levels of one of the subbands owing to redistribution of electrons between the subbands under a change in the magnetic field. The calculation taking into account this redistribution has been performed in a model of the electron system formed by two two-dimensional electron layers. The calculation results describe both the wide capacitance features and the observed disappearance of certain quantum Hall effect states.
Fractionally charged skyrmions in fractional quantum Hall effect
Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; Pinczuk, A.; Jain, J. K.
2015-11-26
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeemanmore » energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.« less
Quantum anomalous Hall effect in magnetic topological insulators
Wang, Jing; Lian, Biao; Zhang, Shou -Cheng
2015-08-25
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimensions (2D) and three-dimensions (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. We presentmore » the phase diagram in thin films of a magnetic topological insulator and review the basic mechanism of ferromagnetic order in magnetically doped topological insulators. We also review the recent experimental observation of the QAH effect. Furthermore, we discuss more recent theoretical work on the coexistence of the helical and chiral edge states, multi-channel chiral edge states, the theory of the plateau transition, and the thickness dependence in the QAH effect.« less
Quantum anomalous Hall effect in magnetic topological insulators
Wang, Jing; Lian, Biao; Zhang, Shou -Cheng
2015-08-25
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimensions (2D) and three-dimensions (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. We present the phase diagram in thin films of a magnetic topological insulator and review the basic mechanism of ferromagnetic order in magnetically doped topological insulators. We also review the recent experimental observation of the QAH effect. Furthermore, we discuss more recent theoretical work on the coexistence of the helical and chiral edge states, multi-channel chiral edge states, the theory of the plateau transition, and the thickness dependence in the QAH effect.
Chiral ladders and the edges of quantum Hall insulators
NASA Astrophysics Data System (ADS)
Hügel, Dario; Paredes, Belén
2014-02-01
The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as readily realizable bridges between one-dimensional spin-orbit (time-reversal) topological insulators and two-dimensional quantum Hall insulators. We reveal three instances of their promising potential: (i) they realize spin-orbit coupling, with the left-right leg degree of freedom playing the role of an effective spin, (ii) their energy bands and eigenstates exactly reproduce the topological chiral edge modes of two-dimensional Chern insulators, and (iii) they can be tailored to realize a topological phase transition from a trivial to a topological insulating phase. We propose realistic schemes to observe the chiral and topological properties of ladder systems with current optical lattice-based experiments. Our findings open a door to the exploration of the physics of the edges of quantum Hall insulators and to the realization of spin-orbit coupling and topological superfluid phases with ultracold atomic gases.
Quantum Anomalous Hall Effects and Topological Phase Transitions in Silicene
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2013-03-01
Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which is experimentally manufactured this year. The low energy theory is described by Dirac electrons, but they are massive due to a relatively large spin-orbit interaction. I will explain the following properties of silicene: 1) The band structure is controllable by applying an electric field. Silicene undergoes a phase transition from a topological insulator to a band insulator by applying external electric field. 2) The topological phase transition can be detected experimentally by way of diamagnetism. 3) There is a novel circular dichroism and spinvalley selection rules by way of photon absorption. 4) Silicene shows a quantum anomalous Hall effects when ferromagnet is attached onto silicone. 5) Silicene shows a photo-induced quantum Hall effects when we apply strong laser onto silicene. 6) Single Dirac cone state emerges when we apply photo-irradiation and electric field, where the gap is open at the K point and closed at the K' point.
NASA Astrophysics Data System (ADS)
Ji, Wei-xiao; Zhang, Chang-wen; Ding, Meng; Zhang, Bao-min; Li, Ping; Li, Feng; Ren, Miao-juan; Wang, Pei-ji; Zhang, Run-wu; Hu, Shu-jun; Yan, Shi-shen
2016-08-01
Bismuth (Bi) has attracted a great deal of attention for its strongest spin–orbit coupling (SOC) strength among main group elements. Although quantum anomalous Hall (QAH) state is predicted in half-hydrogenated Bi honeycomb monolayers Bi2H, the experimental results are still missing. Halogen atoms (X = F, Cl and Br) were also frequently used as modifications, but Bi2X films show a frustrating metallic character that masks the QAH effects. Here, first-principle calculations are performed to predict the full-cyanided bismuthene (Bi2(CN)2) as 2D topological insulator supporting quantum spin Hall state with a record large gap up to 1.10 eV, and more importantly, half-cyanogen saturated bismuthene (Bi2(CN)) as a Chern insulator supporting a valley-polarized QAH state, with a Curie temperature to be 164 K, as well as a large gap reaching 0.348 eV which could be further tuned by bi-axial strain and SOC strength. Our findings provide an appropriate and flexible material family candidate for spintronic and valleytronic devices.
NASA Astrophysics Data System (ADS)
Ji, Wei-xiao; Zhang, Chang-wen; Ding, Meng; Zhang, Bao-min; Li, Ping; Li, Feng; Ren, Miao-juan; Wang, Pei-ji; Zhang, Run-wu; Hu, Shu-jun; Yan, Shi-shen
2016-08-01
Bismuth (Bi) has attracted a great deal of attention for its strongest spin-orbit coupling (SOC) strength among main group elements. Although quantum anomalous Hall (QAH) state is predicted in half-hydrogenated Bi honeycomb monolayers Bi2H, the experimental results are still missing. Halogen atoms (X = F, Cl and Br) were also frequently used as modifications, but Bi2X films show a frustrating metallic character that masks the QAH effects. Here, first-principle calculations are performed to predict the full-cyanided bismuthene (Bi2(CN)2) as 2D topological insulator supporting quantum spin Hall state with a record large gap up to 1.10 eV, and more importantly, half-cyanogen saturated bismuthene (Bi2(CN)) as a Chern insulator supporting a valley-polarized QAH state, with a Curie temperature to be 164 K, as well as a large gap reaching 0.348 eV which could be further tuned by bi-axial strain and SOC strength. Our findings provide an appropriate and flexible material family candidate for spintronic and valleytronic devices.
Correlation effects in quantum spin-Hall insulators: a quantum Monte Carlo study.
Hohenadler, M; Lang, T C; Assaad, F F
2011-03-11
We consider the Kane-Mele model supplemented by a Hubbard U term. The phase diagram is mapped out using projective auxiliary field quantum Monte Carlo simulations. The quantum spin liquid of the Hubbard model is robust against weak spin-orbit interaction, and is not adiabatically connected to the spin-Hall insulating state. Beyond a critical value of U>U(c) both states are unstable toward magnetic ordering. In the quantum spin-Hall state we study the spin, charge, and single-particle dynamics of the helical Luttinger liquid by retaining the Hubbard interaction only on a ribbon edge. The Hubbard interaction greatly suppresses charge currents along the edge and promotes edge magnetism but leaves the single-particle signatures of the helical liquid intact.
Edge mode velocities in the quantum Hall effect from a dc measurement
NASA Astrophysics Data System (ADS)
Zucker, Philip; Feldman, D. E.
Because of the bulk gap, low energy physics in the quantum Hall effect is confined to the edges of the 2D electron liquid. The velocities of edge modes are key parameters of edge physics. They were determined in several quantum Hall systems from time-resolved measurements and high-frequency ac transport. We propose a way to extract edge velocities from dc transport in a point contact geometry defined by narrow gates. The width of the gates assumes two different sizes at small and large distances from the point contact. The Coulomb interaction across the gates depends on the gate width and affects the conductance of the contact. The conductance exhibits two different temperature dependencies at high and low temperatures. The transition between the two regimes is determined by the edge velocity. An interesting feature of the low-temperature I - V curve is current oscillations as a function of the voltage. The oscillations emerge due to charge reflection from the interface of the regions defined by the narrow and wide sections of the gates. This work is available at arXiv:1510.01725 This work was supported by the NSF under Grant No. DMR-1205715.
Scalable quantum memory in the ultrastrong coupling regime.
Kyaw, T H; Felicetti, S; Romero, G; Solano, E; Kwek, L-C
2015-01-01
Circuit quantum electrodynamics, consisting of superconducting artificial atoms coupled to on-chip resonators, represents a prime candidate to implement the scalable quantum computing architecture because of the presence of good tunability and controllability. Furthermore, recent advances have pushed the technology towards the ultrastrong coupling regime of light-matter interaction, where the qubit-resonator coupling strength reaches a considerable fraction of the resonator frequency. Here, we propose a qubit-resonator system operating in that regime, as a quantum memory device and study the storage and retrieval of quantum information in and from the Z2 parity-protected quantum memory, within experimentally feasible schemes. We are also convinced that our proposal might pave a way to realize a scalable quantum random-access memory due to its fast storage and readout performances. PMID:25727251
Scalable quantum memory in the ultrastrong coupling regime.
Kyaw, T H; Felicetti, S; Romero, G; Solano, E; Kwek, L-C
2015-03-02
Circuit quantum electrodynamics, consisting of superconducting artificial atoms coupled to on-chip resonators, represents a prime candidate to implement the scalable quantum computing architecture because of the presence of good tunability and controllability. Furthermore, recent advances have pushed the technology towards the ultrastrong coupling regime of light-matter interaction, where the qubit-resonator coupling strength reaches a considerable fraction of the resonator frequency. Here, we propose a qubit-resonator system operating in that regime, as a quantum memory device and study the storage and retrieval of quantum information in and from the Z2 parity-protected quantum memory, within experimentally feasible schemes. We are also convinced that our proposal might pave a way to realize a scalable quantum random-access memory due to its fast storage and readout performances.
Nonlinear wave propagation and reconnection at magnetic X-points in the Hall MHD regime
NASA Astrophysics Data System (ADS)
Threlfall, J.; Parnell, C. E.; De Moortel, I.; McClements, K. G.; Arber, T. D.
2012-08-01
Context. The highly dynamical, complex nature of the solar atmosphere naturally implies the presence of waves in a topologically varied magnetic environment. Here, the interaction of waves with topological features such as null points is inevitable and potentially important for energetics. The low resistivity of the solar coronal plasma implies that non-magnetohydrodynamic (MHD) effects should be considered in studies of magnetic energy release in this environment. Aims: This paper investigates the role of the Hall term in the propagation and dissipation of waves, their interaction with 2D magnetic X-points and the nature of the resulting reconnection. Methods: A Lagrangian remap shock-capturing code (Lare2d) was used to study the evolution of an initial fast magnetoacoustic wave annulus for a range of values of the ion skin depth (δi) in resistive Hall MHD. A magnetic null-point finding algorithm was also used to locate and track the evolution of the multiple null-points that are formed in the system. Results: Depending on the ratio of ion skin depth to system size, our model demonstrates that Hall effects can play a key role in the wave-null interaction. In particular, the initial fast-wave pulse now consists of whistler and ion-cyclotron components; the dispersive nature of the whistler wave leads to (i) earlier interaction with the null; (ii) the creation of multiple additional, transient nulls and, hence, an increased number of energy release sites. In the Hall regime, the relevant timescales (such as the onset of reconnection and the period of the oscillatory relaxation) of the system are reduced significantly, and the reconnection rate is enhanced.
Terahertz Quantum Plasmonics of Nanoslot Antennas in Nonlinear Regime.
Kim, Joon-Yeon; Kang, Bong Joo; Park, Joohyun; Bahk, Young-Mi; Kim, Won Tae; Rhie, Jiyeah; Jeon, Hyeongtag; Rotermund, Fabian; Kim, Dai-Sik
2015-10-14
Quantum tunneling in plasmonic nanostructures has presented an interesting aspect of incorporating quantum mechanics into classical optics. However, the study has been limited to the subnanometer gap regime. Here, we newly extend quantum plasmonics to gap widths well over 1 nm by taking advantage of the low-frequency terahertz regime. Enhanced electric fields of up to 5 V/nm induce tunneling of electrons in different arrays of ring-shaped nanoslot antennas of gap widths from 1.5 to 10 nm, which lead to a significant nonlinear transmission decrease. These observations are consistent with theoretical calculations considering terahertz-funneling-induced electron tunneling across the gap.
Terahertz Quantum Plasmonics of Nanoslot Antennas in Nonlinear Regime.
Kim, Joon-Yeon; Kang, Bong Joo; Park, Joohyun; Bahk, Young-Mi; Kim, Won Tae; Rhie, Jiyeah; Jeon, Hyeongtag; Rotermund, Fabian; Kim, Dai-Sik
2015-10-14
Quantum tunneling in plasmonic nanostructures has presented an interesting aspect of incorporating quantum mechanics into classical optics. However, the study has been limited to the subnanometer gap regime. Here, we newly extend quantum plasmonics to gap widths well over 1 nm by taking advantage of the low-frequency terahertz regime. Enhanced electric fields of up to 5 V/nm induce tunneling of electrons in different arrays of ring-shaped nanoslot antennas of gap widths from 1.5 to 10 nm, which lead to a significant nonlinear transmission decrease. These observations are consistent with theoretical calculations considering terahertz-funneling-induced electron tunneling across the gap. PMID:26372787
High Resolution Spectroscopy of the Quantum Hall Liquid
NASA Astrophysics Data System (ADS)
Dial, Oliver
2008-03-01
We present precise and unprecedentedly high resolution spectra of the tunneling density of states (TDOS) of a cold two dimensional electron system (2DES) in GaAs over an energy range from 15 meV above to 15 meV below the Fermi surface. The results provide the first direct measurements of the width of the single-particle exchange gap and lifetimes in the quantum Hall system. At higher energies, we show the first observations of exchange-induced spin-splittings in fully filled or unfilled Landau levels not at the Fermi energy. The results demonstrate a counter-intuitive fact: the high energy spectrum reflects correlations that only appear at very low temperatures. For instance, upon raising the temperature from 100 mK (0.01 meV) to 1 K (0.1 meV) changes are seen in the spectrum at 10 meV away from the Fermi energy. Along with measurements of exchange splittings and lifetimes, we observe an unpredicted new structure appearing only at high magnetic fields and low temperatures that appears to be a long lived quasi-particle. The results are made possible by a novel technique, time domain capacitance spectroscopy. It allows us to measure the TDOS of a 2DES with resolution only limited by temperature, even at large tunneling energies. In TDCS, sharp voltage pulses disequilibrate a 2DES from a nearby metallic contact inducing a tunnel current perpendicular to the plane of the 2DES. We detect this current by monitoring the image charge of the tunneling electrons on a distant electrode. No ohmic contact to the 2DES is required. The technique works even when the 2DES is empty or has vanishing in-plane conductivity, as frequently occurs in the quantum Hall effect. Importantly, we can eliminate the effects of ohmic heating in the experiment by using short duty cycle pulses, with currents flowing only 0.01% of the time. The obtained spectra reveal the beautiful and difficult to reach structure present far from the Fermi surface in the quantum Hall system.
Quantum Hall states stabilized in semi-magnetic bilayers of topological insulators
Yoshimi, R.; Yasuda, K.; Tsukazaki, A.; Takahashi, K. S.; Nagaosa, N.; Kawasaki, M.; Tokura, Y.
2015-01-01
By breaking the time-reversal symmetry in three-dimensional topological insulators with the introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect or quantum Hall effect, when the chemical potential locates inside the gap. Further breaking of inversion symmetry is possible by employing magnetic topological insulator heterostructures that host non-degenerate top and bottom surface states. Here we demonstrate the tailored-material approach for the realization of robust quantum Hall states in the bilayer system, in which the cooperative or cancelling combination of the anomalous and ordinary Hall responses from the respective magnetic and non-magnetic layers is exemplified. The appearance of quantum Hall states at filling factor 0 and +1 can be understood by the relationship of energy band diagrams for the two independent surface states. The designable heterostructures of magnetic topological insulator may explore a new arena for intriguing topological transport and functionality. PMID:26497065
Scaling in the quantum Hall regime of graphene Corbino devices
Peters, Eva C.; Burghard, Marko; Giesbers, A. J. M.; Kern, Klaus
2014-05-19
The scaling behavior of graphene devices in Corbino geometry was investigated through temperature dependent conductivity measurements under magnetic field. Evaluation of the Landau level width as a function of temperature yielded a relatively low temperature exponent of κ = 0.16 ± 0.05. Furthermore, an unusually large value close to 7.6 ± 0.9 was found for the universal scaling constant γ, while the determined inelastic scattering exponent of p = 2 is consistent with established scattering mechanisms in graphene. The deviation of the scaling parameters from values characteristic of conventional two-dimensional electron gases is attributed to an inhomogeneous charge carrier distribution in the Corbino devices. Direct evidence for the presence of the latter could be gained by spatially resolved photocurrent microscopy away from the charge neutrality point of the devices.
Partial heating between counter propagating quantum Hall edge channels
NASA Astrophysics Data System (ADS)
Washio, Kazuhisa; Nakazawa, Ryo; Hashisaka, Masayuki; Muraki, Koji; Fujisawa, Toshimasa
2014-03-01
In contrast to clear unidirectional charge flow in quantum Hall edge channels, heat transport and equilibration remain veiled. Most of the previous works were concentrated on heating between co-propagating edge channels, where co-propagating charge and spin modes are formed by the Coulomb interaction. Here, we investigate heating between counter propagating edge channels separated by a narrow surface gate of the width 0.1 μm, where the plasmon coupling forms counter-propagating dragging modes. One edge channel is directly heated up by a quantum point contact at its half transmission, and energy spectrum of the other edge channel is evaluated by quantum dot thermometry. We observed partial heating in the spectrum, where a small fraction (1-5 percent) of electrons is highly excited over the original Fermi distribution, for an interaction length of 5-10 μm in the coupled channels. This can be understood by considering weak scattering process between the channels. The flow of this non-equilibrium distribution will be discussed with different configurations of heating and detecting channels in terms of the chirality and the dragging modes. JSPS KAKENHI Grant Numbers 21000004, 24009291.
Topological superconductivity, topological confinement, and the vortex quantum Hall effect
Diamantini, M. Cristina; Trugenberger, Carlo A.
2011-09-01
Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors, and topological confinement. In conventional superconductivity, because of spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order, and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the Stueckelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.
Superconducting Analogue of the Parafermion Fractional Quantum Hall States
NASA Astrophysics Data System (ADS)
Vaezi, Abolhassan
2014-07-01
Read-Rezayi Zk parafermion wave functions describe ν =2+(k/kM+2) fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this paper, we study the ν=2/k FQH-superconductor heterostructure and find the superconducting analogue of the Zk parafermion FQH state. Our main tool is the mapping of the FQH into coupled one-dimensional chains, each with a pair of counterpropagating modes. We show that by inducing intrachain pairing and charge preserving backscattering with identical couplings, the one-dimensional chains flow into gapless Zk parafermions when k<4. By studying the effect of interchain coupling, we show that every parafermion mode becomes massive except for the two outermost ones. Thus, we achieve a fractional topological superconductor whose chiral edge state is described by a Zk parafermion conformal field theory. For instance, we find that a ν=2/3 FQH in proximity to a superconductor produces a Z3 parafermion superconducting state. This state is topologically indistinguishable from the non-Abelian part of the ν=12/5 Read-Rezayi state. Both of these systems can host Fibonacci anyons capable of performing universal quantum computation through braiding operations.
Manipulating edge transport in quantum anomalous Hall insulators
NASA Astrophysics Data System (ADS)
Kandala, Abhinav
The quantum anomalous Hall (QAH) effect provides a path to obtain dissipation-less, one-dimensional (1D) edge states at zero magnetic field. It's recent experimental realization in magnetic topological insulator thin films lies at the overlap of several areas of condensed matter physics: dilute magnetic semiconductors, low dimensional electron transport and topologically non-trivial material systems. In this talk, we demonstrate how careful compositional and electrical tuning of epitaxial films of Cr-doped (Bi,Sb)2Te3 enables access to a robust zero-field quantized Hall effect, despite sample roughness and low carrier mobility. In samples that show near-dissipation-less transport, we manipulate the intermixing between edge states and dissipative channels via a tilted-field crossover from ballistic 1D edge transport to diffusive transport. This crossover manifests in a gate-tunable giant anisotropic magneto-resistance effect that we use as a quantitative probe of dissipation in our systems. Finally, we discuss experiments with mesoscopic channels of QAH insulator thin films, and discuss the effect of their modified magnetic anisotropy on edge transport. This work was carried out in collaboration with A. Richardella, C-X Liu, M. Liu, W. Wang, N. P. Ong, and N. Samarth. Funded by ARO/MURI, DARPA and ONR.
Critical Supercurrents and Self-Organization in Quantum Hall Bilayers
NASA Astrophysics Data System (ADS)
Eastham, P. R.; Cooper, N. R.; Lee, D. K. K.
2010-12-01
We present a theory of interlayer tunneling in a disordered quantum Hall bilayer at total filling factor one, allowing for the effect of static vortices. In agreement with recent experiments [Phys. Rev. BPRBMDO1098-0121 80, 165120 (2009)10.1103/PhysRevB.80.165120; Phys. Rev. B PRBMDO1098-012178, 075302 (2008)10.1103/PhysRevB.78.075302], we find that the critical current is proportional to the sample area and is comparable in magnitude to observed values. This reflects the formation of a Bean critical state as a result of current injection at the boundary. We predict a crossover to a critical current proportional to the square-root of the area in smaller samples. We also predict a peak in the critical current as the electron density varies at fixed layer separation.
Unconventional spin texture in a noncentrosymmetric quantum spin Hall insulator
NASA Astrophysics Data System (ADS)
Mera Acosta, C.; Babilonia, O.; Abdalla, L.; Fazzio, A.
2016-07-01
We propose that the simultaneous presence of both Rashba and band inversion can lead to a Rashba-like spin splitting formed by two bands with the same in-plane helical spin texture. Because of this unconventional spin texture, the backscattering is forbidden in edge and bulk conductivity channels. We propose a noncentrosymmetric honeycomb-lattice quantum spin Hall (QSH) insulator family formed by the IV, V, and VII elements with this property. The system formed by Bi, Pb, and I atoms is mechanically stable and has both a large Rashba spin splitting of 60 meV and a large nontrivial band gap of 0.14 eV. Since the edge and the bulk states are protected by the time-reversal (TR) symmetry, contrary to what happens in most doped QSH insulators, the bulk states do not contribute to the backscattering in the electronic transport, allowing the construction of a spintronic device with less energy loss.
Electronic simulation of a multiterminal quantum Hall effect device
NASA Astrophysics Data System (ADS)
Sosso, A.; Capra, P. P.
1999-04-01
A circuit with only resistors and unity gain amplifiers can be proven to be equivalent to the Ricketts and Kemeny electrical model of multiterminal quantum Hall effect (QHE) devices. By means of the new equivalent circuit, commercial software for electronic circuit analysis can be used to study a QHE measurement system. Moreover, it can be easily implemented, and we were able to build a circuit that simulates the electrical behavior of a QHE device. Particular care was taken in the design to reduce the effect of parasitic capacitances, which act as loads connected to the device terminals. Bootstrap buffers have been adopted to significantly reduce the capacitance of input stage. The small residual loading effect can be calculated and eliminated, allowing simulation of a QHE device with good accuracy.
The quantum anomalous Hall effect in kagomé lattices
NASA Astrophysics Data System (ADS)
Zhang, Zhi-Yong
2011-09-01
The quantum anomalous Hall (QAH) effect in kagomé lattices is investigated in the presence of both Rashba spin-orbit coupling and an exchange field. In addition to the gap at the Dirac points as found in graphene, a new topological energy gap is opened at the Γ point. With the Fermi energy lying in the first gap, the Chern number 𝒞 = 2 as in graphene, whereas with it lying in the second one, 𝒞 = 1. The distribution of Berry curvature is obtained to reveal the nontrivial topological properties in momentum space. For stripes with ‘armchair’ and ‘zigzag’ edges, the topological characteristics of gapless edge states on the genus g = 2 Riemann surface are studied. The obtained nonzero winding numbers also demonstrate the QAH effect.
Quantum Anomalous Hall Effect in Graphene-based Heterostructure.
Zhang, Jiayong; Zhao, Bao; Yao, Yugui; Yang, Zhongqin
2015-01-01
Quantum anomalous Hall (QAH) effect, with potential applications in low-power-consumption electronics, is predicted in the heterostructure of graphene on the (001) surface of a real antiferromagnetic insulator RbMnCl3, based on density-functional theory and Wannier function methods. Due to the interactions from the substrate, a much large exchange field (about 280 meV) and an enhanced Rashba spin-orbit coupling are induced in graphene, leading to a topologically nontrivial QAH gap opened in the system. The avenues of enhancing the nontrivial gap are also proposed, from which nearly a gap one order large is achieved. Our work demonstrates that this graphene-based heterostructure is an appropriate candidate to be employed to experimentally observe the QAH effect and explore the promising applications.
Pure scaling operators at the integer quantum Hall plateau transition.
Bondesan, R; Wieczorek, D; Zirnbauer, M R
2014-05-01
Stationary wave functions at the transition between plateaus of the integer quantum Hall effect are known to exhibit multifractal statistics. Here we explore this critical behavior for the case of scattering states of the Chalker-Coddington network model with point contacts. We argue that moments formed from the wave amplitudes of critical scattering states decay as pure powers of the distance between the points of contact and observation. These moments in the continuum limit are proposed to be correlation functions of primary fields of an underlying conformal field theory. We check this proposal numerically by finite-size scaling. We also verify the conformal field theory prediction for a three-point function involving two primary fields.
Quantum spin hall insulators in strain-modified arsenene.
Zhang, Haijun; Ma, Yandong; Chen, Zhongfang
2015-12-01
By means of density functional theory (DFT) computations, we predict that the suitable strain modulation of honeycomb arsenene results in a unique two-dimensional (2D) topological insulator (TI) with a sizable bulk gap (up to 696 meV), which could be characterized and utilized at room temperature. Without considering any spin-orbit coupling, the band inversion occurs around the Gamma (G) point at tensile strains larger than 11.7%, which indicates the quantum spin Hall effect in arsenene at appropriate strains. The nontrivial topological phase was further confirmed by the topological invariant ν = 1 and edge states with a single Dirac-type crossing at the G point. Our results provide a promising strategy for designing 2D TIs with large bulk gaps from commonly used materials.
Critical supercurrents and self-organization in quantum Hall bilayers.
Eastham, P R; Cooper, N R; Lee, D K K
2010-12-01
We present a theory of interlayer tunneling in a disordered quantum Hall bilayer at total filling factor one, allowing for the effect of static vortices. In agreement with recent experiments [Phys. Rev. B 80, 165120 (2009); Phys. Rev. B 78, 075302 (2008)], we find that the critical current is proportional to the sample area and is comparable in magnitude to observed values. This reflects the formation of a Bean critical state as a result of current injection at the boundary. We predict a crossover to a critical current proportional to the square-root of the area in smaller samples. We also predict a peak in the critical current as the electron density varies at fixed layer separation.
Quantum spin Hall effect induced by electric field in silicene
NASA Astrophysics Data System (ADS)
An, Xing-Tao; Zhang, Yan-Yang; Liu, Jian-Jun; Li, Shu-Shen
2013-01-01
We investigate the transport properties in a zigzag silicene nanoribbon in the presence of an external electric field. The staggered sublattice potential and two kinds of Rashba spin-orbit couplings can be induced by the external electric field due to the buckled structure of the silicene. A bulk gap is opened by the staggered potential and gapless edge states appear in the gap by tuning the two kinds of Rashba spin-orbit couplings properly. Furthermore, the gapless edge states are spin-filtered and are insensitive to the non-magnetic disorder. These results prove that the quantum spin Hall effect can be induced by an external electric field in silicene, which may have certain practical significance in applications for future spintronics device.
Braiding non-Abelian quasiholes in fractional quantum Hall states.
Wu, Yang-Le; Estienne, B; Regnault, N; Bernevig, B Andrei
2014-09-12
Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the Z_{3} Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the Z_{3} Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the nonunitary Gaffnian wave function. PMID:25259996
Observing the Quantum Spin Hall Effect with Ultracold Atoms
NASA Astrophysics Data System (ADS)
Vaishnav, J. Y.; Stanescu, Tudor D.; Clark, Charles W.; Galitski, Victor
2009-03-01
The quantum spin Hall (QSH) state is a topologically nontrivial state of matter proposed to exist in certain 2-D systems with spin-orbit coupling. While the electronic states of a QSH insulator are gapped in the bulk, a QSH insulator is characterized by gapless edge states of different spins which counterpropagate at a given edge; the spin is correlated with the direction of propagation. Recent proposals ootnotetextT. D. Stanescu, C. Zhang, V. Galitski, Physical Review Letters 99, 110403 (2007), J. Y. Vaishnav, Charles W. Clark, Physical Review Letters 100, 153002 (2008). suggest that synthetic spin-orbit couplings can be created for cold atoms moving in spatially varying light fields. Here, we identify an optical lattice setup which generates an effective QSH effect for cold, multilevel atoms. We also discuss methods for experimental detection of the atomic QSH effect.
Quantum Hall Exciton Condensation at Full Spin Polarization
NASA Astrophysics Data System (ADS)
Finck, A. D. K.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2010-01-01
Using Coulomb drag as a probe, we explore the excitonic phase transition in quantum Hall bilayers at νT=1 as a function of Zeeman energy EZ. The critical layer separation (d/ℓ)c for exciton condensation initially increases rapidly with EZ, but then reaches a maximum and begins a gentle decline. At high EZ, where both the excitonic phase at small d/ℓ and the compressible phase at large d/ℓ are fully spin polarized, we find that the width of the transition, as a function of d/ℓ, is much larger than at small EZ and persists in the limit of zero temperature. We discuss these results in the context of two models in which the system contains a mixture of the two fluids.
Quantum Hall Exciton Condensation at Full Spin Polarization
NASA Astrophysics Data System (ADS)
Finck, A. D. K.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2010-03-01
Using Coulomb drag as a probe, we explore the excitonic phase transition in quantum Hall bilayers at νT=1 as a function of Zeeman energy, EZ. The critical layer separation (d/l)c for exciton condensation initially increases rapidly with EZ, but then reaches a maximum and begins a gentle decline. At high EZ, where both the excitonic phase at small d/l and the compressible phase at large d/l are fully spin polarized, we find that the width of the transition, as a function of d/l, is much larger than at small EZ and persists in the limit of zero temperature. We discuss these results in the context of two models in which the system contains a mixture of the two fluids.
Repulsive interactions in quantum Hall systems as a pairing problem
NASA Astrophysics Data System (ADS)
Ortiz, G.; Nussinov, Z.; Dukelsky, J.; Seidel, A.
2013-10-01
A subtle relation between quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin-type Hamiltonians that arise in (px+ipy) superconductivity. Specifically, we show that general Haldane pseudopotentials (and their sums) can be expressed as a sum of repulsive noncommuting (px+ipy)-type pairing Hamiltonians. The determination of the spectrum and individual null spaces of each of these noncommuting Richardson-Gaudin-type Hamiltonians is nontrivial yet is Bethe ansatz solvable. For the Laughlin sequence, it is observed that this problem is frustration free and zero-energy ground states lie in the common null space of all of these noncommuting Hamiltonians. This property allows for the use of a new truncated basis of pairing configurations in which to express Laughlin states at general filling factors. We prove separability of arbitrary Haldane pseudopotentials, providing explicit expressions for their second quantized forms, and further show by explicit construction how to exploit the topological equivalence between different geometries (disk, cylinder, and sphere) sharing the same topological genus number, in the second quantized formalism, through similarity transformations. As an application of the second quantized approach, we establish a “squeezing principle” that applies to the zero modes of a general class of Hamiltonians, which includes but is not limited to Haldane pseudopotentials. We also show how one may establish (bounds on) “incompressible filling factors” for those Hamiltonians. By invoking properties of symmetric polynomials, we provide explicit second quantized quasihole generators; the generators that we find directly relate to bosonic chiral edge modes and further make aspects of dimensional reduction in the quantum Hall systems
Non-Abelian quantum Hall states of fermions and bosons
NASA Astrophysics Data System (ADS)
Read, Nicholas
2007-03-01
In a non-Abelian quantum Hall state, there are types of elementary excitations or quasiparticles that obey non-Abelian statistics. This is an extension of the idea of fractional statistics that means that when several of these quasiparticles are present in the system and are well-separated at well-defined positions, there is a degenerate space of lowest-energy states. When the quasiparticles are then exchanged adiabatically, the result is a matrix operation on this space of states. Greg Moore and the author^1 introduced this idea to condensed matter physics in 1991. They proposed a basic example called the Moore-Read Pfaffian state. The physics of the existence of the degenerate states for the quasiparticles in this system can be understood by viewing it as a px-ipy paired state of composite fermions, in which quasiparticles are hc/2e vortices that carry Majorana fermion zero modes. This state is expected to be realized in the filling factor ν=5/2 fractional quantum Hall (FQH) state. In later work, a series (labeled by an integer k) of ``parafermion'' states was proposed^2. This talk will review these ideas, and describe recent numerical work that strongly supports the idea that the k=3 member of the sequence occurs in the filling factor 12/5 FQH state for electrons^3, and also^4 in a system of bosons, such as rotating cold atoms, at filling factor 3/2. It will also describe recent analytical results^5 on the explicit quasihole trial wavefunctions of the parafermion states. 1. G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991). 2. N. Read and E. Rezayi, Phys. Rev. B 59, 8084 (1999). 3. E.H. Rezayi and N. Read, cond-mat/0608346. 4. E.H. Rezayi, N. Read, and N.R. Cooper, Phys. Rev. Lett.95, 160404 (2005). 5. N. Read, Phys. Rev. B 73, 245334 (2006).
Lee, Y; Tran, D; Myhro, K; Velasco, J; Gillgren, N; Poumirol, J M; Smirnov, D; Barlas, Y; Lau, C N
2016-01-13
Using transport measurements, we investigate multicomponent quantum Hall (QH) ferromagnetism in dual-gated rhombohedral trilayer graphene (r-TLG) in which the real spin, orbital pseudospin, and layer pseudospins of the lowest Landau level form spontaneous ordering. We observe intermediate QH plateaus, indicating a complete lifting of the degeneracy of the zeroth Landau level (LL) in the hole-doped regime. In charge neutral r-TLG, the orbital degeneracy is broken first, and the layer degeneracy is broken last and only in the presence of an interlayer potential U⊥. In the phase space of U⊥ and filling factor ν, we observe an intriguing "hexagon" pattern, which is accounted for by a model based on crossings between symmetry-broken LLs.
Evidence for a fractional fractal quantum Hall effect in graphene superlattices.
Wang, Lei; Gao, Yuanda; Wen, Bo; Han, Zheng; Taniguchi, Takashi; Watanabe, Kenji; Koshino, Mikito; Hone, James; Dean, Cory R
2015-12-01
The Hofstadter energy spectrum provides a uniquely tunable system to study emergent topological order in the regime of strong interactions. Previous experiments, however, have been limited to low Bloch band fillings where only the Landau level index plays a role. We report measurements of high-mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. We observed coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal Hofstadter spectrum. At large magnetic field, we observed signatures of another series of states, which appeared at fractional Bloch filling index. These fractional Bloch band QHE states are not anticipated by existing theoretical pictures and point toward a distinct type of many-body state.
Long-lived binary tunneling spectrum in the quantum Hall Tomonaga-Luttinger liquid
NASA Astrophysics Data System (ADS)
Washio, K.; Nakazawa, R.; Hashisaka, M.; Muraki, K.; Tokura, Y.; Fujisawa, T.
2016-02-01
The existence of long-lived nonequilibrium states without showing thermalization, which has previously been demonstrated in time evolution of ultracold atoms, suggests the possibility of their spatial analog in transport behavior of interacting electrons in solid-state systems. Here we report long-lived nonequilibrium states in one-dimensional edge channels in the integer quantum Hall regime. An indirect heating scheme in a counterpropagating configuration is employed to generate a nontrivial binary spectrum consisting of high- and low-temperature components. This unusual spectrum is sustained even after traveling 5-10 μ m , much longer than the length for electronic relaxation (about 0.1 μ m ), without showing significant thermalization. This observation is consistent with the integrable model of Tomonaga-Luttinger liquid. The long-lived spectrum implies that the system is well described by noninteracting plasmons, which are attractive for carrying information for a long distance.
Evidence for a fractional fractal quantum Hall effect in graphene superlattices.
Wang, Lei; Gao, Yuanda; Wen, Bo; Han, Zheng; Taniguchi, Takashi; Watanabe, Kenji; Koshino, Mikito; Hone, James; Dean, Cory R
2015-12-01
The Hofstadter energy spectrum provides a uniquely tunable system to study emergent topological order in the regime of strong interactions. Previous experiments, however, have been limited to low Bloch band fillings where only the Landau level index plays a role. We report measurements of high-mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. We observed coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal Hofstadter spectrum. At large magnetic field, we observed signatures of another series of states, which appeared at fractional Bloch filling index. These fractional Bloch band QHE states are not anticipated by existing theoretical pictures and point toward a distinct type of many-body state. PMID:26785484
Observation of fractional Bloch band quantum Hall states in graphene/h-BN superlattices
NASA Astrophysics Data System (ADS)
Wang, Lei; Gao, Yuanda; Wen, Bo; Hone, James; Dean, Cory
The Hofstadter energy spectrum provides a uniquely tunable system to study emergent topological order in the regime of strong interactions. Previous experiments, however, have been limited to low Bloch band fillings where only the Landau level index plays a role. Here we report measurements of high mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. We observe coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal Hofstadter spectrum. At large magnetic field, we observe signatures of another series of states, which appears at fractional Bloch filling index. These fractional Bloch band QHE states are not anticipated by existing theoretical pictures and point towards a distinct type of many-body state.
Evidence for a fractional fractal quantum Hall effect in graphene superlattices
NASA Astrophysics Data System (ADS)
Wang, Lei; Gao, Yuanda; Wen, Bo; Han, Zheng; Taniguchi, Takashi; Watanabe, Kenji; Koshino, Mikito; Hone, James; Dean, Cory R.
2015-12-01
The Hofstadter energy spectrum provides a uniquely tunable system to study emergent topological order in the regime of strong interactions. Previous experiments, however, have been limited to low Bloch band fillings where only the Landau level index plays a role. We report measurements of high-mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. We observed coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal Hofstadter spectrum. At large magnetic field, we observed signatures of another series of states, which appeared at fractional Bloch filling index. These fractional Bloch band QHE states are not anticipated by existing theoretical pictures and point toward a distinct type of many-body state.
Lee, Y; Tran, D; Myhro, K; Velasco, J; Gillgren, N; Poumirol, J M; Smirnov, D; Barlas, Y; Lau, C N
2016-01-13
Using transport measurements, we investigate multicomponent quantum Hall (QH) ferromagnetism in dual-gated rhombohedral trilayer graphene (r-TLG) in which the real spin, orbital pseudospin, and layer pseudospins of the lowest Landau level form spontaneous ordering. We observe intermediate QH plateaus, indicating a complete lifting of the degeneracy of the zeroth Landau level (LL) in the hole-doped regime. In charge neutral r-TLG, the orbital degeneracy is broken first, and the layer degeneracy is broken last and only in the presence of an interlayer potential U⊥. In the phase space of U⊥ and filling factor ν, we observe an intriguing "hexagon" pattern, which is accounted for by a model based on crossings between symmetry-broken LLs. PMID:26636471
Dynamical disentanglement across a point contact in a non-Abelian quantum Hall state.
Fendley, Paul; Fisher, Matthew P A; Nayak, Chetan
2006-07-21
We analyze the tunneling of non-Abelian quasiparticles between the edges of a quantum Hall droplet at the Landau level filling fraction nu=5/2, assuming that the electrons in the first excited Landau level organize themselves in the non-Abelian Moore-Read Pfaffian state. By bosonizing the edge theory, we show that an effective spin-1/2 degree of freedom emerges in the description of a point contact. We show how the crossover from the high-temperature regime of weak quasiparticle tunneling between the edges of the droplet, with the 4-terminal Rxx approximately T(-3/2), to the low-temperature limit, with Rxx(-1/10)(h/e2) approximately-T4, is closely related to the two-channel Kondo effect. We give a physical interpretation for the entropy loss of ln(2[square root of 2) in this crossover.
Robust large-gap quantum spin Hall insulators in chemically decorated arsenene films
NASA Astrophysics Data System (ADS)
Wang, Dongchao; Chen, Li; Shi, Changmin; Wang, Xiaoli; Cui, Guangliang; Zhang, Pinhua; Chen, Yeqing
2016-03-01
Based on first-principles calculations, we propose one new category of two-dimensional topological insulators (2D TIs) in chemically functionalized (-CH3 and -OH) arsenene films. The results show that the surface decorated arsenene (AsCH3 and AsOH) films are intrinsic 2D TIs with sizeable bulk gap. The bulk energy gaps are 0.184 eV, and 0.304 eV in AsCH3 and AsOH films, respectively. Such large bulk gaps make them suitable to realize quantum spin Hall effect in an experimentally accessible temperature regime. Topologically helical edge states in these systems are desirable for dissipationless transport. Moreover, we find that the topological properties in these systems are robust against mechanical deformation by exerting biaxial strain. These novel 2D TIs with large bulk gaps are potential candidate in future electronic devices with ultralow dissipation.
Quantum Plasma Effects in the Classical Regime
Brodin, G.; Marklund, M.; Manfredi, G.
2008-05-02
For quantum effects to be significant in plasmas it is often assumed that the temperature over density ratio must be small. In this paper we challenge this assumption by considering the contribution to the dynamics from the electron spin properties. As a starting point we consider a multicomponent plasma model, where electrons with spin-up and spin-down are regarded as different fluids. By studying the propagation of Alfven wave solitons we demonstrate that quantum effects can survive in a relatively high-temperature plasma. The consequences of our results are discussed.
Selective Equilibration of Spin-Polarized Quantum Hall Edge States in Graphene
NASA Astrophysics Data System (ADS)
Amet, F.; Williams, J. R.; Watanabe, K.; Taniguchi, T.; Goldhaber-Gordon, D.
2014-05-01
We report on transport measurements of dual-gated, single-layer graphene devices in the quantum Hall regime, allowing for independent control of the filling factors in adjoining regions. Progress in device quality allows us to study scattering between edge states when the fourfold degeneracy of the Landau level is lifted by electron correlations, causing edge states to be spin and/or valley polarized. In this new regime, we observe a dramatic departure from the equilibration seen in more disordered devices: edge states with opposite spins propagate without mixing. As a result, the degree of equilibration inferred from transport can reveal the spin polarization of the ground state at each filling factor. In particular, the first Landau level is shown to be spin polarized at half filling, providing an independent confirmation of a conclusion of Young et al. [Nat. Phys. 8, 550 (2012)]. The conductance in the bipolar regime is strongly suppressed, indicating that copropagating edge states, even with the same spin, do not equilibrate along PN interfaces. We attribute this behavior to the formation of an insulating ν =0 stripe at the PN interface.
Theory of Transport Phenomena in Coherent Quantum Hall Bilayers
NASA Astrophysics Data System (ADS)
MacDonald, Allan H.; Chen, Hua; Sodemann, Inti
2015-03-01
We will describe a theory that allows to understand the anomalous transport properties of the excitonic condensate state occurring in quantum quantum Hall bilayers in terms of a picture in which the condensate phase is nearly uniform across the sample, and the strength of condensate coupling to interlayer tunneling processes is substantially reduced compared to the predictions of disorder-free microscopic mean-field theory. These ingredients provide a natural explanation for recently established I-V characteristics which feature a critical current above which the tunneling resistance abruptly increases and a non-local interaction between interlayer tunneling at the inner and outer edges of Corbino rings. We propose a microscopic picture in which disorder is the main agent responsible for the reduction of the effective interlayer tunneling strength. IS is supported by the Pappalardo Fellowship in Physics. HC and AHM are supported by DOE Division of Materials Sciences and Engineering Grant DE-FG03- 02ER45958 and Welch Foundation Grant TBF1473.
Critical integer quantum Hall topology in the integrable Maryland model
NASA Astrophysics Data System (ADS)
Ganeshan, Sriram; Kechedzhi, Kostyantyn
2014-03-01
One-dimensional tight binding models such as Aubry-Andre-Harper (AAH) model (with onsite cosine potential) and the integrable Maryland model (with onsite tangent potential) have been the subjects of extensive theoretical research in localization studies. AAH can be directly mapped onto the two-dimensional Hofstadter model that manifests the integer quantum Hall topology on a lattice. However, no such connection has been made for the Maryland model (MM). In this talk, we present a generalized model that contains AAH and MM as the limiting cases with the MM lying precisely at a topological quantum phase transition (TQPT) point. A remarkable feature of this critical point is that the 1D MM retains well-defined energy gaps whereas the equivalent 2D model becomes gapless, signifying the 2D nature of the TQPT. The criticality allows us to associate topological invariants with the Maryland model in a restricted mathematical sense at the special filling factors that are adiabatically connected to the spectral gaps in the 1D Aubry-Andre-Harper model. Our theory presented in this work establishes deep and unexpected mathematical connections between 2D topological models and a family of 1D incommensurate localization models. This work is supported by JQI-NSF-PFC, Microsoft Q and JQI-ARO-MU.
Fibonacci anyons from Abelian bilayer quantum Hall states.
Vaezi, Abolhassan; Barkeshli, Maissam
2014-12-01
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this Letter, we consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous "Fibonacci" anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν=2/3 in bilayers, as past experiments may not have definitively ruled them out. PMID:25526149
Anisotropic Quantum Hall Liquid States with No Translational Invariance in the Lowest Landau Level
NASA Astrophysics Data System (ADS)
Ciftja, Orion
2016-05-01
Strongly correlated two-dimensional electron systems in a high perpendicular magnetic field have displayed remarkable new physics leading to the discovery of phenomena such as the integer and the fractional quantum Hall effect, to mention a few. Laughlin's theoretical model and the composite fermion's (CFs) approach provide a good description of the liquid electronic phases in the lowest Landau level (LLL) at relatively large filling factors. Other electronic phases at smaller filling factors of the LLL likely represent electronic Wigner solid states. It is believed that no other phases with intermediate order stabilize at the liquid-solid transition region. The current study deals with filling factor 1/6 in the LLL, a state which is very close to the critical filling factor where the liquid-solid transition takes place. With the assumption that the underlying signs of crystalline order are starting to appear at this transitional regime, we focus our attention and study the properties of a hybrid electronic phase that lacks translational invariance. To describe such a state, we consider a wave function that lies entirely in the LLL but, unlike a typical quantum Hall liquid phase, does not possess translational invariance. Although inspired by Laughlin's approach, the wave function we introduce differs from Laughlin's or CFs wave functions that describe translationally invariant uniform electronic phases. We perform quantum Monte Carlo simulations in a standard disk geometry to gain a better understanding of the properties of this wave function that may be considered as a precursor to the more conventional Wigner crystal phase.
Understanding the physics of a possible non-Abelian fractional quantum hall effect state.
Pan, Wei; Crawford, Matthew; Tallakulam, Madhu; Ross, Anthony Joseph, III
2010-10-01
We wish to present in this report experimental results from a one-year Senior Council Tier-1 LDRD project that focused on understanding the physics of a possible non-Abelian fractional quantum Hall effect state. We first give a general introduction to the quantum Hall effect, and then present the experimental results on the edge-state transport in a special fractional quantum Hall effect state at Landau level filling {nu} = 5/2 - a possible non-Abelian quantum Hall state. This state has been at the center of current basic research due to its potential applications in fault-resistant topological quantum computation. We will also describe the semiconductor 'Hall-bar' devices we used in this project. Electron physics in low dimensional systems has been one of the most exciting fields in condensed matter physics for many years. This is especially true of quantum Hall effect (QHE) physics, which has seen its intellectual wealth applied in and has influenced many seemingly unrelated fields, such as the black hole physics, where a fractional QHE-like phase has been identified. Two Nobel prizes have been awarded for discoveries of quantum Hall effects: in 1985 to von Klitzing for the discovery of integer QHE, and in 1998 to Tsui, Stormer, and Laughlin for the discovery of fractional QHE. Today, QH physics remains one of the most vibrant research fields, and many unexpected novel quantum states continue to be discovered and to surprise us, such as utilizing an exotic, non-Abelian FQHE state at {nu} = 5/2 for fault resistant topological computation. Below we give a briefly introduction of the quantum Hall physics.
Photon mirror acceleration in the quantum regime
Mendonça, J. T.; Fedele, R.
2014-12-15
Reflection of an electron beam by an intense laser pulse is considered. This is the so-called photon mirror configuration for laser acceleration in vacuum, where the energy of the incident electron beam is nearly double-Doppler shifted due to reflection on the laser pulse front. A wave-electron optical description for electron reflection and resonant backscattering, due to both linear electric field force and quadratic ponderomotive force, is provided beyond the paraxial approximation. This is done by assuming that the single electron of the beam is spin-less and therefore its motion can be described by a quantum scalar field whose spatiotemporal evolution is governed by the Klein-Gordon equation (Klein-Gordon field). Our present model, not only confirms the classical results but also shows the occurrence of purely quantum effects, such as partial reflection of the incident electron beam and enhanced backscattering due to Bragg resonance.
NASA Astrophysics Data System (ADS)
Kazakov, Alexander; Kolkovsky, V.; Adamus, Z.; Karczewski, G.; Wojtowicz, T.; Rokhinson, Leonid
2015-03-01
Several experiments detected signatures of Majorana fermions in nanowires, and the focus of current research is shifting toward systems where non-Abelian statistics of excitations can be demonstrated. To achieve this goal we are developing a new platform where non-Abelian excitations can be created and manipulated in a two-dimensional plane, with support for Majorana and higher order non-Abelian excitations. The system is based on CdTe quantum wells non-uniformly doped with paramagnetic impurities, which result in a complicate field-dependence of Zeeman splitting. A unique property of the system is that at high fields we can form a quantum Hall ferromagnet with gate-controllable spin polarization. Helical 1D edge channels formed along the edges of electrostatic gates may support generalized non-Abelian excitations in the fractional qunatum Hall regime, and Majorana and parafermion excitations in the presence of induced superconductivity. We will present results on the gate control of s-d exchange in specially designed heterostructures, demonstrate gate control of spin polarization at filling factor ν = 2 , and show spatial separation of quantum Hall states with different spin polarization using lithographically defined gates.
Long-term research in Inmetro on samples of quantum Hall resistance standards made by PTB
NASA Astrophysics Data System (ADS)
Carvalho, H. R.; Briones, R. E. M.; Pierz, K.; Gotz, M.
2016-07-01
This paper shows up to date results of Inmetro's investigations on aging effects of quantum Hall samples fabricated by PTB in the frame of a mutual scientific agreement established between the Brazilian and German National Metrology Institutes.
Electrically tunable spin polarization of chiral edge modes in a quantum anomalous Hall insulator
NASA Astrophysics Data System (ADS)
Zhang, Rui-Xing; Hsu, Hsiu-Chuan; Liu, Chao-Xing
2016-06-01
In the quantum anomalous Hall effect, chiral edge modes are expected to conduct spin polarized current without dissipation and thus hold great promise for future electronics and spintronics with low energy consumption. However, spin polarization of chiral edge modes has never been established in experiments. In this work, we theoretically study spin polarization of chiral edge modes in the quantum anomalous Hall effect, based on both the effective model and more realistic tight-binding model constructed from first-principles calculations. We find that spin polarization can be manipulated by tuning either a local gate voltage or the Fermi energy. We also propose to extract spin information of chiral edge modes by contacting the quantum anomalous Hall insulator to a ferromagnetic lead. The establishment of spin polarization of chiral edge modes, as well as the manipulation and detection in a fully electrical manner, will pave the way to the applications of the quantum anomalous Hall effect in spintronics.
Long-lived non-equilibrium states in a quantum-Hall Tomonaga-Luttinger liquid
NASA Astrophysics Data System (ADS)
Fujisawa, Toshimasa; Washio, Kazuhisa; Nakazawa, Ryo; Hashisaka, Masayuki; Muraki, Koji; Tokura, Yasuhiro
The existence of long-lived non-equilibrium states without showing thermalization, which has previously been demonstrated in time evolution of ultracold atoms (quantum quench), suggests the possibility of their spatial analogue in transport behavior of interacting electrons in solid-state systems. Here we report long-lived non-equilibrium states in one-dimensional edge channels in the integer quantum Hall regime. For this purpose, non-trivial binary spectrum composed of hot and cold carriers is prepared by an indirect heating scheme using weakly coupled counterpropagating edge channels in an AlGaAs/GaAs heterostructure. Quantum dot spectroscopy clearly reveals that the carriers with the non-trivial binary spectrum propagate over a long distance (5 - 10 um), much longer than the length required for electronic relaxation (about 0.1 um), without thermalization into a trivial Fermi distribution. This observation is consistent with the integrable model of Tomonaga-Luttinger liquid. The long-lived spectrum implies that the system is well described by non-interacting plasmons, which are attractive for carrying information for a long distance. This work was supported by the JSPS 26247051 and 15H05854, and Nanotechnology Platform Program of MEXT.
Statistical theory of relaxation of high-energy electrons in quantum Hall edge states
NASA Astrophysics Data System (ADS)
Lunde, Anders Mathias; Nigg, Simon E.
2016-07-01
We investigate theoretically the energy exchange between the electrons of two copropagating, out-of-equilibrium edge states with opposite spin polarization in the integer quantum Hall regime. A quantum dot tunnel coupled to one of the edge states locally injects electrons at high energy. Thereby a narrow peak in the energy distribution is created at high energy above the Fermi level. A second downstream quantum dot performs an energy-resolved measurement of the electronic distribution function. By varying the distance between the two dots, we are able to follow every step of the energy exchange and relaxation between the edge states, even analytically under certain conditions. In the absence of translational invariance along the edge, e.g., due to the presence of disorder, energy can be exchanged by non-momentum-conserving two-particle collisions. For weakly broken translational invariance, we show that the relaxation is described by coupled Fokker-Planck equations. From these we find that relaxation of the injected electrons can be understood statistically as a generalized drift-diffusion process in energy space for which we determine the drift velocity and the dynamical diffusion parameter. Finally, we provide a physically appealing picture in terms of individual edge-state heating as a result of the relaxation of the injected electrons.
Quantum Hall transitions: An exact theory based on conformal restriction
NASA Astrophysics Data System (ADS)
Bettelheim, E.; Gruzberg, I. A.; Ludwig, A. W. W.
2012-10-01
We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, and for other two-dimensional disordered systems, based on the theory of “conformal restriction.” This is a mathematical theory that was recently developed within the context of the Schramm-Loewner evolution which describes the “stochastic geometry” of fractal curves and other stochastic geometrical fractal objects in two-dimensional space. Observables elucidating the connection with the plateau transition include the so-called point-contact conductances (PCCs) between points on the boundary of the sample, described within the language of the Chalker-Coddington network model for the transition. We show that the disorder-averaged PCCs are characterized by a classical probability distribution for certain geometric objects in the plane (which we call pictures), occurring with positive statistical weights, that satisfy the crucial so-called restriction property with respect to changes in the shape of the sample with absorbing boundaries; physically, these are boundaries connected to ideal leads. At the transition point, these geometrical objects (pictures) become fractals. Upon combining this restriction property with the expected conformal invariance at the transition point, we employ the mathematical theory of “conformal restriction measures” to relate the disorder-averaged PCCs to correlation functions of (Virasoro) primary operators in a conformal field theory (of central charge c=0). We show how this can be used to calculate these functions in a number of geometries with various boundary conditions. Since our results employ only the conformal restriction property, they are equally applicable to a number of other critical disordered electronic systems in two spatial dimensions, including for example the spin quantum Hall effect, the thermal metal phase in symmetry class D, and classical diffusion in two
Conformal field theory approach to Abelian and non-Abelian quantum Hall quasielectrons.
Hansson, T H; Hermanns, M; Regnault, N; Viefers, S
2009-04-24
The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.
NASA Astrophysics Data System (ADS)
Mirza, Babur M.
2016-05-01
A microscopic theory of integer and fractional quantum Hall effects is presented here. In quantum density wave representation of charged particles, it is shown that, in a two-dimensional electron gas coherent structures form under the low temperature and high density conditions. With a sufficiently high applied magnetic field, the combined N particle quantum density wave exhibits collective periodic oscillations. As a result the corresponding quantum Hall voltage function shows a step-wise change in multiples of the ratio h/e2. At lower temperatures further subdivisions emerge in the Hall resistance, exhibiting the fractional quantum Hall effect.
Giant quantum Hall plateaus generated by charge transfer in epitaxial graphene.
Alexander-Webber, J A; Huang, J; Maude, D K; Janssen, T J B M; Tzalenchuk, A; Antonov, V; Yager, T; Lara-Avila, S; Kubatkin, S; Yakimova, R; Nicholas, R J
2016-01-01
Epitaxial graphene has proven itself to be the best candidate for quantum electrical resistance standards due to its wide quantum Hall plateaus with exceptionally high breakdown currents. However one key underlying mechanism, a magnetic field dependent charge transfer process, is yet to be fully understood. Here we report measurements of the quantum Hall effect in epitaxial graphene showing the widest quantum Hall plateau observed to date extending over 50 T, attributed to an almost linear increase in carrier density with magnetic field. This behaviour is strong evidence for field dependent charge transfer from charge reservoirs with exceptionally high densities of states in close proximity to the graphene. Using a realistic framework of broadened Landau levels we model the densities of donor states and predict the field dependence of charge transfer in excellent agreement with experimental results, thus providing a guide towards engineering epitaxial graphene for applications such as quantum metrology.
Giant quantum Hall plateaus generated by charge transfer in epitaxial graphene.
Alexander-Webber, J A; Huang, J; Maude, D K; Janssen, T J B M; Tzalenchuk, A; Antonov, V; Yager, T; Lara-Avila, S; Kubatkin, S; Yakimova, R; Nicholas, R J
2016-01-01
Epitaxial graphene has proven itself to be the best candidate for quantum electrical resistance standards due to its wide quantum Hall plateaus with exceptionally high breakdown currents. However one key underlying mechanism, a magnetic field dependent charge transfer process, is yet to be fully understood. Here we report measurements of the quantum Hall effect in epitaxial graphene showing the widest quantum Hall plateau observed to date extending over 50 T, attributed to an almost linear increase in carrier density with magnetic field. This behaviour is strong evidence for field dependent charge transfer from charge reservoirs with exceptionally high densities of states in close proximity to the graphene. Using a realistic framework of broadened Landau levels we model the densities of donor states and predict the field dependence of charge transfer in excellent agreement with experimental results, thus providing a guide towards engineering epitaxial graphene for applications such as quantum metrology. PMID:27456765
Giant quantum Hall plateaus generated by charge transfer in epitaxial graphene
NASA Astrophysics Data System (ADS)
Alexander-Webber, J. A.; Huang, J.; Maude, D. K.; Janssen, T. J. B. M.; Tzalenchuk, A.; Antonov, V.; Yager, T.; Lara-Avila, S.; Kubatkin, S.; Yakimova, R.; Nicholas, R. J.
2016-07-01
Epitaxial graphene has proven itself to be the best candidate for quantum electrical resistance standards due to its wide quantum Hall plateaus with exceptionally high breakdown currents. However one key underlying mechanism, a magnetic field dependent charge transfer process, is yet to be fully understood. Here we report measurements of the quantum Hall effect in epitaxial graphene showing the widest quantum Hall plateau observed to date extending over 50 T, attributed to an almost linear increase in carrier density with magnetic field. This behaviour is strong evidence for field dependent charge transfer from charge reservoirs with exceptionally high densities of states in close proximity to the graphene. Using a realistic framework of broadened Landau levels we model the densities of donor states and predict the field dependence of charge transfer in excellent agreement with experimental results, thus providing a guide towards engineering epitaxial graphene for applications such as quantum metrology.
Quantum spin Hall phase in 2D trigonal lattice.
Wang, Z F; Jin, Kyung-Hwan; Liu, Feng
2016-01-01
The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, px, py) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin-orbit coupling (SOC)-induced s-p band inversion or p-p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ∼73 meV, facilitating the possible room-temperature measurement. Our results will extend the search for substrate supported QSH materials to new lattice and orbital types. PMID:27599580
Quantum spin Hall phase in 2D trigonal lattice
NASA Astrophysics Data System (ADS)
Wang, Z. F.; Jin, Kyung-Hwan; Liu, Feng
2016-09-01
The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, px, py) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin-orbit coupling (SOC)-induced s-p band inversion or p-p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ~73 meV, facilitating the possible room-temperature measurement. Our results will extend the search for substrate supported QSH materials to new lattice and orbital types.
Time- and spectrally resolved terahertz photoconductivity of quantum Hall systems
NASA Astrophysics Data System (ADS)
Stellmach, C.; Vasile, G.; Hirsch, A.; Bonk, R.; Vasilyev, Yu. B.; Hein, G.; Becker, C. R.; Nachtwei, G.
2007-07-01
We present terahertz photoconductivity measurements on GaAs/AlGaAs and HgTe/HgCdTe heterostructures. The photoresponse is investigated time and spectrally resolved under quantum Hall conditions. The samples are excited by a pulsed p-Ge laser, which emits photons of frequencies around 2THz (corresponding to photon energies around 10meV ). Corbino-shaped GaAs/AlGaAs samples show relaxation times τ down to 10ns . The dependence of τ on the applied source-drain voltage is explained by a two-level picture after normalizing the data. All spectrally resolved measurements show contributions of the cyclotron resonance and the bolometric effect. These results are compared to numerical calculations based on a self-consistent Born approximation method. The measurements on HgTe/HgCdTe samples show comparable results. However, the effective mass in these samples is only mc=0.026m0 (approximately 1/3 of the mass in GaAs/AlGaAs ). Thus the cyclotron resonance is shifted to smaller magnetic fields around 2T . This fact makes HgTe/HgCdTe systems especially interesting for terahertz detector applications.
A bifunctional spin detector made of quantum anomalous Hall insulator
NASA Astrophysics Data System (ADS)
Shi, Zhangsheng; Wu, Jiansheng
2016-10-01
The spin selection of the topological boundary states (TBS) which are protected by the chiral-like symmetry in quantum anomalous Hall insulator (QAHI) can be used to construct a bifunctional spin detector (SD). Such device made of QAHIs in parallel with opposite chirality can divide an incoming spin-polarized current into two outgoing currents. The agreement between numerical and analytical calculation proves that the SD device functions as both spin filter and spin separator well in reflecting the spin polarization of source material from the ratio of two currents. The monotonic relation of spin polarization and current ratio suggests that using such kind of device, the spin polarization can be obtained directly. We also find that such device has a broad working energy region attributed by the TBS within the bulk gap. Combining with the result that the current ratio is barely dependent on the coupling between candidate materials and device, it is reasonable to apply this technique with a stable measuring accuracy. Furthermore, the features such as having simple geometry, being manipulated without external magnetic field, and the prospect of working at room temperature make this proposed device seem promising in developing future low-power-consumption spintronic device.
Coulomb drag and tunneling studies in quantum Hall bilayers
NASA Astrophysics Data System (ADS)
Nandi, Debaleena
The bilayer quantum Hall state at total filling factor νT=1, where the total electron density matches the degeneracy of the lowest Landau level, is a prominent example of Bose-Einstein condensation of excitons. A macroscopically ordered state is realized where an electron in one layer is tightly bound to a "hole" in the other layer. If exciton transport were the only bulk transportmechanism, a current driven in one layer would spontaneously generate a current of equal magnitude and opposite sign in the other layer. The Corbino Coulomb drag measurements presented in this thesis demonstrate precisely this phenomenon. Excitonic superfluidity has been long sought in the νT=1 state. The tunneling between the two electron gas layers exihibit a dc Josephson-like effect. A simple model of an over-damped voltage biased Josephson junction is in reasonable agreement with the observed tunneling I -- V. At small tunneling biases, it exhibits a tunneling "supercurrent". The dissipation is carefully studied in this tunneling "supercurrent" and found to remain small but finite.
Quantum spin Hall phase in 2D trigonal lattice
Wang, Z. F.; Jin, Kyung-Hwan; Liu, Feng
2016-01-01
The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, px, py) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin–orbit coupling (SOC)-induced s–p band inversion or p–p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ∼73 meV, facilitating the possible room-temperature measurement. Our results will extend the search for substrate supported QSH materials to new lattice and orbital types. PMID:27599580
Non-abelian fractional quantum hall effect for fault-resistant topological quantum computation.
Pan, Wei; Thalakulam, Madhu; Shi, Xiaoyan; Crawford, Matthew; Nielsen, Erik; Cederberg, Jeffrey George
2013-10-01
Topological quantum computation (TQC) has emerged as one of the most promising approaches to quantum computation. Under this approach, the topological properties of a non-Abelian quantum system, which are insensitive to local perturbations, are utilized to process and transport quantum information. The encoded information can be protected and rendered immune from nearly all environmental decoherence processes without additional error-correction. It is believed that the low energy excitations of the so-called =5/2 fractional quantum Hall (FQH) state may obey non-Abelian statistics. Our goal is to explore this novel FQH state and to understand and create a scientific foundation of this quantum matter state for the emerging TQC technology. We present in this report the results from a coherent study that focused on obtaining a knowledge base of the physics that underpins TQC. We first present the results of bulk transport properties, including the nature of disorder on the 5/2 state and spin transitions in the second Landau level. We then describe the development and application of edge tunneling techniques to quantify and understand the quasiparticle physics of the 5/2 state.
NASA Astrophysics Data System (ADS)
Abanin, D. A.; Skachko, I.; Du, X.; Andrei, E. Y.; Levitov, L. S.
2010-03-01
Fractional quantum Hall effect (FQHE), observed recently in suspended graphene (SG) [1], was found to persist up to temperatures much higher than in previously studied systems, such as GaAs. This suggests strong electron interactions in SG. Can the interaction strength be inferred from the measurements? The best results on FQHE were obtained on micron-size SG flakes, where only two-terminal measurements could be performed. This talk will address the problem of determining transport coefficients from the two-terminal conductance in the FQHE regime. A general approach, which relies on the conformal invariance of two-dimensional magnetotransport, is used to extract σxx and σxy. From the temperature dependence of σxx we estimate the energy gap of quasiparticle excitations in the ν= 1/3 state. The gap value, which is found to be well above that measured in GaAs systems [2], is compared to theoretical predictions. Our approach provides a new tool for the studies of quantum transport in suspended graphene and other nanoscale systems. [1] X. Du et al, Nature 462, 192 (2009); K. Bolotin et al, ibid., 196 (2009). [2] G. S. Boebinger et al, Phys. Rev. Lett. 55, 1606 (1985).
Quantum Hall effect in HgTe quantum wells at nitrogen temperatures
Kozlov, D. A. Kvon, Z. D.; Mikhailov, N. N.; Dvoretskii, S. A.; Weishäupl, S.; Krupko, Y.; Portal, J.-C.
2014-09-29
We report on the observation of quantized Hall plateaus in a system of two-dimensional Dirac fermions, implemented in a 6.6 nm HgTe quantum well at magnetic fields up to 34 T at nitrogen temperatures. The activation energies determined from the temperature dependence of the longitudinal resistivity are found to be almost equal for the filling factors ν of 1 and 2. This indicates that the large values of the g-factor (about 30–40) remain unchanged at very strong magnetic fields.
Observation of a fractional quantum Hall state at v=1/4 in a wide GaAs quantum well.
Pan, Wei; Tsui, Daniel Chee; Baldwin, K. W.; West, Ken W.; Pfeiffer, Loren N.; Luhman, D. R.
2008-10-01
We report the observation of an even-denominator fractional quantum Hall state at {nu}=1/4 in a high quality, wide GaAs quantum well. The sample has a quantum well width of 50 nm and an electron density of n{sub e}=2.55 x 10{sup 11} cm{sup -2}. We have performed transport measurements at T{approx}35 mK in magnetic fields up to 45 T. When the sample is perpendicular to the applied magnetic field, the diagonal resistance displays a kink at {nu}=1/4. Upon tilting the sample to an angle of {theta}=20.3{sup o} a clear fractional quantum Hall state emerges at {nu}=1/4 with a plateau in the Hall resistance and a strong minimum in the diagonal resistance.
Fractional quantum Hall effect on the two-sphere: A matrix model proposal
Morariu, Bogdan; Polychronakos, Alexios P.
2005-12-15
We present a Chern-Simons matrix model describing the fractional quantum Hall effect on the two sphere. We demonstrate the equivalence of our proposal to particular restrictions of the Calogero-Sutherland model, reproduce the quantum states and filling fraction and show the compatibility of our result with the Haldane spherical wave functions.
Universal transport signatures of topological superconductivity in quantum spin Hall architectures
NASA Astrophysics Data System (ADS)
Lee, Shu-Ping; Aasen, David; Karzig, Torsten; Alicea, Jason
2015-03-01
Interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to ``engineered'' topological superconductivity. Given exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce power-law-localized ``parafermion'' excitations at a superconductor/quantum spin Hall junction. NSF Grant DMR-1341822. (2) Institute for Quantum Information and Matter, an NSF physics frontier center with support from the Moore Foundation.
Anomalous resistance overshoot in the integer quantum Hall effect
Kendirlik, E. M.; Sirt, S.; Kalkan, S. B.; Dietsche, W.; Wegscheider, W.; Ludwig, S.; Siddiki, A.
2013-01-01
In this work we report on experiments performed on smooth edge-narrow Hall bars. The magneto-transport properties of intermediate mobility two-dimensional electron systems are investigated and analyzed within the screening theory of the integer quantized Hall effect. We observe a non-monotonic increase of Hall resistance at the low magnetic field ends of the quantized plateaus, known as the overshoot effect. Unexpectedly, for Hall bars that are defined by shallow chemical etching the overshoot effect becomes more pronounced at elevated temperatures. We observe the overshoot effect at odd and even integer plateaus, which favor a spin independent explanation, in contrast to discussion in the literature. In a second set of the experiments, we investigate the overshoot effect in gate defined Hall bar and explicitly show that the amplitude of the overshoot effect can be directly controlled by gate voltages. We offer a comprehensive explanation based on scattering between evanescent incompressible channels. PMID:24190162
Anomalous resistance overshoot in the integer quantum Hall effect.
Kendirlik, E M; Sirt, S; Kalkan, S B; Dietsche, W; Wegscheider, W; Ludwig, S; Siddiki, A
2013-01-01
In this work we report on experiments performed on smooth edge-narrow Hall bars. The magneto-transport properties of intermediate mobility two-dimensional electron systems are investigated and analyzed within the screening theory of the integer quantized Hall effect. We observe a non-monotonic increase of Hall resistance at the low magnetic field ends of the quantized plateaus, known as the overshoot effect. Unexpectedly, for Hall bars that are defined by shallow chemical etching the overshoot effect becomes more pronounced at elevated temperatures. We observe the overshoot effect at odd and even integer plateaus, which favor a spin independent explanation, in contrast to discussion in the literature. In a second set of the experiments, we investigate the overshoot effect in gate defined Hall bar and explicitly show that the amplitude of the overshoot effect can be directly controlled by gate voltages. We offer a comprehensive explanation based on scattering between evanescent incompressible channels.
Fano-Andreev effect in Quantum Dots in Kondo regime
NASA Astrophysics Data System (ADS)
Orellana, Pedro; Calle, Ana Maria; Pacheco, Monica; Apel, Victor
In the present work, we investigate the transport through a T-shaped double quantum dot system coupled to two normal leads and to a superconducting lead. We study the role of the superconducting lead in the quantum interferometric features of the double quantum dot and by means of a slave boson mean field approximation at low temperature regime. We inquire into the influence of intradot interactions in the electronic properties of the system as well. Our results show that Fano resonances due to Andreev bound states are exhibited in the transmission from normal to normal lead as a consequence of quantum interference and proximity effect. This Fano effect produced by Andreev bound states in a side quantum dot was called Fano-Andreev effect, which remains valid even if the electron-electron interaction are taken into account, that is, the Fano-Andreev effect is robust against e-e interactions even in Kondo regime. We acknowledge the financial support from FONDECYT program Grants No. 3140053 and 11400571.
Evolution of Plasmonic Metamolecule Modes in the Quantum Tunneling Regime.
Scholl, Jonathan A; Garcia-Etxarri, Aitzol; Aguirregabiria, Garikoitz; Esteban, Ruben; Narayan, Tarun C; Koh, Ai Leen; Aizpurua, Javier; Dionne, Jennifer A
2016-01-26
Plasmonic multinanoparticle systems exhibit collective electric and magnetic resonances that are fundamental for the development of state-of-the-art optical nanoantennas, metamaterials, and surface-enhanced spectroscopy substrates. While electric dipolar modes have been investigated in both the classical and quantum realm, little attention has been given to magnetic and other "dark" modes at the smallest dimensions. Here, we study the collective electric, magnetic, and dark modes of colloidally synthesized silver nanosphere trimers with varying interparticle separation using scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy (EELS). This technique enables direct visualization and spatially selective excitation of individual trimers, as well as manipulation of the interparticle distance into the subnanometer regime with the electron beam. Our experiments reveal that bonding electric and magnetic modes are significantly impacted by quantum effects, exhibiting a relative blueshift and reduced EELS amplitude compared to classical predictions. In contrast, the trimer's electric dark mode is not affected by quantum tunneling for even Ångström-scale interparticle separations. We employ a quantum-corrected model to simulate the effect of electron tunneling in the trimer which shows excellent agreement with experimental results. This understanding of classical and quantum-influenced hybridized modes may impact the development of future quantum plasmonic materials and devices, including Fano-like molecular sensors and quantum metamaterials. PMID:26639023
Evolution of Plasmonic Metamolecule Modes in the Quantum Tunneling Regime.
Scholl, Jonathan A; Garcia-Etxarri, Aitzol; Aguirregabiria, Garikoitz; Esteban, Ruben; Narayan, Tarun C; Koh, Ai Leen; Aizpurua, Javier; Dionne, Jennifer A
2016-01-26
Plasmonic multinanoparticle systems exhibit collective electric and magnetic resonances that are fundamental for the development of state-of-the-art optical nanoantennas, metamaterials, and surface-enhanced spectroscopy substrates. While electric dipolar modes have been investigated in both the classical and quantum realm, little attention has been given to magnetic and other "dark" modes at the smallest dimensions. Here, we study the collective electric, magnetic, and dark modes of colloidally synthesized silver nanosphere trimers with varying interparticle separation using scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy (EELS). This technique enables direct visualization and spatially selective excitation of individual trimers, as well as manipulation of the interparticle distance into the subnanometer regime with the electron beam. Our experiments reveal that bonding electric and magnetic modes are significantly impacted by quantum effects, exhibiting a relative blueshift and reduced EELS amplitude compared to classical predictions. In contrast, the trimer's electric dark mode is not affected by quantum tunneling for even Ångström-scale interparticle separations. We employ a quantum-corrected model to simulate the effect of electron tunneling in the trimer which shows excellent agreement with experimental results. This understanding of classical and quantum-influenced hybridized modes may impact the development of future quantum plasmonic materials and devices, including Fano-like molecular sensors and quantum metamaterials.
Disorder-assisted quantum transport in suboptimal decoherence regimes
NASA Astrophysics Data System (ADS)
Novo, Leonardo; Mohseni, Masoud; Omar, Yasser
2016-01-01
We investigate quantum transport in binary tree structures and in hypercubes for the disordered Frenkel-exciton Hamiltonian under pure dephasing noise. We compute the energy transport efficiency as a function of disorder and dephasing rates. We demonstrate that dephasing improves transport efficiency not only in the disordered case, but also in the ordered one. The maximal transport efficiency is obtained when the dephasing timescale matches the hopping timescale, which represent new examples of the Goldilocks principle at the quantum scale. Remarkably, we find that in weak dephasing regimes, away from optimal levels of environmental fluctuations, the average effect of increasing disorder is to improve the transport efficiency until an optimal value for disorder is reached. Our results suggest that rational design of the site energies statistical distributions could lead to better performances in transport systems at nanoscale when their natural environments are far from the optimal dephasing regime.
Disorder-assisted quantum transport in suboptimal decoherence regimes
Novo, Leonardo; Mohseni, Masoud; Omar, Yasser
2016-01-01
We investigate quantum transport in binary tree structures and in hypercubes for the disordered Frenkel-exciton Hamiltonian under pure dephasing noise. We compute the energy transport efficiency as a function of disorder and dephasing rates. We demonstrate that dephasing improves transport efficiency not only in the disordered case, but also in the ordered one. The maximal transport efficiency is obtained when the dephasing timescale matches the hopping timescale, which represent new examples of the Goldilocks principle at the quantum scale. Remarkably, we find that in weak dephasing regimes, away from optimal levels of environmental fluctuations, the average effect of increasing disorder is to improve the transport efficiency until an optimal value for disorder is reached. Our results suggest that rational design of the site energies statistical distributions could lead to better performances in transport systems at nanoscale when their natural environments are far from the optimal dephasing regime. PMID:26726133
Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor
NASA Astrophysics Data System (ADS)
Arrachea, Liliana; von Oppen, Felix
2015-11-01
The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer-Büttiker theory. Scattering theory provides a microscopic derivation of the Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.
NASA Astrophysics Data System (ADS)
Ganeshan, Sriram; Kechedzhi, K.; Das Sarma, S.
2014-07-01
One-dimensional tight binding models such as the Aubry-André-Harper (AAH) model (with an on-site cosine potential) and the integrable Maryland model (with an on-site tangent potential) have been the subject of extensive theoretical research in localization studies. AAH can be directly mapped onto the two-dimensional (2D) Hofstadter model which manifests the integer quantum Hall topology on a lattice. However, such a connection needs to be made for the Maryland model (MM). Here we describe a generalized model that contains AAH and MM as the limiting cases with the MM lying precisely at a topological quantum phase transition (TQPT) point. A remarkable feature of this critical point is that the one-dimensional MM retains well defined energy gaps whereas the equivalent 2D model becomes gapless, signifying the 2D nature of the TQPT.
Reprint of : Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor
NASA Astrophysics Data System (ADS)
Arrachea, Liliana; von Oppen, Felix
2016-08-01
The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer-Büttiker theory. Scattering theory provides a microscopic derivation of the Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.
Universal Quantum Computation From 2/3 Bilayer Quantum Hall States
NASA Astrophysics Data System (ADS)
Vaezi, Abolhassan; Barkeshli, Maissam
2015-03-01
In this talk, I consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer, in the presence of interlayer tunneling. I show that interlayer tunneling can drive a continuous phase transition to an exotic non-Abelian state that contains the famous ``Fibonacci anyon,'' whose non-Abelian statistics is powerful enough for universal topological quantum computation. The analysis that I will present towards this result rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. The charge gap remains open at the phase transition while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν = 2 / 3 in bilayers, as past experiments may not have definitively ruled them out.
Signature candidate of quantum chaos far from the semiclassical regime
Li, Shang-Bin Xu, Zhengyuan
2014-03-15
We numerically investigated the entanglement product in the simplest coupled kicked top model with the spin j = 1. Different from the dynamical pattern of entanglement in the semiclassical regime, two similar initial states may have discordant entanglement oscillations. A candidate of the quantum signature of this classical chaotic system was proposed. The potential antimonotonic relation between the rank correlation coefficient qualifying the concordant of two entanglement evolutions and the stationary entanglement was preliminarily revealed.
NASA Astrophysics Data System (ADS)
Shimizu, Yosuke; Yamakage, Ai; Nomura, Kentaro
2015-05-01
We study the quantum anomalous thermal Hall effect in a topological superconductor, which possesses an integer bulk topological number and supports Majorana excitations on the surface. To realize the quantum thermal Hall effect, a finite gap at the surface is induced by applying an external magnetic field or by the proximity effects with magnetic materials or s -wave superconductors with complex pair potentials. Basing on the lattice model Hamiltonian for superconducting states in Cu-doped Bi2Se3 , we compute the thermal Hall conductivity as a function of various parameters such as the chemical potential, the pair potential, and the spin-orbit coupling-induced band gap. It is argued that the bulk topological invariant corresponds to the quantization rule of the thermal Hall conductivity induced by complex s -wave pair potentials.
Quasiparticle Tunneling in the Fractional Quantum Hall effect at filling fraction ν=5/2
NASA Astrophysics Data System (ADS)
Radu, Iuliana P.
2009-03-01
In a two-dimensional electron gas (2DEG), in the fractional quantum Hall regime, the quasiparticles are predicted to have fractional charge and statistics, as well as modified Coulomb interactions. The state at filling fraction ν=5/2 is predicted by some theories to have non-abelian statistics, a property that might be exploited for topological quantum computing. However, alternative models with abelian properties have been proposed as well. Weak quasiparticle tunneling between counter-propagating edges is one of the methods that can be used to learn about the properties of the state and potentially distinguish between models describing it. We employ an electrostatically defined quantum point contact (QPC) fabricated on a high mobility GaAs/AlGaAs 2DEG to create a constriction where quasiparticles can tunnel between counter-propagating edges. We study the temperature and dc bias dependence of the tunneling conductance, while preserving the same filling fraction in the constriction and the bulk of the sample. The data show scaling of the bias-dependent tunneling over a range of temperatures, in agreement with the theory of weak quasiparticle tunneling, and we extract values for the effective charge and interaction parameter of the quasiparticles. The ranges of values obtained are consistent with those predicted by certain models describing the 5/2 state, indicating as more probable a non-abelian state. This work was done in collaboration with J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer and K. W. West. This work was supported in part by the Army Research Office (W911NF-05-1-0062), the Nanoscale Science and Engineering Center program of NSF (PHY-0117795), NSF (DMR-0701386), the Center for Materials Science and Engineering program of NSF (DMR-0213282) at MIT, the Microsoft Corporation Project Q, and the Center for Nanoscale Systems at Harvard University.
Quantum anomalous Hall effect and tunable topological states in 3d transition metals doped silicene.
Zhang, Xiao-Long; Liu, Lan-Feng; Liu, Wu-Ming
2013-01-01
Silicene is an intriguing 2D topological material which is closely analogous to graphene but with stronger spin orbit coupling effect and natural compatibility with current silicon-based electronics industry. Here we demonstrate that silicene decorated with certain 3d transition metals (Vanadium) can sustain a stable quantum anomalous Hall effect using both analytical model and first-principles Wannier interpolation. We also predict the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition metal doped silicene where the energy band inversion occurs. Our findings provide new scheme for the realization of quantum anomalous Hall effect and platform for electrically controllable topological states which are highly desirable for future nanoelectronics and spintronics application. PMID:24105063
Split-quaternionic Hopf map, quantum Hall effect, and twistor theory
Hasebe, Kazuki
2010-02-15
Introducing a noncompact version of the Hopf map, we demonstrate remarkable close relations between quantum Hall effect and twistor theory. We first construct quantum Hall effect on a hyperboloid based on the noncompact 2nd Hopf map of split-quaternions. We analyze a hyperbolic one-particle mechanics, and explore many-body problem, where a many-body ground state wave function and membrane-like excitations are derived explicitly. In the lowest Landau level, the symmetry is enhanced from SO(3,2) to the SU(2,2) conformal symmetry. We point out that the quantum Hall effect naturally realizes the philosophy of twistor theory. In particular, emergence mechanism of fuzzy space-time is discussed somehow in detail.
Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Gromov, Andrey; Abanov, Alexander; Cho, Gil Young; You, Yizhi; Fradkin, Eduardo
2015-03-01
While the classical Chern-Simons theory is topological, it's quantum version is not as it depends on the metric of the base manifold through the path integral measure. This phenomenon is known as the framing anomaly. It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions of fractional quantum Hall systems (FQH). In the lowest order in gradients the effective action includes Chern-Simons, Wen-Zee and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and generates a ``finite size correction'' to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses of non-Abelian FQH states.
Suppression of interference in quantum Hall Mach-Zehnder geometry by upstream neutral modes
NASA Astrophysics Data System (ADS)
Gefen, Yuval; Goldstein, Moshe
Mach-Zehnder interferometry has been suggested as a probe for anyonic quasiparticles in fractional quantum Hall states. However, all experimental attempts to measure such an interference signal have failed to date, despite the high visibility of interference fringes in the integer quantum Hall case. In our work we have studied the relation between this null result and another recent surprising experimental finding, namely the detection of upstream neutral modes in virtually all fractional quantum Hall states (including, e.g., filling 1/3), not only in hole-like filling factors (such as 2/3). We have found that the excitation of upstream modes makes the interference visibility in the Mach-Zehnder geometry decay exponentially with the total length of the interferometer arms, even when the lengths are exactly equal. We also suggest ways to overcome this suppression.
Engineering the quantum anomalous Hall effect in graphene with uniaxial strains
NASA Astrophysics Data System (ADS)
Diniz, G. S.; Guassi, M. R.; Qu, F.
2013-12-01
We theoretically investigate the manipulation of the quantum anomalous Hall effect (QAHE) in graphene by means of the uniaxial strain. The values of Chern number and Hall conductance demonstrate that the strained graphene in presence of Rashba spin-orbit coupling and exchange field, for vanishing intrinsic spin-orbit coupling, possesses non-trivial topological phase, which is robust against the direction and modulus of the strain. Besides, we also find that the interplay between Rashba and intrinsic spin-orbit couplings results in a topological phase transition in the strained graphene. Remarkably, as the strain strength is increased beyond approximately 7%, the critical parameters of the exchange field for triggering the quantum anomalous Hall phase transition show distinct behaviors—decrease (increase) for strains along zigzag (armchair) direction. Our findings open up a new platform for manipulation of the QAHE by an experimentally accessible strain deformation of the graphene structure, with promising application on novel quantum electronic devices with high efficiency.
Metallic phase of the quantum Hall effect in four-dimensional space
NASA Astrophysics Data System (ADS)
Edge, Jonathan; Tworzydlo, Jakub; Beenakker, Carlo
2013-03-01
We study the phase diagram of the quantum Hall effect in four-dimensional (4D) space. Unlike in 2D, in 4D there exists a metallic as well as an insulating phase, depending on the disorder strength. The critical exponent ν ~ 1 . 2 of the diverging localization length at the quantum Hall insulator-to-metal transition differs from the semiclassical value ν = 1 of 4D Anderson transitions in the presence of time-reversal symmetry. Our numerical analysis is based on a mapping of the 4D Hamiltonian onto a 1D dynamical system, providing a route towards the experimental realization of the 4D quantum Hall effect. NanoCTM, FOM/NWO, ERC
Effective field theory and projective construction for Zk parafermion fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Barkeshli, Maissam; Wen, Xiao-Gang
2010-04-01
The projective construction is a powerful approach to deriving the bulk and edge field theories of non-Abelian fractional quantum Hall (FQH) states and yields an understanding of non-Abelian FQH states in terms of the simpler integer quantum Hall states. Here we show how to apply the projective construction to the Zk parafermion (Laughlin/Moore-Read/Read-Rezayi) FQH states, which occur at filling fraction ν=k/(kM+2) . This allows us to derive the bulk low-energy effective field theory for these topological phases, which is found to be a Chern-Simons theory at level 1 with a U(M)×Sp(2k) gauge field. This approach also helps us understand the non-Abelian quasiholes in terms of holes of the integer quantum Hall states.
Fragility of Nonlocal Edge-Mode Transport in the Quantum Spin Hall State
NASA Astrophysics Data System (ADS)
Mani, Arjun; Benjamin, Colin
2016-07-01
Nonlocal currents and voltages are better at withstanding the deleterious effects of dephasing than local currents and voltages in nanoscale systems. This hypothesis is known to be true in quantum Hall setups. We test this hypothesis in a four-terminal quantum spin Hall setup wherein we compare the local resistance measurement with the nonlocal one. In addition to inelastic-scattering-induced dephasing, we also test the resilience of the resistance measurements in the aforesaid setups to disorder and spin-flip scattering. We find the axiom that nonlocal resistance is less affected by the detrimental effects of disorder and dephasing to be untrue, in general, for the quantum spin Hall case. This has important consequences since it is widely communicated that nonlocal transport through edge channels in topological insulators have potential applications in low-power information processing.
Mukherjee, Sutirtha; Mandal, Sudhansu S
2015-04-17
We show a generic formation of the primary magnetorotons in the collective modes of the observed "unconventional" fractional quantum Hall effect states of the composite fermions at the filling factors 4/11, 4/13, 5/13, 5/17, and 3/8 at very low wave vectors with anomalously low energies which do not have any analog to the conventional fractional quantum Hall states. Rather slow decay of the oscillations of the pair-correlation functions in these states is responsible for the low-energy magnetorotons. This is a manifestation of the distinct topology predicted previously for these fractional quantum Hall effect states. Experimental consequences of our theory are also discussed.
Tunable band topology reflected by fractional quantum Hall States in two-dimensional lattices.
Wang, Dong; Liu, Zhao; Cao, Junpeng; Fan, Heng
2013-11-01
Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from the Hofstadter model and demonstrate that the band topology transitions can be realized by simply introducing tunable longer-range hopping. The rich phase diagram of band Chern numbers is obtained for the simple rational flux density and a classification of phases is presented. In the presence of interactions, the existence of fractional quantum Hall states in both |C| = 1 and |C| > 1 bands is confirmed, which can reflect the band topologies in different phases. In contrast, when our model reduces to a one-dimensional lattice, the ground states are crucially different from fractional quantum Hall states. Our results may provide insights into the study of new fractional quantum Hall states and experimental realizations of various topological phases in optical lattices.
Morimoto, Takahiro; Aoki, Hideo
2013-12-04
Flow diagram of (σ{sub xx},σ{sub xy}) in finite-frequency (ω) regime is numerically studied for the graphene quantum Hall effect (QHE). In a small-ω regime, the ac flow diagram exhibits a behavior qualitatively similar to the dc flow diagram, where the dynamical length scale acts as a cutoff in the ac region, and the flows are between σ{sub xy} = ±(1/2)e{sup 2}/h reflecting the graphene QHE. The dynamical flow is compared with the temperature-driven flow.
Spin-orbit coupling and quantum spin Hall effect for neutral atoms without spin flips.
Kennedy, Colin J; Siviloglou, Georgios A; Miyake, Hirokazu; Burton, William Cody; Ketterle, Wolfgang
2013-11-27
We propose a scheme which realizes spin-orbit coupling and the quantum spin Hall effect for neutral atoms in optical lattices without relying on near resonant laser light to couple different spin states. The spin-orbit coupling is created by modifying the motion of atoms in a spin-dependent way by laser recoil. The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient. Alternatively, a quantum spin Hall Hamiltonian can be created by all-optical means using a period-tripling, spin-dependent superlattice. PMID:24329453
Large-Chern-number quantum anomalous Hall effect in thin-film topological crystalline insulators.
Fang, Chen; Gilbert, Matthew J; Bernevig, B Andrei
2014-01-31
We theoretically predict that thin-film topological crystalline insulators can host various quantum anomalous Hall phases when doped by ferromagnetically ordered dopants. Any Chern number between ±4 can, in principle, be reached as a result of the interplay between (a) the induced Zeeman field, depending on the magnetic doping concentration, (b) the structural distortion, either intrinsic or induced by a piezoelectric material through the proximity effect, and (c) the thickness of the thin film. We propose a heterostructure to realize quantum anomalous Hall phases with Chern numbers that can be tuned by electric fields. PMID:24580476
Tomimatsu, Toru Shirai, Shota; Hashimoto, Katsushi Sato, Ken; Hirayama, Yoshiro
2015-08-15
Electric-field-induced nuclear resonance (NER: nuclear electric resonance) involving quantum Hall states (QHSs) was studied at various filling factors by exploiting changes in nuclear spins polarized at quantum Hall breakdown. Distinct from the magnetic dipole interaction in nuclear magnetic resonance, the interaction of the electric-field gradient with the electric quadrupole moment plays the dominant role in the NER mechanism. The magnitude of the NER signal strongly depends on whether electronic states are localized or extended. This indicates that NER is sensitive to the screening capability of the electric field associated with QHSs.
Exact conductance through point contacts in the {nu}=1/3 fractional quantum Hall Effect
Fendley, P.; Ludwig, A.W.W.; Saleur, H. |
1995-04-10
The conductance for tunneling through an impurity in a Luttinger liquid is described by a universal scaling function. We compute this scaling function exactly, by using the thermodynamic Bethe ansatz and a kinetic (Boltzmann) equation. This model has been proposed to describe resonant tunneling through a point contact between two {nu}=1/3 quantum Hall edges. Recent experiments on quantum Hall devices agree well with our exact results. We also derive the exact conductance and {ital I}({ital V}) curve, out of equilibrium, in this fully interacting system.
Simulating and detecting the quantum spin Hall effect in the kagome optical lattice
Liu Guocai; Jiang Shaojian; Sun Fadi; Liu, W. M.; Zhu Shiliang
2010-11-15
We propose a model which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian in the kagome lattice and promises to host the transition from the quantum spin Hall insulator to the normal insulator. In addition, we design an experimental scheme to simulate and detect this transition in the ultracold atom system. The lattice intrinsic spin-orbit coupling is generated via the laser-induced-gauge-field method. Furthermore, we establish the connection between the spin Chern number and the spin-atomic density which enables us to detect the quantum spin Hall insulator directly by the standard density-profile technique used in atomic systems.
Bernevig, B Andrei; Haldane, F D M
2009-02-13
We present model wave functions for quasielectron (as opposed to quasihole) excitations of the unitary Z_{k} parafermion sequence (Laughlin, Moore-Read, or Read-Rezayi) of fractional quantum Hall states. We uniquely define these states through two generalized clustering conditions: they vanish when either a cluster of k+2 electrons is put together or when two clusters of k+1 electrons are formed at different positions. For Abelian fractional quantum Hall states (k=1), our construction reproduces the Jain quasielectron wave function and elucidates the difference between the Jain and Laughlin quasielectrons. PMID:19257618
NASA Astrophysics Data System (ADS)
Bernevig, B. Andrei; Haldane, F. D. M.
2009-02-01
We present model wave functions for quasielectron (as opposed to quasihole) excitations of the unitary Zk parafermion sequence (Laughlin, Moore-Read, or Read-Rezayi) of fractional quantum Hall states. We uniquely define these states through two generalized clustering conditions: they vanish when either a cluster of k+2 electrons is put together or when two clusters of k+1 electrons are formed at different positions. For Abelian fractional quantum Hall states (k=1), our construction reproduces the Jain quasielectron wave function and elucidates the difference between the Jain and Laughlin quasielectrons.
Role of the spin connection in quantum Hall effect: A perspective from geometric quantization
NASA Astrophysics Data System (ADS)
Karabali, Dimitra; Nair, V. P.
2016-09-01
The topological terms of the bulk effective action for the integer quantum Hall effect, capturing the dynamics of gauge and gravitational fluctuations, reveal a curiosity, namely, the Abelian potential for the magnetic field appears in a particular combination with the Abelian spin connection. This seems to hold for the quantum Hall effect on complex projective spaces of arbitrary dimensions. An interpretation of this in terms of the algebra of symplectic transformations is given. This can also be viewed in terms of the metaplectic correction in geometric quantization.
NASA Astrophysics Data System (ADS)
Zhou, Jian; Sun, Qiang; Wang, Qian; Kawazoe, Yoshiyuki; Jena, Puru
2016-05-01
Exploring a two-dimensional intrinsic quantum spin Hall state with a large band gap as well as an anomalous Hall state in realizable materials is one of the most fundamental and important goals for future applications in spintronics, valleytronics, and quantum computing. Here, by combining first-principles calculations with a tight-binding model, we predict that Sb or Bi can epitaxially grow on a stable and ferromagnetic MnO2 thin film substrate, forming a flat honeycomb sheet. The flatness of Sb or Bi provides an opportunity for the existence of Dirac points in the Brillouin zone, with its position effectively tuned by surface hydrogenation. The Dirac points in spin up and spin down channels split due to the proximity effects induced by MnO2. In the presence of both intrinsic and Rashba spin-orbit coupling, we find two band gaps exhibiting a large band gap quantum spin Hall state and a nearly quantized anomalous Hall state which can be tuned by adjusting the Fermi level. Our findings provide an efficient way to realize both quantized intrinsic spin Hall conductivity and anomalous Hall conductivity in a single material.Exploring a two-dimensional intrinsic quantum spin Hall state with a large band gap as well as an anomalous Hall state in realizable materials is one of the most fundamental and important goals for future applications in spintronics, valleytronics, and quantum computing. Here, by combining first-principles calculations with a tight-binding model, we predict that Sb or Bi can epitaxially grow on a stable and ferromagnetic MnO2 thin film substrate, forming a flat honeycomb sheet. The flatness of Sb or Bi provides an opportunity for the existence of Dirac points in the Brillouin zone, with its position effectively tuned by surface hydrogenation. The Dirac points in spin up and spin down channels split due to the proximity effects induced by MnO2. In the presence of both intrinsic and Rashba spin-orbit coupling, we find two band gaps exhibiting a large
Hořava-Lifshitz gravity and effective theory of the fractional quantum Hall effect
NASA Astrophysics Data System (ADS)
Wu, Chaolun; Wu, Shao-Feng
2015-01-01
We show that Hořava-Lifshitz gravity theory can be employed as a covariant framework to build an effective field theory for the fractional quantum Hall effect that respects all the spacetime symmetries such as non-relativistic diffeomorphism invariance and anisotropic Weyl invariance as well as the gauge symmetry. The key to this formalism is a set of correspondence relations that maps all the field degrees of freedom in the Hořava-Lifshitz gravity theory to external background (source) fields among others in the effective action of the quantum Hall effect, according to their symmetry transformation properties. We originally derive the map as a holographic dictionary, but its form is independent of the existence of holographic duality. This paves the way for the application of Hořava-Lifshitz holography on fractional quantum Hall effect. Using the simplest holographic Chern-Simons model, we compute the low energy effective action at leading orders and show that it captures universal electromagnetic and geometric properties of quantum Hall states, including the Wen-Zee shift, Hall viscosity, angular momentum density and their relations. We identify the shift function in Hořava-Lifshitz gravity theory as minus of guiding center velocity and conjugate to guiding center momentum. This enables us to distinguish guiding center angular momentum density from the internal one, which is the sum of Landau orbit spin and intrinsic (topological) spin of the composite particles. Our effective action shows that Hall viscosity is minus half of the internal angular momentum density and proportional to Wen-Zee shift, and Hall bulk viscosity is half of the guiding center angular momentum density.
Broken SU(4) Symmetry and The Fractional Quantum Hall Effect in Graphene
NASA Astrophysics Data System (ADS)
Sodemann, Inti; MacDonald, Allan
2014-03-01
We describe a simple variational approach to understand the spin-valley broken symmetry states in the fractional quantum Hall regime of graphene. Our approach allows to predict the incompressible ground states and their charge gaps and is able to explain the observed differences between filling factor ranges | ν | < 1 and 1 < | ν | < 2 . We find that in the SU(4) invariant case the incompressible ground state at | ν | = 1 / 3 is a three-component incompressible state, not the Laughlin state, and discuss the competition between these two states in the presence of SU(4) spin-valley symmetry breaking terms. We find that the lowest energy fractionally charged quasi-particles involve spin/valley flips in several prominent fractions. We discuss the expected behavior of the gaps under tilting the magnetic field away from normal which allows to tune the relative strength of Zeeman and valley symmetry breaking interactions. Supported by DOE Division of Materials Sciences and Engineering under grant DE-FG03-02ER45958 and by the Welch foundation under grant TBF1473.
Fermi pockets and quantum oscillations of the Hall coefficient in high-temperature superconductors
Chakravarty, Sudip; Kee, Hae-Young
2008-01-01
Recent quantum oscillation measurements in high-temperature superconductors in high magnetic fields and low temperatures have ushered in a new era. These experiments explore the normal state from which superconductivity arises and provide evidence of a reconstructed Fermi surface consisting of electron and hole pockets in a regime in which such a possibility was previously considered to be remote. More specifically, the Hall coefficient has been found to oscillate according to the Onsager quantization condition, involving only fundamental constants and the areas of the pockets, but with a sign that is negative. Here, we explain the observations with the theory that the alleged normal state exhibits a hidden order, the d-density wave, which breaks symmetries signifying time reversal, translation by a lattice spacing, and a rotation by an angle π/2, while the product of any two symmetry operations is preserved. The success of our analysis underscores the importance of spontaneous breaking of symmetries, Fermi surface reconstruction, and conventional quasiparticles. We primarily focus on the version of the order that is commensurate with the underlying crystalline lattice, but we also touch on the consequences if the order were to incommensurate. It is shown that whereas commensurate order results in two independent oscillation frequencies as a function of the inverse of the applied magnetic field, incommensurate order leads to three independent frequencies. The oscillation amplitudes, however, are determined by the mobilities of the charge carriers comprising the Fermi pockets. PMID:18577585
Tunneling at νT = 1 in a bilayer quantum Hall exciton condensate
NASA Astrophysics Data System (ADS)
Nandi, D.; Khaire, T.; Finck, A. D. K.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2014-03-01
Closely-spaced bilayer quantum Hall systems at total filling factor νT = 1 exhibit spontaneous interlayer phase coherence. This phase coherence, which is tantamount to excitonic Bose condensation, is most dramatically revealed via interlayer tunneling measurements.In the condensed phase the tunneling current-voltage (IV) characteristic of this semiconductor system strongly resembles the dc Josephson effect observed in superconducting tunnel junctions. Here we report on a detailed study of this phenomenon. We find the maximum, or critical tunneling current Ic to be a well-defined global property of the macroscopic tunnel junction, insensitive to external circuit elements and the precise contact configuration used to observe it. Interestingly, the temperature dependence of Ic displays an unexpected scaling behavior. At the lowest temperatures the slope of the ``supercurrent'' branch of the tunneling IV curve, while extremely large, remains finite. Careful measurements in this regime suggest that dissipative processes arising from in-plane exciton transport limit the maximum tunneling conductance. Finally, comparisons of the experimentally observed IV with recent theoretical predictions will be discussed.
Condensation of lattice defects and melting transitions in quantum Hall phases
NASA Astrophysics Data System (ADS)
Cho, Gil Young; Parrikar, Onkar; You, Yizhi; Leigh, Robert G.; Hughes, Taylor L.
2015-01-01
Motivated by recent progress in understanding the interplay between lattice and electronic topological phases, we consider quantum-melting transitions of weak quantum liquid crystals, a crystal and a nematic phase, in which electrons form a quantum Hall state. In certain classes of Chern band insulators and quantum Hall phases, it has been previously demonstrated that there are topological Chern-Simons terms such as a Hall viscosity term and a gravitational Chern-Simons term for local lattice deformations. The Chern-Simons terms can induce anyonic statistics for the topological lattice defects and, furthermore, dress the defects with certain symmetry quantum numbers. On the other hand, the melting transitions of such liquid-crystalline orders are driven by the condensation of lattice defects. Based on these observations, we show how the topological terms can change the nature of the proximate disordered phases of the quantum liquid-crystalline phases. We derive and study the effective dual field theories for the liquid-crystalline phases with the geometric Chern-Simons terms, and carefully examine the symmetry quantum numbers and statistics of defects. We show that a crystal may go through a continuous phase transition into another crystal with the different discrete translational symmetries because the dislocation, the topological defect in the crystal, carries nonzero crystal momentum due to the Hall viscosity term. For the nematic phase, the disclination will condense at the phase transition to the isotropic phase, and we show that the isotropic phase may support a deconfined fractionally charged excitation due to the Wen-Zee term, and thus the isotropic phase and the nematic phase have different electromagnetic Hall responses.
Quantum spin Hall effect in α -Sn /CdTe(001 ) quantum-well structures
NASA Astrophysics Data System (ADS)
Küfner, Sebastian; Matthes, Lars; Bechstedt, Friedhelm
2016-01-01
The electronic and topological properties of heterovalent and heterocrystalline α -Sn/CdTe(001) quantum wells (QWs) are studied in dependence on the thickness of α -Sn by means of ab initio calculations. We calculate the topological Z2 invariants of the respective bulk crystals, which identify α -Sn as strong three-dimensional (3D) topological insulators (TIs), whereas CdTe is a trivial insulator. We predict the existence of two-dimensional (2D) topological interface states between both materials and show that a topological phase transition from a trivial insulating phase into the quantum spin Hall (QSH) phase in the QW structures occurs at much higher thicknesses than in the HgTe case. The QSH effect is characterized by the localization, dispersion, and spin polarization of the topological interface states. We address the distinction of the 3D and 2D TI characters of the studied QW structures, which is inevitable for an understanding of the underlying quantum state of matter. The 3D TI nature is characterized by two-dimensional topological interface states, while the 2D phase exhibits one-dimensional edge states. The two different state characteristics are often intermixed in the discussion of the topology of 2D QW structures, especially, the comparison of ab initio calculations and experimental transport studies.
Realizing Tao-Thouless-like state in fractional quantum spin Hall effect.
Liu, Chen-Rong; Guo, Yao-Wu; Li, Zhuo-Jun; Li, Wei; Chen, Yan
2016-01-01
The quest for exotic quantum states of matter has become one of the most challenging tasks in modern condensed matter communications. Interplay between topology and strong electron-electron interactions leads to lots of fascinating effects since the discovery of the fractional quantum Hall effect. Here, we theoretically study the Rashba-type spin-orbit coupling effect on a fractional quantum spin Hall system by means of finite size exact diagonalization. Numerical evidences from the ground degeneracies, states evolutions, entanglement spectra, and static structure factor calculations demonstrate that non-trivial fractional topological Tao-Thouless-like quantum state can be realized in the fractional quantum spin Hall effect in a thin torus geometric structure by tuning the strength of spin-orbit coupling. Furthermore, the experimental realization of the Tao-Thouless-like state as well as its evolution in optical lattices are also proposed. The importance of this prediction provides significant insight into the realization of exotic topological quantum states in optical lattice, and also opens a route for exploring the exotic quantum states in condensed matters in future. PMID:27649678
Realizing Tao-Thouless-like state in fractional quantum spin Hall effect
Liu, Chen-Rong; Guo, Yao-Wu; Li, Zhuo-Jun; Li, Wei; Chen, Yan
2016-01-01
The quest for exotic quantum states of matter has become one of the most challenging tasks in modern condensed matter communications. Interplay between topology and strong electron-electron interactions leads to lots of fascinating effects since the discovery of the fractional quantum Hall effect. Here, we theoretically study the Rashba-type spin-orbit coupling effect on a fractional quantum spin Hall system by means of finite size exact diagonalization. Numerical evidences from the ground degeneracies, states evolutions, entanglement spectra, and static structure factor calculations demonstrate that non-trivial fractional topological Tao-Thouless-like quantum state can be realized in the fractional quantum spin Hall effect in a thin torus geometric structure by tuning the strength of spin-orbit coupling. Furthermore, the experimental realization of the Tao-Thouless-like state as well as its evolution in optical lattices are also proposed. The importance of this prediction provides significant insight into the realization of exotic topological quantum states in optical lattice, and also opens a route for exploring the exotic quantum states in condensed matters in future. PMID:27649678
Realizing Tao-Thouless-like state in fractional quantum spin Hall effect.
Liu, Chen-Rong; Guo, Yao-Wu; Li, Zhuo-Jun; Li, Wei; Chen, Yan
2016-09-21
The quest for exotic quantum states of matter has become one of the most challenging tasks in modern condensed matter communications. Interplay between topology and strong electron-electron interactions leads to lots of fascinating effects since the discovery of the fractional quantum Hall effect. Here, we theoretically study the Rashba-type spin-orbit coupling effect on a fractional quantum spin Hall system by means of finite size exact diagonalization. Numerical evidences from the ground degeneracies, states evolutions, entanglement spectra, and static structure factor calculations demonstrate that non-trivial fractional topological Tao-Thouless-like quantum state can be realized in the fractional quantum spin Hall effect in a thin torus geometric structure by tuning the strength of spin-orbit coupling. Furthermore, the experimental realization of the Tao-Thouless-like state as well as its evolution in optical lattices are also proposed. The importance of this prediction provides significant insight into the realization of exotic topological quantum states in optical lattice, and also opens a route for exploring the exotic quantum states in condensed matters in future.
Quantum Theory as a Critical Regime of Language Dynamics
NASA Astrophysics Data System (ADS)
Grinbaum, Alexei
2015-10-01
Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the continuity assumption as two pillars of quantum theory. Our approach sits on these pillars and combines new mathematics with a testable prediction. If the observer is defined by a limit on string complexity, information dynamics leads to an emergent continuous model in the critical regime. Restricting it to a family of binary codes describing `bipartite systems,' we find strong evidence of an upper bound on bipartite correlations equal to 2.82537. This is measurably different from the Tsirelson bound. The Hilbert space formalism emerges from this mathematical investigation as an effective description of a fundamental discrete theory in the critical regime.
From Floquet to Dicke: Quantum Spin Hall Insulator Interacting with Quantum Light.
Gulácsi, Balázs; Dóra, Balázs
2015-10-16
Time-periodic perturbations due to classical electromagnetic fields are useful to engineer the topological properties of matter using the Floquet theory. Here we investigate the effect of quantized electromagnetic fields by focusing on the quantized light-matter interaction on the edge state of a quantum spin Hall insulator. A Dicke-type superradiant phase transition occurs at arbitrary weak coupling, the electronic spectrum acquires a finite gap, and the resulting ground-state manifold is topological with a Chern number of ±1. When the total number of excitations is conserved, a photocurrent is generated along the edge, being pseudoquantized as ωln(1/ω) in the low-frequency limit and decaying as 1/ω for high frequencies with ω the photon frequency. The photon spectral function exhibits a clean Goldstone mode, a Higgs-like collective mode at the optical gap and the polariton continuum.
Half integer features in the quantum Hall Effect: experiment and theory
NASA Astrophysics Data System (ADS)
Kramer, Tobias; Heller, E. J.; Parrott, R. E.; Liang, C.-T.; Huang, C. F.; Chen, K. Y.; Lin, L.-H.; Wu, J.-Y.; Lin, S.-D.
2009-03-01
We discuss experimental data and a new model of the integer quantum Hall effect (IQHE), which explains an intriguing substructure within Landau levels observed at higher currents. The experiments show inflection points in the Hall resistivity around filling factors 5/2 and 7/2. The experiments require to revisit the foundations of the IQHE and to establish an injection model which incorporates the correct boundary conditions imposed by a real Hall device and the Lorentz force. We have to follow the electrons to their source: one corner of the Hall bar and its steep electric field gradients, rather than focusing on the middle of the Hall device. We find the entire Hall resistivity curve is calculable as a function of magnetic field, temperature, and current. In contrast to previous theories of the IQHE, disorder plays no fundamental role in our theory. Contrary to the standard picture of Landau levels in disorder system, we predict and observe gaps right in the middle of certain Landau levels. The Hall plateaus and half integer inflections are shown to result from the LDOS appropriate to the magnetic field and the strong electric field at the injection corner.
Theory of the three-dimensional quantum Hall effect in graphite.
Bernevig, B Andrei; Hughes, Taylor L; Raghu, Srinivas; Arovas, Daniel P
2007-10-01
We predict the existence of a three-dimensional quantum Hall effect plateau in a graphite crystal subject to a magnetic field. The plateau has a Hall conductivity quantized at 4e2/variant Planck's over 2pi 1/c0 with c0 the c-axis lattice constant. We analyze the three-dimensional Hofstadter problem of a realistic tight-binding Hamiltonian for graphite, find the gaps in the spectrum, and estimate the critical value of the magnetic field above which the Hall plateau appears. When the Fermi level is in the bulk Landau gap, Hall transport occurs through the appearance of chiral surface states. We estimate the magnetic field necessary for the appearance of the effect to be 15.4 T for electron carriers and 7.0 T for holes.
Multimode regimes in quantum cascade lasers with optical feedback.
Columbo, L L; Brambilla, M
2014-05-01
We study the instability thresholds of the stationary emission of a quantum cascade laser with optical feedback described by the Lang Kobayashi model. We introduce an exact linear stability analysis and an approximated one for an unipolar lasers, who does not exhibit relaxation oscillations, and investigate the regimes of the emitter beyond the continuous wave instability threshold, depending on the number and density of the external cavity modes. We then show that a unipolar laser with feedback can exhibit coherent multimode oscillations that indicate spontaneous phase-locking.
Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice.
Zhu, W; Gong, Shou-Shu; Zeng, Tian-Sheng; Fu, Liang; Sheng, D N
2016-08-26
Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. Here, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry. We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Importantly, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Thus, we identify the liquid phase as a quantum Hall phase, which provides a "proof-of-principle" demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band. PMID:27610866
Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Gromov, Andrey; Cho, Gil Young; You, Yizhi; Abanov, Alexander G.; Fradkin, Eduardo
2015-01-01
We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.
Fractional Quantum Hall Effects in a Two-Dimensional Atomic Gas
NASA Astrophysics Data System (ADS)
Zhao, Jianshi; Jacome, Louis; Gemelke, Nathan
2014-03-01
Fractional Hall effects in two-dimensional electron gases have dramatically altered the way we look at ordering in quantum many body systems. Despite heroic advances since their discovery, many predictions regarding unique behavior have yet to be observed. We describe new efforts to produce similar effects in cold atomic Bose gases. Previous experiments have observed strong correlation in large ensembles of rapidly rotating few body samples consistent with a description using bosonic analogues of fractional hall states. We describe extensions of these experiments to observe individual systems in a quantum gas micropscope, introduce strong interactions through Feshbach resonance, and extend effects to larger numbers of atoms. The use of impurity atoms to probe fractional hall droplets will also be discussed, as will the extension of these effects to higher spin samples by using multiple internal states of Rubidium-87.
Framing anomaly in the effective theory of the fractional quantum Hall effect.
Gromov, Andrey; Cho, Gil Young; You, Yizhi; Abanov, Alexander G; Fradkin, Eduardo
2015-01-01
We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.
Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice
NASA Astrophysics Data System (ADS)
Zhu, W.; Gong, Shou-Shu; Zeng, Tian-Sheng; Fu, Liang; Sheng, D. N.
2016-08-01
Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. Here, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry. We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Importantly, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Thus, we identify the liquid phase as a quantum Hall phase, which provides a "proof-of-principle" demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band.
Spin-orbit coupling effect on quantum hall ferromagnets with vanishing zeeman energy
Fal'ko; Iordanskii
2000-01-01
We present the phase diagram of a ferromagnetic nu = 2N+1 quantum Hall liquid in a narrow quantum well with vanishing single-particle Zeeman splitting, varepsilon(Z), and a pronounced spin-orbit coupling. Upon decreasing varepsilon(Z) the spin-polarization field of a liquid takes, first, the easy-axis configuration, followed by the formation of a helical state which affects the transport and NMR properties of a liquid and the form of topological defects in it.
NASA Astrophysics Data System (ADS)
Basu, B.; Ghosh, Subir
2005-10-01
We have presented a quantum mechanical toy model for the study of Coulomb interactions in Quantum Hall (QH) system. Inclusion of Coulomb interaction is essential for the study of bilayer QH system and our model can simulate it, in the compound state, in a perturbative framework. We also show that in the noncommutative plane, the Coulomb interaction is modified at a higher order in the noncommutativity parameter θ, and only if θ varies from layer to layer in the QH system.
Operation of graphene quantum Hall resistance standard in a cryogen-free table-top system
NASA Astrophysics Data System (ADS)
Janssen, T. J. B. M.; Rozhko, S.; Antonov, I.; Tzalenchuk, A.; Williams, J. M.; Melhem, Z.; He, H.; Lara-Avila, S.; Kubatkin, S.; Yakimova, R.
2015-09-01
We demonstrate quantum Hall resistance measurements with metrological accuracy in a small cryogen-free system operating at a temperature of around 3.8 K and magnetic fields below 5 T. Operating this system requires little experimental knowledge or laboratory infrastructure, thereby greatly advancing the proliferation of primary quantum standards for precision electrical metrology. This significant advance in technology has come about as a result of the unique properties of epitaxial graphene on SiC.
Prediction of Near-Room-Temperature Quantum Anomalous Hall Effect on Honeycomb Materials
NASA Astrophysics Data System (ADS)
Yan, Binghai; Wu, Shu-Chun; Shan, Guangcun
2015-03-01
Recently, this long-sought quantum anomalous Hall effect was realized in the magnetic topological insulator. However, the requirement of an extremely low temperature (~ 30 mK) hinders realistic applications. Based on honeycomb lattices comprised of Sn and Ge, which are found to be 2D topological insulators, we propose a quantum anomalous Hall platform with large energy gap of 0.34 and 0.06 eV, respectively. The ferromagnetic order forms in one sublattice of the honeycomb structure by controlling the surface functionalization rather than dilute magnetic doping, which is expected to be visualized by spin polarized STM in experiment. Strong coupling between the inherent quantum spin Hall state and ferromagnetism results in considerable exchange splitting and consequently an ferromagnetic insulator with large energy gap. The estimated mean-field Curie temperature is 243 and 509 K for Sn and Ge lattices, respectively. The large energy gap and high Curie temperature indicate the feasibility of the quantum anomalous Hall effect in the near-room-temperature and even room-temperature regions. We thank the helpful discussions with C. Felser, S. Kanugo, C.-X. Liu, Z. Wang, Y. Xu, K. Wu, and Y. Zhou.
NASA Astrophysics Data System (ADS)
Deng, Nianpei
The two dimensional electron gas subjected to a magnetic field has been a model system in contemporary condensed matter physics which generated many beautiful experiments as well as novel fundamental concepts. These novel concepts are of broad interests and have benefited other fields of research. For example, the observations of conventional odd-denominator fractional quantum Hall states have enriched many-body physics with important concepts such as fractional statistics and composite fermions. The subsequent discovery of the enigmatic even-denominator nu=5/2 fractional quantum Hall state has led to more interesting concepts such as non-Abelian statistics and pairing of composite fermions which can be intimately connected to the electron pairing in superconductivity. Moreover, the observations of stripe phases and reentrant integer quantum Hall states have stimulated research on exotic electron solids which have more intricate structures than the Wigner Crystal. In contrast to fractional quantum Hall states and stripes phases, the reentrant integer quantum Hall states are very little studied and their ground states are the least understood. There is a lack of basic information such as exact filling factors, temperature dependence and energy scales for the reentrant integer quantum Hall states. A critical experimental condition in acquiring this information is a stable ultra-low temperature environment. In the first part of this dissertation, I will discuss our unique setup of 3He immersion cell in a state-of-art dilution refrigerator which achieves the required stability of ultra-low temperature. With this experimental setup, we are able to observe for the first time very sharp magnetotransport features of reentrant integer quantum Hall states across many Landau levels for the first time. I will firstly present our results in the second Landau level. The temperature dependence measurements reveal a surprisingly sharp peak signature that is unique to the reentrant
Quantum Hall effect in an InAs /AlSb double quantum well
NASA Astrophysics Data System (ADS)
Yakunin, M. V.; Podgornykh, S. M.; Sadofyev, Yu. G.
2009-01-01
Double quantum wells (DQWs) were first implemented in the InAs /AlSb heterosystem, which is characterized by a large Landé g factor ∣g∣=15 of the InAs layers forming the well, much larger than the bulk g factor ∣g∣=0.4 of the GaAs in conventional GaAs /AlGaAs DQWs. The quality of the samples is good enough to permit observation of a clear picture of the quantum Hall effect (QHE). Despite the small tunneling gap, which is due to the large barrier height (1.4eV), features with odd filling factors ν =3,5,7,… are present in the QHE, due to collectivized interlayer states of the DQW. When the field is rotated relative to the normal to the layers, the ν =3 state is suppressed, confirming the collectivized nature of that state and denying that it could owe its existence to a strong asymmetry of the DQW. Previously the destruction of the collectivized QHE states by a parallel field had been observed only for the ν =1 state. The observation of a similar effect for ν =3 in an InAs /AlSb DQW may be due to the large bulk g factor of InAs.
THz photoresponse of quantum Hall devices based on HgTe-Quantum wells
NASA Astrophysics Data System (ADS)
Gouider, F.; Hein, G.; Brüne, C.; Buhmann, H.; Vasilyev, Yu. B.; Nachtwei, G.
2010-01-01
This study concerns the experimental investigation of the Terahertz -(THz-) photoresponse in systems under quantum-Hall-(QH-) conditions. These investigations are interesting regarding a potential application of QH-systems as fast and spectrally sensitive THz-detectors. The measurements of the THz-photoresponse (PR) of devices with HgTe quantum wells (QWs) embedded in CdHgTe barriers are aimed at obtaining photosignals at smaller magnetic fields in comparison to detectors made of GaAs/AlGaAs wafers. This can be realized by changing the electron density (application of a gate electrode). The QWs have a thickness of dQW between 7 nm and 12 nm, so that the material HgTe of the QW possesses a semimetallic band structure. We found a cyclotron mass of about mc = 0.026 m0 for our samples from cyclotron resonance measurements (also approximately determined from our PR). As this cyclotron mass is by about a factor 3 smaller than the one of electrons in GaAs, the same Landau level splitting is reached at about 1/3 of the magnetic field as in GaAs.
NASA Astrophysics Data System (ADS)
Georgiev, Lachezar S.
2004-02-01
Using the effective conformal field theory for the quantum Hall edge states we propose a compact and convenient scheme for the computation of the periods, amplitudes, and temperature behavior of the chiral persistent currents and the magnetic susceptibilities in the mesoscopic disk version of the Zk parafermion quantum Hall states in the second Landau level. Our numerical calculations show that the persistent currents are periodic in the Aharonov Bohm flux with period exactly one flux quantum and have a diamagnetic nature. In the high-temperature regime their amplitudes decay exponentially with increasing the temperature and the corresponding exponents are universal characteristics of non-Fermi liquids. Our theoretical results for these exponents are in perfect agreement with those extracted from the numerical data and demonstrate that there is in general a nontrivial contribution coming from the neutral sector. We emphasize the crucial role of the nonholomorphic factors, first proposed by Cappelli and Zemba in the context of the conformal field theory partition functions for the quantum Hall states, which ensure the invariance of the annulus partition function under the Laughlin spectral flow.
Zhou, Jian; Sun, Qiang; Wang, Qian; Kawazoe, Yoshiyuki; Jena, Puru
2016-06-01
Exploring a two-dimensional intrinsic quantum spin Hall state with a large band gap as well as an anomalous Hall state in realizable materials is one of the most fundamental and important goals for future applications in spintronics, valleytronics, and quantum computing. Here, by combining first-principles calculations with a tight-binding model, we predict that Sb or Bi can epitaxially grow on a stable and ferromagnetic MnO2 thin film substrate, forming a flat honeycomb sheet. The flatness of Sb or Bi provides an opportunity for the existence of Dirac points in the Brillouin zone, with its position effectively tuned by surface hydrogenation. The Dirac points in spin up and spin down channels split due to the proximity effects induced by MnO2. In the presence of both intrinsic and Rashba spin-orbit coupling, we find two band gaps exhibiting a large band gap quantum spin Hall state and a nearly quantized anomalous Hall state which can be tuned by adjusting the Fermi level. Our findings provide an efficient way to realize both quantized intrinsic spin Hall conductivity and anomalous Hall conductivity in a single material. PMID:27181160
Barkeshli, Maissam; Wen, Xiao-Gang
2010-11-19
We find a series of possible continuous quantum phase transitions between fractional quantum Hall states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p,p,p-3) Abelian two-component state, while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at ν=2/3 and single-component systems at ν=8/3. PMID:21231341
NASA Astrophysics Data System (ADS)
Barkeshli, Maissam; Wen, Xiao-Gang
2010-11-01
We find a series of possible continuous quantum phase transitions between fractional quantum Hall states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p,p,p-3) Abelian two-component state, while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at ν=2/3 and single-component systems at ν=8/3.
Insulator, semiclassical oscillations and quantum Hall liquids at low magnetic fields.
Lo, Shun-Tsung; Wang, Yi-Ting; Bohra, G; Comfort, E; Lin, T-Y; Kang, M-G; Strasser, G; Bird, J P; Huang, C F; Lin, Li-Hung; Chen, J C; Liang, C-T
2012-10-10
Magneto-transport measurements are performed on two-dimensional GaAs electron systems to probe the quantum Hall (QH) effect at low magnetic fields. Oscillations following the Shubnikov-de Haas (SdH) formula are observed in the transition from the insulator to QH liquid when the observed almost temperature-independent Hall slope indicates insignificant interaction correction. Our study shows that the existence of SdH oscillations in such a transition can be understood based on the non-interacting model.
Circularly polarized near-field optical mapping of spin-resolved quantum Hall chiral edge states.
Mamyouda, Syuhei; Ito, Hironori; Shibata, Yusuke; Kashiwaya, Satoshi; Yamaguchi, Masumi; Akazaki, Tatsushi; Tamura, Hiroyuki; Ootuka, Youiti; Nomura, Shintaro
2015-04-01
We have successfully developed a circularly polarized near-field scanning optical microscope (NSOM) that enables us to irradiate circularly polarized light with spatial resolution below the diffraction limit. As a demonstration, we perform real-space mapping of the quantum Hall chiral edge states near the edge of a Hall-bar structure by injecting spin polarized electrons optically at low temperature. The obtained real-space mappings show that spin-polarized electrons are injected optically to the two-dimensional electron layer. Our general method to locally inject spins using a circularly polarized NSOM should be broadly applicable to characterize a variety of nanomaterials and nanostructures.
Devil's Staircase Phase Diagram of the Fractional Quantum Hall Effect in the Thin-Torus Limit
NASA Astrophysics Data System (ADS)
Rotondo, Pietro; Molinari, Luca Guido; Ratti, Piergiorgio; Gherardi, Marco
2016-06-01
After more than three decades, the fractional quantum Hall effect still poses challenges to contemporary physics. Recent experiments point toward a fractal scenario for the Hall resistivity as a function of the magnetic field. Here, we consider the so-called thin-torus limit of the Hamiltonian describing interacting electrons in a strong magnetic field, restricted to the lowest Landau level, and we show that it can be mapped onto a one-dimensional lattice gas with repulsive interactions, with the magnetic field playing the role of the chemical potential. The statistical mechanics of such models leads us to interpret the sequence of Hall plateaux as a fractal phase diagram whose landscape shows a qualitative agreement with experiments.
Devil's Staircase Phase Diagram of the Fractional Quantum Hall Effect in the Thin-Torus Limit.
Rotondo, Pietro; Molinari, Luca Guido; Ratti, Piergiorgio; Gherardi, Marco
2016-06-24
After more than three decades, the fractional quantum Hall effect still poses challenges to contemporary physics. Recent experiments point toward a fractal scenario for the Hall resistivity as a function of the magnetic field. Here, we consider the so-called thin-torus limit of the Hamiltonian describing interacting electrons in a strong magnetic field, restricted to the lowest Landau level, and we show that it can be mapped onto a one-dimensional lattice gas with repulsive interactions, with the magnetic field playing the role of the chemical potential. The statistical mechanics of such models leads us to interpret the sequence of Hall plateaux as a fractal phase diagram whose landscape shows a qualitative agreement with experiments. PMID:27391740
Fractional quantum Hall effect at Landau level filling ν = 4/11
Pan, W.; Baldwin, K. W.; West, K. W.; Pfeiffer, L. N.; Tsui, D. C.
2015-01-09
In this study, we report low temperature electronic transport results on the fractional quantum Hall effect of composite fermions at Landau level filling ν = 4/11 in a very high mobility and low density sample. Measurements were carried out at temperatures down to 15mK, where an activated magnetoresistance R_{xx} and a quantized Hall resistance R_{xy}, within 1% of the expected value of h/(4/11)e^{2}, were observed. The temperature dependence of the R_{xx} minimum at 4/11 yields an activation energy gap of ~ 7 mK. Developing Hall plateaus were also observed at the neighboring states at ν = 3/8 and 5/13.
NASA Astrophysics Data System (ADS)
Sitte, M.; Rosch, A.; Altman, E.; Fritz, L.
2012-03-01
We investigate how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. The Hall effect, measured by contacting those channels, remains quantized even in situations where the θ term in the bulk and the associated surface Hall conductivities, σxyS, are not quantized due to the breaking of time-reversal symmetry. The quantization arises as the θ term changes by ±2πn along a loop around n edge channels. Model calculations show how an interplay of orbital and Zeeman effects leads to quantum Hall transitions, where channels get redistributed along the edges of the crystal. The network of edges opens new possibilities to investigate the coupling of edge channels.
Fractional quantum Hall effect at Landau level filling ν = 4/11
Pan, W.; Baldwin, K. W.; West, K. W.; Pfeiffer, L. N.; Tsui, D. C.
2015-01-09
In this study, we report low temperature electronic transport results on the fractional quantum Hall effect of composite fermions at Landau level filling ν = 4/11 in a very high mobility and low density sample. Measurements were carried out at temperatures down to 15mK, where an activated magnetoresistance Rxx and a quantized Hall resistance Rxy, within 1% of the expected value of h/(4/11)e2, were observed. The temperature dependence of the Rxx minimum at 4/11 yields an activation energy gap of ~ 7 mK. Developing Hall plateaus were also observed at the neighboring states at ν = 3/8 and 5/13.
Effects of Landau level mixing on the fractional quantum Hall effect in monolayer graphene.
Peterson, Michael R; Nayak, Chetan
2014-08-22
We report results of exact diagonalization studies of the spin- and valley-polarized fractional quantum Hall effect in the N = 0 and N = 1 Landau levels in graphene. We use an effective model that incorporates Landau level mixing to lowest order in the parameter κ = ((e(2)/εℓ)/(ħv(F)/ℓ)) = (e(2)/εv(F)ħ), which is magnetic field independent and can only be varied through the choice of substrate. We find Landau level mixing effects are negligible in the N = 0 Landau level for κ ≲ 2. In fact, the lowest Landau level projected Coulomb Hamiltonian is a better approximation to the real Hamiltonian for graphene than it is for semiconductor based quantum wells. Consequently, the principal fractional quantum Hall states are expected in the N = 0 Landau level over this range of κ. In the N = 1 Landau level, fractional quantum Hall states are expected for a smaller range of κ and Landau level mixing strongly breaks particle-hole symmetry, producing qualitatively different results compared to the N = 0 Landau level. At half filling of the N = 1 Landau level, we predict the anti-Pfaffian state will occur for κ ∼ 0.25-0.75.
Observation of the quantum Hall effect in δ-doped SrTiO3
NASA Astrophysics Data System (ADS)
Matsubara, Y.; Takahashi, K. S.; Bahramy, M. S.; Kozuka, Y.; Maryenko, D.; Falson, J.; Tsukazaki, A.; Tokura, Y.; Kawasaki, M.
2016-05-01
The quantum Hall effect is a macroscopic quantum phenomenon in a two-dimensional electron system. The two-dimensional electron system in SrTiO3 has sparked a great deal of interest, mainly because of the strong electron correlation effects expected from the 3d orbitals. Here we report the observation of the quantum Hall effect in a dilute La-doped SrTiO3-two-dimensional electron system, fabricated by metal organic molecular-beam epitaxy. The quantized Hall plateaus are found to be solely stemming from the low Landau levels with even integer-filling factors, ν=4 and 6 without any contribution from odd ν's. For ν=4, the corresponding plateau disappears on decreasing the carrier density. Such peculiar behaviours are proposed to be due to the crossing between the Landau levels originating from the two subbands composed of d orbitals with different effective masses. Our findings pave a way to explore unprecedented quantum phenomena in d-electron systems.
Observation of the quantum Hall effect in δ-doped SrTiO3.
Matsubara, Y; Takahashi, K S; Bahramy, M S; Kozuka, Y; Maryenko, D; Falson, J; Tsukazaki, A; Tokura, Y; Kawasaki, M
2016-01-01
The quantum Hall effect is a macroscopic quantum phenomenon in a two-dimensional electron system. The two-dimensional electron system in SrTiO3 has sparked a great deal of interest, mainly because of the strong electron correlation effects expected from the 3d orbitals. Here we report the observation of the quantum Hall effect in a dilute La-doped SrTiO3-two-dimensional electron system, fabricated by metal organic molecular-beam epitaxy. The quantized Hall plateaus are found to be solely stemming from the low Landau levels with even integer-filling factors, ν=4 and 6 without any contribution from odd ν's. For ν=4, the corresponding plateau disappears on decreasing the carrier density. Such peculiar behaviours are proposed to be due to the crossing between the Landau levels originating from the two subbands composed of d orbitals with different effective masses. Our findings pave a way to explore unprecedented quantum phenomena in d-electron systems. PMID:27228903
Observation of the quantum Hall effect in δ-doped SrTiO3
Matsubara, Y.; Takahashi, K. S.; Bahramy, M. S.; Kozuka, Y.; Maryenko, D.; Falson, J.; Tsukazaki, A.; Tokura, Y.; Kawasaki, M.
2016-01-01
The quantum Hall effect is a macroscopic quantum phenomenon in a two-dimensional electron system. The two-dimensional electron system in SrTiO3 has sparked a great deal of interest, mainly because of the strong electron correlation effects expected from the 3d orbitals. Here we report the observation of the quantum Hall effect in a dilute La-doped SrTiO3-two-dimensional electron system, fabricated by metal organic molecular-beam epitaxy. The quantized Hall plateaus are found to be solely stemming from the low Landau levels with even integer-filling factors, ν=4 and 6 without any contribution from odd ν's. For ν=4, the corresponding plateau disappears on decreasing the carrier density. Such peculiar behaviours are proposed to be due to the crossing between the Landau levels originating from the two subbands composed of d orbitals with different effective masses. Our findings pave a way to explore unprecedented quantum phenomena in d-electron systems. PMID:27228903
Operating Spin Echo in the Quantum Regime for an Atomic-Ensemble Quantum Memory
NASA Astrophysics Data System (ADS)
Rui, Jun; Jiang, Yan; Yang, Sheng-Jun; Zhao, Bo; Bao, Xiao-Hui; Pan, Jian-Wei
2015-09-01
Spin echo is a powerful technique to extend atomic or nuclear coherence times by overcoming the dephasing due to inhomogeneous broadenings. However, there are disputes about the feasibility of applying this technique to an ensemble-based quantum memory at the single-quanta level. In this experimental study, we find that noise due to imperfections of the rephasing pulses has both intense superradiant and weak isotropic parts. By properly arranging the beam directions and optimizing the pulse fidelities, we successfully manage to operate the spin echo technique in the quantum regime by observing nonclassical photon-photon correlations as well as the quantum behavior of retrieved photons. Our work for the first time demonstrates the feasibility of harnessing the spin echo method to extend the lifetime of ensemble-based quantum memories at the single-quanta level.
Operating Spin Echo in the Quantum Regime for an Atomic-Ensemble Quantum Memory.
Rui, Jun; Jiang, Yan; Yang, Sheng-Jun; Zhao, Bo; Bao, Xiao-Hui; Pan, Jian-Wei
2015-09-25
Spin echo is a powerful technique to extend atomic or nuclear coherence times by overcoming the dephasing due to inhomogeneous broadenings. However, there are disputes about the feasibility of applying this technique to an ensemble-based quantum memory at the single-quanta level. In this experimental study, we find that noise due to imperfections of the rephasing pulses has both intense superradiant and weak isotropic parts. By properly arranging the beam directions and optimizing the pulse fidelities, we successfully manage to operate the spin echo technique in the quantum regime by observing nonclassical photon-photon correlations as well as the quantum behavior of retrieved photons. Our work for the first time demonstrates the feasibility of harnessing the spin echo method to extend the lifetime of ensemble-based quantum memories at the single-quanta level.
NASA Astrophysics Data System (ADS)
Kharitonov, Maxim; Juergens, Stefan; Trauzettel, Björn
2016-07-01
We consider a class of quantum Hall topological insulators: topologically nontrivial states with zero Chern number at finite magnetic field, in which the counterpropagating edge states are protected by a symmetry (spatial or spin) other than time-reversal. HgTe-type heterostructures and graphene are among the relevant systems. We study the effect of electron interactions on the topological properties of the system. We particularly focus on the vicinity of the topological phase transition, marked by the crossing of two Landau levels, where the system is a strongly interacting quantum Hall ferromagnet. We analyze the edge properties using the formalism of the nonlinear σ -model. We establish the symmetry requirement for the topological protection in this interacting system: effective continuous U(1) symmetry with respect to uniaxial isospin rotations must be preserved. If U(1) symmetry is preserved, the topologically nontrivial phase persists; its edge is a helical Luttinger liquid with highly tunable effective interactions. We obtain explicit analytical expressions for the parameters of the Luttinger liquid in the quantum-Hall-ferromagnet regime. However, U(1) symmetry may be broken, either spontaneously or by U(1)-asymmetric interactions. In either case, interaction-induced transitions occur to the respective topologically trivial phases with gapped edge charge excitations.
Space Charge Saturated Sheath Regime and Electron Temperature Saturation in Hall Thrusters
Y. Raitses; D. Staack; A. Smirnov; N.J. Fisch
2005-03-16
Secondary electron emission in Hall thrusters is predicted to lead to space charge saturated wall sheaths resulting in enhanced power losses in the thruster channel. Analysis of experimentally obtained electron-wall collision frequency suggests that the electron temperature saturation, which occurs at high discharge voltages, appears to be caused by a decrease of the Joule heating rather than by the enhancement of the electron energy loss at the walls due to a strong secondary electron emission.
Quantum Hall resistance standard in graphene devices under relaxed experimental conditions
NASA Astrophysics Data System (ADS)
Ribeiro-Palau, R.; Lafont, F.; Brun-Picard, J.; Kazazis, D.; Michon, A.; Cheynis, F.; Couturaud, O.; Consejo, C.; Jouault, B.; Poirier, W.; Schopfer, F.
2015-11-01
The quantum Hall effect provides a universal standard for electrical resistance that is theoretically based on only the Planck constant h and the electron charge e. Currently, this standard is implemented in GaAs/AlGaAs, but graphene's electronic properties have given hope for a more practical device. Here, we demonstrate that the experimental conditions necessary for the operation of devices made of high-quality graphene grown by chemical vapour deposition on silicon carbide can be extended and significantly relaxed compared with those for state-of-the-art GaAs/AlGaAs devices. In particular, the Hall resistance can be accurately quantized to within 1 × 10-9 over a 10 T wide range of magnetic flux density, down to 3.5 T, at a temperature of up to 10 K or with a current of up to 0.5 mA. This experimental simplification highlights the great potential of graphene in the development of user-friendly and versatile quantum standards that are compatible with broader industrial uses beyond those in national metrology institutes. Furthermore, the measured agreement of the quantized Hall resistance in graphene and GaAs/AlGaAs, with an ultimate uncertainty of 8.2 × 10-11, supports the universality of the quantum Hall effect. This also provides evidence of the relation of the quantized Hall resistance with h and e, which is crucial for the new Système International d'unités to be based on fixing such fundamental constants of nature.
``Perfect'' Coulomb Drag in a Bilayer Quantum Hall System
NASA Astrophysics Data System (ADS)
Nandi, D.; Finck, A. D. K.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2012-02-01
We report Coulomb drag measurements in Corbino geometry which reveal that equal but oppositely directed electrical currents can freely propagate across the insulating bulk of the bilayer quantized Hall state at νT=1 even when the two 2D layers are electrically isolated and interlayer tunneling has been heavily suppressed by an in-plane magnetic field. This effect, which we dub ``perfect'' Coulomb drag, reflects the transport of charge neutral excitons across the bulk of the 2D system. The equal magnitude of the drive and drag currents is lost at high current and when either the temperature or effective separation between the two 2D layers is increased. In each of these cases, ordinary quasiparticle charge transport across the annulus has grown to dominate over exciton transport.
Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators
NASA Astrophysics Data System (ADS)
Chang, Cui-Zu; Li, Mingda
2016-03-01
The quantum anomalous Hall effect (QAHE), the last member of Hall family, was predicted to exhibit quantized Hall conductivity {σyx}=\\frac{{{e}2}}{h} without any external magnetic field. The QAHE shares a similar physical phenomenon with the integer quantum Hall effect (QHE), whereas its physical origin relies on the intrinsic topological inverted band structure and ferromagnetism. Since the QAHE does not require external energy input in the form of magnetic field, it is believed that this effect has unique potential for applications in future electronic devices with low-power consumption. More recently, the QAHE has been experimentally observed in thin films of the time-reversal symmetry breaking ferromagnetic (FM) topological insulators (TI), Cr- and V- doped (Bi,Sb)2Te3. In this topical review, we review the history of TI based QAHE, the route to the experimental observation of the QAHE in the above two systems, the current status of the research of the QAHE, and finally the prospects for future studies.
Domain wall in a quantum anomalous Hall insulator as a magnetoelectric piston
NASA Astrophysics Data System (ADS)
Upadhyaya, Pramey; Tserkovnyak, Yaroslav
2016-07-01
We theoretically study the magnetoelectric coupling in a quantum anomalous Hall insulator state induced by interfacing a dynamic magnetization texture to a topological insulator. In particular, we propose that the quantum anomalous Hall insulator with a magnetic configuration of a domain wall, when contacted by electrical reservoirs, acts as a magnetoelectric piston. A moving domain wall pumps charge current between electrical leads in a closed circuit, while applying an electrical bias induces reciprocal domain-wall motion. This pistonlike action is enabled by a finite reflection of charge carriers via chiral modes imprinted by the domain wall. Moreover, we find that, when compared with the recently discovered spin-orbit torque-induced domain-wall motion in heavy metals, the reflection coefficient plays the role of an effective spin-Hall angle governing the efficiency of the proposed electrical control of domain walls. Quantitatively, this effective spin-Hall angle is found to approach a universal value of 2, providing an efficient scheme to reconfigure the domain-wall chiral interconnects for possible memory and logic applications.
Lu Yuanming; Wang Ziqiang; Wen Xiaogang; Wang Zhenghan
2010-03-15
In the pattern-of-zeros approach to quantum Hall states, a set of data (n;m;S{sub a}|a=1,...,n;n,m,S{sub a} is n element of N) (called the pattern of zeros) is introduced to characterize a quantum Hall wave function. In this paper we find sufficient conditions on the pattern of zeros so that the data correspond to a valid wave function. Some times, a set of data (n;m;S{sub a}) corresponds to a unique quantum Hall state, while other times, a set of data corresponds to several different quantum Hall states. So in the latter cases, the pattern of zeros alone does not completely characterize the quantum Hall states. In this paper, we find that the following expanded set of data (n;m;S{sub a};c|a=1,...,n;n,m,S{sub a} is an element of N;c is an element of R) provides a more complete characterization of quantum Hall states. Each expanded set of data completely characterizes a unique quantum Hall state, at least for the examples discussed in this paper. The result is obtained by combining the pattern of zeros and Z{sub n} simple-current vertex algebra which describes a large class of Abelian and non-Abelian quantum Hall states PHI{sub Z{sub n}{sup sc}}. The more complete characterization in terms of (n;m;S{sub a};c) allows us to obtain more topological properties of those states, which include the central charge c of edge states, the scaling dimensions and the statistics of quasiparticle excitations.
Simulation of the many-body dynamical quantum Hall effect in an optical lattice
NASA Astrophysics Data System (ADS)
Zhang, Dan-Wei; Yang, Xu-Chen
2016-05-01
We propose an experimental scheme to simulate the many-body dynamical quantum Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice. We first show that the required model Hamiltonian of a spin-1/2 Heisenberg chain with an effective magnetic field and tunable parameters can be realized in this system. For dynamical response to ramping the external fields, the quantized plateaus emerge in the Berry curvature of the interacting atomic spin chain as a function of the effective spin-exchange interaction. The quantization of this response in the parameter space with the interaction-induced topological transition characterizes the many-body dynamical quantum Hall effect. Furthermore, we demonstrate that this phenomenon can be observed in practical cold atom experiments with numerical simulations.
Fragile Fractional Quantum Hall States in the Lowest and the Second Landau Level
NASA Astrophysics Data System (ADS)
Csathy, Gabor; Kleinbaum, Ethan; Kumar, Ashwani; Samkharadze, Nodar; Pfeiffer, Loren; West, Ken
Ultra-low temperature measurements of the two-dimensional electron gas have revealed some of the most fragile fractional quantum Hall states. In these experiments electron thermalization was achieved using a He-3 immersion cell and the temperature of the bath is monitored using a quartz tuning fork viscometer. We will review the recently discovered fractional quantum Hall state at filling factor ν = 3 + 1 / 3 observed in the second Landau level and those at the filling factor ν = 4 / 11 and 5 / 13 in the lowest Landau level. The work at Purdue was supported by NSF DMR 1207375 and 1505866 grants. The work at Princeton University was funded by the Gordon and Betty Moore Foundation through the EPiQS initiative Grant GBMF4420, and by the National Science Foundation MRSEC Grant DMR-1420541.
Jack Polynomials, W-algebras and application to Fractional Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Simon, Steven H.; Bernevig, B. Andrei; Gurarie, Victor
2009-03-01
We examine Jack symmetric functions and certain W-algebras as schemes for generating fractioanl quantum Hall wavefunctions. We add substantially to the evidence that the Jack functions correspond to certain W-algebras, by calculating the central charge and scaling dimensions of some of the fields in both cases and showing that they match. Except for the Read-Rezayi series all of these Jack symmetric functions turn out to be nonunitary theories. We discuss the (perhaps optimistic) possibility that these approaches may have relevance to various physical quantum Hall systems. Open questions in the field, as well as why this is of importance to those concerned with real experiments, will also be discussed.
Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures
Xiao, Di; Zhu, Wenguang; Ran, Ying; Nagaosa, Naoto; Okamoto, Satoshi
2011-01-01
Topological insulators (TIs) are characterized by a non-trivial band topology driven by the spin-orbit coupling. To fully explore the fundamental science and application of TIs, material realization is indispensable. Here we predict, based on tight-binding modeling and first-principles calculations, that bilayers of perovskite-type transition-metal oxides grown along the [111] crystallographic axis are potential candidates for two-dimensional TIs. The topological band structure of these materials can be fine-tuned by changing dopant ions, substrates and external gate voltages. We predict that LaAuO$_3$ bilayers have a topologically non-trivial energy gap of about 0.15~eV, which is sufficiently large to realize the quantum spin Hall effect at room temperature. Intriguing phenomena, such as fractional quantum Hall effect, associated with the nearly flat topologically non-trivial bands found in $e_g$ systems are also discussed.
Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures.
Xiao, Di; Zhu, Wenguang; Ran, Ying; Nagaosa, Naoto; Okamoto, Satoshi
2011-01-01
Topological insulators are characterized by a non-trivial band topology driven by the spin-orbit coupling. To fully explore the fundamental science and application of topological insulators, material realization is indispensable. Here we predict, based on tight-binding modelling and first-principles calculations, that bilayers of perovskite-type transition-metal oxides grown along the [111] crystallographic axis are potential candidates for two-dimensional topological insulators. The topological band structure of these materials can be fine-tuned by changing dopant ions, substrates and external gate voltages. We predict that LaAuO(3) bilayers have a topologically non-trivial energy gap of about 0.15 eV, which is sufficiently large to realize the quantum spin Hall effect at room temperature. Intriguing phenomena, such as fractional quantum Hall effect, associated with the nearly flat topologically non-trivial bands found in e(g) systems are also discussed.
Coincidence of superparamagnetism and perfect quantization in the quantum anomalous Hall state
NASA Astrophysics Data System (ADS)
Grauer, S.; Schreyeck, S.; Winnerlein, M.; Brunner, K.; Gould, C.; Molenkamp, L. W.
2015-11-01
Topological insulators doped with transition metals have recently been found to host a strong ferromagnetic state with perpendicular to plane anisotropy as well as support a quantum Hall state with edge channel transport, even in the absence of an external magnetic field. It remains unclear, however, why a robust magnetic state should emerge in materials of relatively low crystalline quality and dilute magnetic doping. Indeed, recent experiments suggest that the ferromagnetism exhibits at least some superparamagnetic character. We report on transport measurements in a sample that shows perfect quantum anomalous Hall quantization, while at the same time exhibits traits in its transport data which suggest inhomogeneities. We speculate that this may be evidence that the percolation path interpretation used to explain the transport during the magnetic reversal may actually have relevance over the entire field range.
Valley polarized quantum Hall effect and topological insulator phase transitions in silicene.
Tahir, M; Schwingenschlögl, U
2013-01-01
The electronic properties of silicene are distinct from both the conventional two dimensional electron gas and the famous graphene due to strong spin orbit interaction and the buckled structure. Silicene has the potential to overcome limitations encountered for graphene, in particular the zero band gap and weak spin orbit interaction. We demonstrate a valley polarized quantum Hall effect and topological insulator phase transitions. We use the Kubo formalism to discuss the Hall conductivity and address the longitudinal conductivity for elastic impurity scattering in the first Born approximation. We show that the combination of an electric field with intrinsic spin orbit interaction leads to quantum phase transitions at the charge neutrality point, providing a tool to experimentally tune the topological state. Silicene constitutes a model system for exploring the spin and valley physics not accessible in graphene due to the small spin orbit interaction.
Filling the Bose sea: symmetric quantum Hall edge states and affine characters
NASA Astrophysics Data System (ADS)
Ardonne, Eddy; Kedem, Rinat; Stone, Michael
2005-01-01
We explore the structure of the bosonic analogues of the k-clustered 'parafermion' quantum Hall states. We show how the many-boson wavefunctions of k-clustered quantum Hall droplets appear naturally as matrix elements of ladder operators in integrable representations of the affine Lie algebra \\widehat{su}(2)_k . Using results of Feigin and Stoyanovsky, we count the dimensions of spaces of symmetric polynomials with given k-clustering properties and show that as the droplet size grows the partition function of its edge excitations evolves into the character of the representation. This confirms that the Hilbert space of edge states coincides with the representation space of the \\widehat{su}(2)_k edge-current algebra. We also show that a spin-singlet, two-component k-clustered boson fluid is similarly related to integrable representations of \\widehat{su}(3) . Parafermions are not necessary for these constructions.
Properties of Non-Abelian Fractional Quantum Hall States at Filling ν=k/r
NASA Astrophysics Data System (ADS)
Bernevig, B. Andrei; Haldane, F. D. M.
2008-12-01
We compute the physical properties of non-Abelian fractional quantum Hall (FQH) states described by Jack polynomials at general filling ν=k/r. For r=2, these states are the Zk Read-Rezayi parafermions, whereas for r>2 they represent new FQH states. The r=k+1 states, multiplied by a Vandermonde determinant, are a non-Abelian alternative construction of states at fermionic filling 2/5,3/7,4/9,…. We obtain the thermal Hall coefficient, the quantum dimensions, the electron scaling exponent, and the non-Abelian quasihole propagator. The properties of the r>2 Jack polynomials indicate they are correlators of fields of nonunitary conformal field theories (CFT), but the CFT-FQH connection fails when invoked to compute physical properties such as the quasihole propagator. The quasihole wave function, written as a coherent state representation of Jack polynomials, has an identical structure for all non-Abelian states.
Spin-singlet quantum Hall states and Jack polynomials with a prescribed symmetry
NASA Astrophysics Data System (ADS)
Estienne, Benoit; Bernevig, B. Andrei
2012-04-01
We show that a large class of bosonic spin-singlet Fractional Quantum Hall model wavefunctions and their quasihole excitations can be written in terms of Jack polynomials with a prescribed symmetry. Our approach describes new spin-singlet quantum Hall states at filling fraction ν=2k/2r-1 and generalizes the (k,r) spin-polarized Jack polynomial states. The NASS and Halperin spin-singlet states emerge as specific cases of our construction. The polynomials express many-body states which contain configurations obtained from a root partition through a generalized squeezing procedure involving spin and orbital degrees of freedom. The corresponding generalized Pauli principle for root partitions is obtained, allowing for counting of the quasihole states. We also extract the central charge and quasihole scaling dimension, and propose a conjecture for the underlying CFT of the (k,r) spin-singlet Jack states.
NASA Astrophysics Data System (ADS)
Zhang, Junyi; Beugnon, Jérôme; Nascimbene, Sylvain
2016-10-01
We describe a protocol to prepare clusters of ultracold bosonic atoms in strongly interacting states reminiscent of fractional quantum Hall states. Our scheme consists in injecting a controlled amount of angular momentum to an atomic gas using Raman transitions carrying orbital angular momentum. By injecting one unit of angular momentum per atom, one realizes a single-vortex state, which is well described by mean-field theory for large enough particle numbers. We also present schemes to realize fractional quantum Hall states, namely, the bosonic Laughlin and Moore-Read states. We investigate the requirements for adiabatic nucleation of such topological states, in particular comparing linear Landau-Zener ramps and arbitrary ramps obtained from optimized control methods. We also show that this protocol requires excellent control over the isotropic character of the trapping potential.
S-duality constraints on 1D patterns associated with fractional quantum Hall states.
Seidel, Alexander
2010-07-01
Using the modular invariance of the torus, constraints on the 1D patterns are derived that are associated with various fractional quantum Hall ground states, e.g., through the thin torus limit. In the simplest case, these constraints enforce the well-known odd-denominator rule, which is seen to be a necessary property of all 1D patterns associated to quantum Hall states with minimum torus degeneracy. However, the same constraints also have implications for the non-Abelian states possible within this framework. In simple cases, including the ν=1 Moore-Read state and the ν=3/2 level 3 Read-Rezayi state, the filling factor and the torus degeneracy uniquely specify the possible patterns, and thus all physical properties that are encoded in them. It is also shown that some states, such as the "strong p-wave pairing state," cannot in principle be described through 1D patterns.
Edge-channel interferometer at the graphene quantum Hall pn junction
Morikawa, Sei; Moriya, Rai; Masubuchi, Satoru Machida, Tomoki; Watanabe, Kenji; Taniguchi, Takashi
2015-05-04
We demonstrate a quantum Hall edge-channel interferometer in a high-quality graphene pn junction under a high magnetic field. The co-propagating p and n quantum Hall edge channels traveling along the pn interface functions as a built-in Aharonov-Bohm-type interferometer, the interferences in which are sensitive to both the external magnetic field and the carrier concentration. The trajectories of peak and dip in the observed resistance oscillation are well reproduced by our numerical calculation that assumes magnetic flux quantization in the area enclosed by the co-propagating edge channels. Coherent nature of the co-propagating edge channels is confirmed by the checkerboard-like pattern in the dc-bias and magnetic-field dependences of the resistance oscillations.
Interplay between snake and quantum edge states in a graphene Hall bar with a pn-junction
Milovanović, S. P. Peeters, F. M.; Ramezani Masir, M.
2014-09-22
The magneto- and Hall resistance of a locally gated cross shaped graphene Hall bar is calculated. The edge of the top gate is placed diagonally across the center of the Hall cross. Four-probe resistance is calculated using the Landauer-Büttiker formalism, while the transmission coefficients are obtained using the non-equilibrium Green's function approach. The interplay between transport due to edge channels and snake states is investigated. When two edge channels are occupied, we predict oscillations in the Hall and the bend resistance as function of the magnetic field, which are a consequence of quantum interference between the occupied snake states.
Effective-field-theory model for the fractional quantum Hall effect
NASA Technical Reports Server (NTRS)
Zhang, S. C.; Hansson, T. H.; Kivelson, S.
1989-01-01
Starting directly from the microscopic Hamiltonian, a field-theory model is derived for the fractional quantum Hall effect. By considering an approximate coarse-grained version of the same model, a Landau-Ginzburg theory similar to that of Girvin (1986) is constructed. The partition function of the model exhibits cusps as a function of density. It is shown that the collective density fluctuations are massive.
Many-Body Generalization of the Z2 Topological Invariant for the Quantum Spin Hall Effect
NASA Astrophysics Data System (ADS)
Lee, Sung-Sik; Ryu, Shinsei
2008-05-01
We propose a many-body generalization of the Z2 topological invariant for the quantum spin Hall insulator, which does not rely on single-particle band structures. The invariant is derived as a topological obstruction that distinguishes topologically distinct many-body ground states on a torus. It is also expressed as a Wilson loop of the SU(2) Berry gauge field, which is quantized due to time-reversal symmetry.
Understanding the 5/2 fractional quantum Hall effect without the Pfaffian wave function.
Toke, Csaba; Jain, Jainendra K
2006-06-23
It is demonstrated that an understanding of the 5/2 fractional quantum Hall effect can be achieved within the composite fermion theory without appealing to the Pfaffian wave function. The residual interaction between composite fermions plays a crucial role in establishing incompressibility at this filling factor. This approach has the advantage of being amenable to systematic perturbative improvements, and produces ground as well as excited states. It, however, does not relate to non-Abelian statistics in any obvious manner.
Fractional charge and statistics in the fractional quantum spin Hall effect.
Lan, Yuanpei; Wan, Shaolong
2012-04-25
In this paper, we consider there exist two types of fundamental quasihole excitation in the fractional quantum spin Hall state and investigate their topological properties by both Chern-Simons field theory and the Berry phase technique. By the two different techniques, we obtain the identical charge and statistical angle for each type of quasihole, as well as the identical mutual statistics between two different types of quasihole excitation.
A spin-filter made of quantum anomalous Hall insulator nanowires
Wu, Jiansheng
2014-07-28
Topological end states (TES) in quantum anomalous Hall insulator nanowires can induce tunneling within the gap. Such TES are spin polarized, thus the induced current is spin polarized as well, which can be used to construct a spin-filter applied in spintronics. An interferometry device is designed to control the polarized current as well. The advantage and finite size effect on this system are discussed.
NASA Astrophysics Data System (ADS)
Aasen, David; Lee, Shu-Ping; Karzig, Torsten; Alicea, Jason
2016-10-01
Interfacing s -wave superconductors and quantum spin Hall edges produces time-reversal-invariant topological superconductivity of a type that can not arise in strictly one-dimensional systems. With the aim of establishing sharp fingerprints of this phase, we use renormalization-group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as leads. We determine scaling forms for the conductance through a grounded superconductor and show that the results depend sensitively on the interaction strength in the leads, the size of the superconducting region, and the presence or absence of time-reversal-breaking perturbations. We also study transport across a floating superconducting island isolated by magnetic barriers. Here, we predict e -periodic Coulomb-blockade peaks, as recently observed in nanowire devices [S. M. Albrecht et al., Nature (London) 531, 206 (2016), 10.1038/nature17162], with the added feature that the island can support fractional charge tunable via the relative orientation of the barrier magnetizations. As an interesting corollary, when the magnetic barriers arise from strong interactions at the edge that spontaneously break time-reversal symmetry, the Coulomb-blockade periodicity changes from e to e /2 . These findings suggest several future experiments that probe unique characteristics of topological superconductivity at the quantum spin Hall edge.
Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene.
Ki, Dong-Keun; Fal'ko, Vladimir I; Abanin, Dmitry A; Morpurgo, Alberto F
2014-01-01
We investigate low-temperature magneto-transport in recently developed, high-quality multiterminal suspended bilayer graphene devices, enabling the independent measurement of the longitudinal and transverse resistance. We observe clear signatures of the fractional quantum Hall effect with different states that are either fully developed, and exhibit a clear plateau in the transverse resistance with a concomitant dip in longitudinal resistance or incipient, and exhibit only a longitudinal resistance minimum. All observed states scale as a function of filling factor ν, as expected. An unprecedented even-denominator fractional state is observed at ν = -1/2 on the hole side, exhibiting a clear plateau in Rxy quantized at the expected value of 2h/e(2) with a precision of ∼0.5%. Many of our observations, together with a recent electronic compressibility measurement performed in graphene bilayers on hexagonal boron-nitride (hBN) substrates, are consistent with a recent theory that accounts for the effect of the degeneracy between the N = 0 and N = 1 Landau levels in the fractional quantum Hall effect and predicts the occurrence of a Moore-Read type ν = -1/2 state. Owing to the experimental flexibility of bilayer graphene, which has a gate-dependent band structure, can be easily accessed by scanning probes, and can be contacted with materials such as superconductors, our findings offer new possibilities to explore the microscopic nature of even-denominator fractional quantum Hall effect.
Stier, A V; Ellis, C T; Kwon, J; Xing, H; Zhang, H; Eason, D; Strasser, G; Morimoto, T; Aoki, H; Zeng, H; McCombe, B D; Cerne, J
2015-12-11
We measure the Hall conductivity of a two-dimensional electron gas formed at a GaAs/AlGaAs heterojunction in the terahertz regime close to the cyclotron resonance frequency using highly sensitive Faraday rotation measurements. The sample is electrically gated, allowing the electron density to be changed continuously by more than a factor of 3. We observe clear plateaulike and steplike features in the Faraday rotation angle vs electron density and magnetic field (Landau-level filling factor) even at fields or frequencies very close to cyclotron resonance absorption. These features are the high frequency manifestation of quantum Hall plateaus-a signature of topologically protected edge states. We observe both odd and even filling factor plateaus and explore the temperature dependence of these plateaus. Although dynamical scaling theory begins to break down in the frequency region of our measurements, we find good agreement with theory. PMID:26705653
Stier, A V; Ellis, C T; Kwon, J; Xing, H; Zhang, H; Eason, D; Strasser, G; Morimoto, T; Aoki, H; Zeng, H; McCombe, B D; Cerne, J
2015-12-11
We measure the Hall conductivity of a two-dimensional electron gas formed at a GaAs/AlGaAs heterojunction in the terahertz regime close to the cyclotron resonance frequency using highly sensitive Faraday rotation measurements. The sample is electrically gated, allowing the electron density to be changed continuously by more than a factor of 3. We observe clear plateaulike and steplike features in the Faraday rotation angle vs electron density and magnetic field (Landau-level filling factor) even at fields or frequencies very close to cyclotron resonance absorption. These features are the high frequency manifestation of quantum Hall plateaus-a signature of topologically protected edge states. We observe both odd and even filling factor plateaus and explore the temperature dependence of these plateaus. Although dynamical scaling theory begins to break down in the frequency region of our measurements, we find good agreement with theory.
Inmetro's Quantum Hall System verification on the basis of BIPM calibration results
NASA Astrophysics Data System (ADS)
Carvalho, H. R.; Briones, R. E. M.; Silva, J. R. B.
2015-01-01
This article presents the analysis generated by the primary resistance measurement system based on the Quantum Hall Effect, currently being implemented in the Quantum Electrical Metrology Laboratory (Lameq) of the National Institute of Metrology, Quality and Technology (Inmetro). It has as reference the calibration results emitted by the Bureau International des Poids et Mesures (BIPM) for the reference resistors maintained by the Electrical Standardization Metrology Laboratory (Lampe), also of Inmetro, thus offering a preliminary parameter of the compatibility status between the primary systems of these two institutions.
DC resistance comparison between a current comparator bridge and the quantum Hall system at Inmetro
NASA Astrophysics Data System (ADS)
da Silva, M. C.; Carvalho, H. R.; Vasconcellos, R. T. B.
2016-07-01
This paper presents a comparison results between the Quantum Hall System (QHS) under development at the Quantum Electrical Metrology Laboratory (Lameq) and the current comparator calibration system, traceable to the Bureau International des Poids et Mesures (BIPM), at the Electrical Standardization Metrology Laboratory (Lampe), both part of the Electrical Metrology Division, at Inmetro. Comparisons were performed with 1 Ω, 10 Ω, 100 Ω, 1 kΩ and 10 kΩ resistors. The results obtained over two years of work are presented here, showing that the comparison contributed to improve the calibration systems of both Lampe and Lameq.
NASA Astrophysics Data System (ADS)
Radzihovsky, Leo
2001-12-01
We predict that in νT = 1 bilayer quantum Hall (QH) pseudoferromagnets, an in-plane magnetic field can induce a reentrant pseudospin ``canting'' transition between interlayer charge balanced (planar) to imbalanced (canted) QH states. At T = 0 ( T>0) this quantum (classical) transition is in a new, anisotropic, compressible (2+1)D (2D) Ising universality class. The striking experimental signatures are the universal nonlinear charge-voltage and in-plane field relations, and the divergence of the differential bilayer capacitance at the transition, resulting in a bilayer capacitor that spontaneously charges itself, even in the absence of an applied interlayer voltage.
Radzihovsky, L
2001-12-01
We predict that in nu(T) = 1 bilayer quantum Hall (QH) pseudoferromagnets, an in-plane magnetic field can induce a reentrant pseudospin "canting" transition between interlayer charge balanced (planar) to imbalanced (canted) QH states. At T = 0 ( T>0) this quantum (classical) transition is in a new, anisotropic, compressible (2+1)D (2D) Ising universality class. The striking experimental signatures are the universal nonlinear charge-voltage and in-plane field relations, and the divergence of the differential bilayer capacitance at the transition, resulting in a bilayer capacitor that spontaneously charges itself, even in the absence of an applied interlayer voltage. PMID:11736469
Even-odd effect in spontaneously coherent bilayer quantum Hall droplets.
Park, K; Scarola, V W; Das Sarma, S
2003-07-11
Using exact diagonalization in the disk geometry we predict a novel even-odd effect in the Coulomb-blockade spectra of vertically coupled double quantum dots under an external magnetic field. The even-odd effect in the tunneling conductance is a direct manifestation of spontaneous interlayer phase coherence, and is similar to the even-odd resonance in the Cooper pair box problem in mesoscopic superconducting grains. Coherent fluctuations in the number of Cooper pairs in superconductors are analogous to the fluctuations in the relative number difference between the two layers in quantum Hall droplets.
Long-distance entanglement of spin qubits via quantum Hall edge states
NASA Astrophysics Data System (ADS)
Yang, Guang; Hsu, Chen-Hsuan; Stano, Peter; Klinovaja, Jelena; Loss, Daniel
2016-02-01
The implementation of a functional quantum computer involves entangling and coherent manipulation of a large number of qubits. For qubits based on electron spins confined in quantum dots, which are among the most investigated solid-state qubits at present, architectural challenges are often encountered in the design of quantum circuits attempting to assemble the qubits within the very limited space available. Here, we provide a solution to such challenges based on an approach to realizing entanglement of spin qubits over long distances. We show that long-range Ruderman-Kittel-Kasuya-Yosida interaction of confined electron spins can be established by quantum Hall edge states, leading to an exchange coupling of spin qubits. The coupling is anisotropic and can be either Ising type or XY type, depending on the spin polarization of the edge state. Such a property, combined with the dependence of the electron spin susceptibility on the chirality of the edge state, can be utilized to gain valuable insights into the topological nature of various quantum Hall states.
Long-distance entanglement of spin qubits via quantum Hall edge states
NASA Astrophysics Data System (ADS)
Yang, Guang; Hsu, Chen-Hsuan; Stano, Peter; Klinovaja, Jelena; Loss, Daniel
The implementation of a functional quantum computer involves entangling and coherent manipulation of a large number of qubits. For qubits based on electron spins confined in quantum dots, which are among the most investigated solid-state qubits at present, architectural challenges are often encountered in the design of quantum circuits attempting to assemble the qubits within the very limited space available. Here, we provide a solution to such challenges based on an approach to realizing entanglement of spin qubits over long distances. We show that long-range Ruderman-Kittel-Kasuya-Yosida interaction of confined electron spins can be established by quantum Hall edge states, leading to an exchange coupling of spin qubits. The coupling is anisotropic and can be either Ising-type or XY-type, depending on the spin polarization of the edge state. Such a property, combined with the dependence of the electron-spin susceptibility on the chirality of the edge state, can be utilized to gain valuable insights into the topological nature of various quantum Hall states.
Direct measurements of fractional quantum Hall effect gaps.
Khrapai, V S; Shashkin, A A; Trokina, M G; Dolgopolov, V T; Pellegrini, V; Beltram, F; Biasiol, G; Sorba, L
2007-08-24
We measure the chemical potential jump across the fractional gap in the low-temperature limit in the two-dimensional electron system of GaAs/AlGaAs single heterojunctions. In the fully spin-polarized regime, the gap for filling factor nu=1/3 increases linearly with the magnetic field and is coincident with that for nu=2/3, reflecting the electron-hole symmetry in the spin-split Landau level. In low magnetic fields, at the ground-state spin transition for nu=2/3, a correlated behavior of the nu=1/3 and nu=2/3 gaps is observed.
Proximity semiconducting nanowire junctions from Josephson to quantum dot regimes
NASA Astrophysics Data System (ADS)
Gharavi, Kaveh; Holloway, Gregory; Baugh, Jonathan
Experimental low-temperature transport results are presented on proximity-effect Josephson junctions made from low bandgap III-V semiconductor nanowires contacted with Nb. Two regimes are explored in terms of the Nb/nanowire interface transparency t. (i) High t allows a supercurrent to flow across the junction with magnitude Ic, which can be modulated using the voltage Vg on a global back gate or a local gate. Relatively high values are obtained for the figure-of-merit parameter IcRN / (eΔ) ~ 0 . 5 , and t ~ 0 . 75 , where RN is the normal state resistance and Δ the superconducting gap of the Nb leads. With the application of an axial magnetic field, Ic decays but exhibits oscillations before being fully suppressed. The period and amplitude of the oscillations depend on Vg. Possible explanations for this behaviour are presented, including Josephson interference of the orbital subbands in the nanowire. (ii) Lower transparency correlates with a spontaneous quantum dot (QD) formed in the nanowire channel. Pairs of Andreev Bound States (ABS) appear at energies | E | < Δ , with one pair unexpectedly pinned at E = 0 for a wide range of Vg. A description of the QD-ABS system beyond the Anderson model is presented to explain the latter results.
Cooper-pair injection into quantum spin Hall insulators.
Sato, Koji; Loss, Daniel; Tserkovnyak, Yaroslav
2010-11-26
We theoretically study tunneling of Cooper pairs from a superconductor spanning a two-dimensional topological insulator strip into its helical edge states. The coherent low-energy electron-pair tunneling sets off positive current cross correlations along the edges, which reflect an interplay of two quantum-entanglement processes. Most importantly, superconducting spin pairing dictates a Cooper pair partitioning into the helical edge liquids, which transport electrons in opposite directions for opposite spin orientations. At the same time, Luttinger-liquid correlations fractionalize electrons injected at a given edge into counterpropagating charge pulses carrying definite fractions of the elementary electron charge.
NASA Astrophysics Data System (ADS)
Kazakov, Aleksandr; Simion, George; Lyanda-Geller, Yuli; Kolkovsky, Valery; Adamus, Zbigniew; Karczewski, Grzegorz; Wojtowicz, Tomasz; Rokhinson, Leonid P.
2016-08-01
Ferromagnetic transitions between quantum Hall states with different polarization at a fixed filling factor can be studied by varying the ratio of cyclotron and Zeeman energies in tilted magnetic field experiments. However, an ability to locally control such transitions at a fixed magnetic field would open a range of attractive applications, e.g., formation of a reconfigurable network of one-dimensional helical domain walls in a two-dimensional plane. Coupled to a superconductor, such domain walls can support non-Abelian excitations. In this paper we report development of heterostructures where quantum Hall ferromagnetic (QHFm) transition can be controlled locally by electrostatic gating. A high mobility two-dimensional electron gas is formed in CdTe quantum wells with engineered placement of paramagnetic Mn impurities. A gate-induced electrostatic field shifts the electron wave function in the growth direction and changes an overlap between electrons in the quantum well and d -shell electrons on Mn, thus controlling the s -d exchange interaction and the field of the QHFm transition. The demonstrated shift of the QHFm transition at a filling factor ν =2 is large enough to allow full control of spin polarization at a fixed magnetic field.
Lafont, F.; Ribeiro-Palau, R.; Kazazis, D.; Michon, A.; Couturaud, O.; Consejo, C.; Chassagne, T.; Zielinski, M.; Portail, M.; Jouault, B.; Schopfer, F.; Poirier, W.
2015-01-01
Replacing GaAs by graphene to realize more practical quantum Hall resistance standards (QHRS), accurate to within 10−9 in relative value, but operating at lower magnetic fields than 10 T, is an ongoing goal in metrology. To date, the required accuracy has been reported, only few times, in graphene grown on SiC by Si sublimation, under higher magnetic fields. Here, we report on a graphene device grown by chemical vapour deposition on SiC, which demonstrates such accuracies of the Hall resistance from 10 T up to 19 T at 1.4 K. This is explained by a quantum Hall effect with low dissipation, resulting from strongly localized bulk states at the magnetic length scale, over a wide magnetic field range. Our results show that graphene-based QHRS can replace their GaAs counterparts by operating in as-convenient cryomagnetic conditions, but over an extended magnetic field range. They rely on a promising hybrid and scalable growth method and a fabrication process achieving low-electron-density devices. PMID:25891533
Quantum anomalous Hall states in the p-orbital honeycomb optical lattices
Zhang Machi; Hung Hsianghsuan; Wu Congjun; Zhang Chuanwei
2011-02-15
We study the quantum anomalous Hall states in the p-orbital bands of the honeycomb optical lattices loaded with single-component fermions. Such an effect has not yet been realized in both condensed-matter and cold-atom systems. By applying the available experimental techniques to rotate each lattice site around its own center, the band structures become topologically nontrivial. At a certain rotation angular velocity {Omega}, a flat band structure appears with localized eigenstates carrying chiral current moments. By imposing the soft confining potential, the density profile exhibits a wedding-cake-shaped distribution with insulating plateaus at commensurate fillings. Moreover, the inhomogeneous confining potential induces dissipationless circulation currents, the magnitudes and chiralities of which vary with the distance from the trap center. In the insulating regions, the Hall conductances are quantized, and in the metallic regions, the directions and magnitudes of chiral currents can not be described by the usual local-density approximation. The quantum anomalous Hall effects are robust at temperature scales that are small compared to band gaps, which increase the feasibility of experimental realizations.
NASA Astrophysics Data System (ADS)
Durganandini, P.
2015-03-01
We consider thin planar charged quantum rings on the surface of a three dimensional topological insulator coated with a thin ferromagnetic layer. We show theoretically, that when the ring is threaded by a magnetic field, then, due to the Aharanov-Bohm effect, there are not only the well known circulating persistent currents in the ring but also oscillating persistent Hall voltages across the thin ring. Such oscillating persistent Hall voltages arise due to the topological magneto-electric effect associated with the axion electrodynamics exhibited by the surface electronic states of the three dimensional topological insulator when time reversal symmetry is broken. We further generalize to the case of dipole currents and show that analogous Hall dipole voltages arise. We also discuss the robustness of the effect and suggest possible experimental realizations in quantum rings made of semiconductor heterostructures. Such experiments could also provide new ways of observing the predicted topological magneto-electric effect in three dimensional topological insulators with time reversal symmetry breaking. I thank BCUD, Pune University, Pune for financial support through research grant.
Glorieux, Quentin; Guidoni, Luca; Guibal, Samuel; Likforman, Jean-Pierre; Coudreau, Thomas
2011-11-15
We study the generation of intensity quantum correlations using four-wave mixing in a rubidium vapor. The absence of cavities in these experiments allows to deal with several spatial modes simultaneously. In the standard amplifying configuration, we measure relative intensity squeezing up to 9.2 dB below the standard quantum limit. We also theoretically identify and experimentally demonstrate an original regime where, despite no overall amplification, quantum correlations are generated. In this regime, a four-wave mixing setup can play the role of a photonic beam splitter with nonclassical properties, that is, a device that splits a coherent state input into two quantum-correlated beams.
Hwang, Kyusung; Kim, Yong Baek
2016-01-01
We theoretically investigate emergent quantum phases in the thin film geometries of the pyrochore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases as well as novel quantum states that may arise only in the thin film platforms, are studied via a theoretical model that allows layer-dependent magnetic structures. It is found that the magnetic order develop in inhomogeneous fashions in the thin film geometries. This leads to a variety of magnetic metal phases with modulated magnetic ordering patterns across different layers. Both the bulk and boundary electronic states in these phases conspire to promote unusual electronic properties. In particular, such phases are akin to the Weyl semimetal phase in the bulk system and they would exhibit an unusually large anomalous Hall effect. PMID:27418293
Hwang, Kyusung; Kim, Yong Baek
2016-01-01
We theoretically investigate emergent quantum phases in the thin film geometries of the pyrochore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases as well as novel quantum states that may arise only in the thin film platforms, are studied via a theoretical model that allows layer-dependent magnetic structures. It is found that the magnetic order develop in inhomogeneous fashions in the thin film geometries. This leads to a variety of magnetic metal phases with modulated magnetic ordering patterns across different layers. Both the bulk and boundary electronic states in these phases conspire to promote unusual electronic properties. In particular, such phases are akin to the Weyl semimetal phase in the bulk system and they would exhibit an unusually large anomalous Hall effect. PMID:27418293
NASA Astrophysics Data System (ADS)
Hwang, Kyusung; Kim, Yong Baek
2016-07-01
We theoretically investigate emergent quantum phases in the thin film geometries of the pyrochore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases as well as novel quantum states that may arise only in the thin film platforms, are studied via a theoretical model that allows layer-dependent magnetic structures. It is found that the magnetic order develop in inhomogeneous fashions in the thin film geometries. This leads to a variety of magnetic metal phases with modulated magnetic ordering patterns across different layers. Both the bulk and boundary electronic states in these phases conspire to promote unusual electronic properties. In particular, such phases are akin to the Weyl semimetal phase in the bulk system and they would exhibit an unusually large anomalous Hall effect.
Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
Claassen, Martin; Lee, Ching-Hua; Thomale, Ronny; Qi, Xiao-Liang; Devereaux, Thomas P
2015-06-11
We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as duals of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.
Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
Claassen, Martin; Lee, Ching-Hua; Thomale, Ronny; Qi, Xiao-Liang; Devereaux, Thomas P
2015-06-11
We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as dualsmore » of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.« less
Hwang, Kyusung; Kim, Yong Baek
2016-07-15
We theoretically investigate emergent quantum phases in the thin film geometries of the pyrochore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases as well as novel quantum states that may arise only in the thin film platforms, are studied via a theoretical model that allows layer-dependent magnetic structures. It is found that the magnetic order develop in inhomogeneous fashions in the thin film geometries. This leads to a variety of magnetic metal phases with modulated magnetic ordering patterns across different layers. Both the bulk and boundary electronic states in these phases conspire to promote unusual electronic properties. In particular, such phases are akin to the Weyl semimetal phase in the bulk system and they would exhibit an unusually large anomalous Hall effect.
Circuit models and SPICE macro-models for quantum Hall effect devices
NASA Astrophysics Data System (ADS)
Ortolano, Massimo; Callegaro, Luca
2015-08-01
Precise electrical measurement technology based on the quantum Hall effect is one of the pillars of modern quantum electrical metrology. Electrical networks including one or more QHE elements can be used as quantum resistance and impedance standards. The analysis of these networks allows metrologists to evaluate the effect of the inevitable parasitic parameters on their performance as standards. This paper presents a concise review of the various circuit models for QHE elements proposed in the literature, and the development of a new model. This last model is particularly suited to be employed with the analogue electronic circuit simulator SPICE. The SPICE macro-model and examples of SPICE simulations, validated by comparison with the corresponding analytical solution and/or experimental data, are provided.
Phase Space for the Breakdown of the Quantum Hall Effect in Epitaxial Graphene
NASA Astrophysics Data System (ADS)
Alexander-Webber, J. A.; Baker, A. M. R.; Janssen, T. J. B. M.; Tzalenchuk, A.; Lara-Avila, S.; Kubatkin, S.; Yakimova, R.; Piot, B. A.; Maude, D. K.; Nicholas, R. J.
2013-08-01
We report the phase space defined by the quantum Hall effect breakdown in polymer gated epitaxial graphene on SiC (SiC/G) as a function of temperature, current, carrier density, and magnetic fields up to 30 T. At 2 K, breakdown currents (Ic) almost 2 orders of magnitude greater than in GaAs devices are observed. The phase boundary of the dissipationless state (ρxx=0) shows a [1-(T/Tc)2] dependence and persists up to Tc>45K at 29 T. With magnetic field Ic was found to increase ∝B3/2 and Tc∝B2. As the Fermi energy approaches the Dirac point, the ν=2 quantized Hall plateau appears continuously from fields as low as 1 T up to at least 19 T due to a strong magnetic field dependence of the carrier density.
Landau-level dispersion and the quantum Hall plateaus in bilayer graphene
Zarenia, M.; Peeters, F. M.; Vasilopoulos, P.; Pourtolami, N.
2013-12-04
We study the quantum Hall effect (QHE) in bilayer graphene using the Kubo-Greenwood formula. At zero temperature the Hall conductivity σ{sub yx} is given by σ{sub yx} = 4(N+1)e{sup 2}/h with N the index of the highest occupied Landau level (LL). Including the dispersion of the LLs and their width, due to e.g. scattering by impurities, produces the plateau of the n = 0 LL in agreement with experimental results on doped samples and similar theoretical results on single-layer graphene plateaus widen with impurity concentration. Further, the evaluated resistivity ρ{sub xx} exhibits a strong, oscillatory dependence on the electron concentration. Explicit results are obtained for δ-function impurities.
Magnon Hall effect in AB-stacked bilayer honeycomb quantum magnets
NASA Astrophysics Data System (ADS)
Owerre, S. A.
2016-09-01
Motivated by the fact that many bilayer quantum magnets occur in nature, we generalize the study of thermal Hall transports of spin excitations to bilayer magnetic systems. It is shown that bilayer magnetic systems can be coupled either ferromagnetically or antiferromagnetically. We study both scenarios on the honeycomb lattice and show that the system realizes topologically nontrivial magnon bands induced by alternating next-nearest-neighbor Dzyaloshinsky-Moriya interaction. As a result, the bilayer system realizes both magnon Hall effect and magnon spin Nernst effect. We show that antiferromagnetically coupled layers differ from ferromagnetically coupled layers by a sign change in the conductivities as the magnetic field is reversed. Furthermore, Chern number protected magnon edge states are observed and propagate in the same direction on the top and bottom layers in ferromagnetically coupled layers, whereas the magnon edge states propagate in opposite directions for antiferromagnetically coupled layers.
NASA Astrophysics Data System (ADS)
Greshnov, A. A.; Kolesnikova, E. N.; Utesov, O. I.; Zegrya, G. G.
2010-02-01
The divergent at ω=0 quantum correction to conductivity δσ2(ω) of the leading order in (kFl)-1 has been calculated neglecting Cooperon-type contributions suppressed by moderate or strong magnetic field. In the so-called diffusion approximation this quantity is equal to zero up to the second order in (kFl)-1. More subtle treatment of the problem shows that δσ2(ω) is non-zero due to ballistic contributions neglected previously. Knowledge of δσ2(ω) allows to estimate value of the so-called unitary localization length as ξu≈lexp(1.6g2) where Drude conductivity is given by σ0=ge2/h. This estimation underpins the statement of the linear growth of σxx peaks with Landau level number n in the integer quantum Hall effect regime [1] (Greshnov and Zegrya, 2008; Greshnov et al., 2008) at least for n≤2 and calls Pruisken-Khmelnitskii hypothesis of universality [2] (Levine et al., 1983; Khmelnitskii, 1983) in question.
Computer-automated tuning of semiconductor double quantum dots into the single-electron regime
NASA Astrophysics Data System (ADS)
Baart, T. A.; Eendebak, P. T.; Reichl, C.; Wegscheider, W.; Vandersypen, L. M. K.
2016-05-01
We report the computer-automated tuning of gate-defined semiconductor double quantum dots in GaAs heterostructures. We benchmark the algorithm by creating three double quantum dots inside a linear array of four quantum dots. The algorithm sets the correct gate voltages for all the gates to tune the double quantum dots into the single-electron regime. The algorithm only requires (1) prior knowledge of the gate design and (2) the pinch-off value of the single gate T that is shared by all the quantum dots. This work significantly alleviates the user effort required to tune multiple quantum dot devices.
High-Temperature Quantum Anomalous Hall Effect in n-p Codoped Topological Insulators.
Qi, Shifei; Qiao, Zhenhua; Deng, Xinzhou; Cubuk, Ekin D; Chen, Hua; Zhu, Wenguang; Kaxiras, Efthimios; Zhang, S B; Xu, Xiaohong; Zhang, Zhenyu
2016-07-29
The quantum anomalous Hall effect (QAHE) is a fundamental quantum transport phenomenon that manifests as a quantized transverse conductance in response to a longitudinally applied electric field in the absence of an external magnetic field, and it promises to have immense application potential in future dissipationless quantum electronics. Here, we present a novel kinetic pathway to realize the QAHE at high temperatures by n-p codoping of three-dimensional topological insulators. We provide a proof-of-principle numerical demonstration of this approach using vanadium-iodine (V-I) codoped Sb_{2}Te_{3} and demonstrate that, strikingly, even at low concentrations of ∼2% V and ∼1% I, the system exhibits a quantized Hall conductance, the telltale hallmark of QAHE, at temperatures of at least ∼50 K, which is 3 orders of magnitude higher than the typical temperatures at which it has been realized to date. The underlying physical factor enabling this dramatic improvement is tied to the largely preserved intrinsic band gap of the host system upon compensated n-p codoping. The proposed approach is conceptually general and may shed new light in experimental realization of high-temperature QAHE.
Topological phase transition and quantum spin Hall edge states of antimony few layers
Kim, Sung Hwan; Jin, Kyung-Hwan; Park, Joonbum; Kim, Jun Sung; Jhi, Seung-Hoon; Yeom, Han Woong
2016-01-01
While two-dimensional (2D) topological insulators (TI’s) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi2Te2Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition. PMID:27624972
Non-Abelian fractional quantum Hall states for hard-core bosons in one dimension
NASA Astrophysics Data System (ADS)
Paredes, Belén
2012-05-01
I present a family of one-dimensional bosonic liquids analogous to non-Abelian fractional quantum Hall states. A new quantum number is introduced to characterize these liquids, the chiral momentum, which differs from the usual angular or linear momentum in one dimension. As their two-dimensional counterparts, these liquids minimize a k-body hard-core interaction with the minimum total chiral momentum. They exhibit global order, with a hidden organization of the particles in k identical copies of a one-dimensional Laughlin state. For k=2 the state is a p-wave paired phase corresponding to the Pfaffian quantum Hall state. By imposing conservation of the total chiral momentum, an exact parent Hamiltonian is derived which involves long-range tunneling and interaction processes with an amplitude decaying with the chord distance. This family of non-Abelian liquids is shown to be in formal correspondence with a family of spin-(k)/(2) liquids which are total singlets made out of k indistinguishable resonating valence bond states. The corresponding spin Hamiltonians are obtained.
High-Temperature Quantum Anomalous Hall Effect in n-p Codoped Topological Insulators.
Qi, Shifei; Qiao, Zhenhua; Deng, Xinzhou; Cubuk, Ekin D; Chen, Hua; Zhu, Wenguang; Kaxiras, Efthimios; Zhang, S B; Xu, Xiaohong; Zhang, Zhenyu
2016-07-29
The quantum anomalous Hall effect (QAHE) is a fundamental quantum transport phenomenon that manifests as a quantized transverse conductance in response to a longitudinally applied electric field in the absence of an external magnetic field, and it promises to have immense application potential in future dissipationless quantum electronics. Here, we present a novel kinetic pathway to realize the QAHE at high temperatures by n-p codoping of three-dimensional topological insulators. We provide a proof-of-principle numerical demonstration of this approach using vanadium-iodine (V-I) codoped Sb_{2}Te_{3} and demonstrate that, strikingly, even at low concentrations of ∼2% V and ∼1% I, the system exhibits a quantized Hall conductance, the telltale hallmark of QAHE, at temperatures of at least ∼50 K, which is 3 orders of magnitude higher than the typical temperatures at which it has been realized to date. The underlying physical factor enabling this dramatic improvement is tied to the largely preserved intrinsic band gap of the host system upon compensated n-p codoping. The proposed approach is conceptually general and may shed new light in experimental realization of high-temperature QAHE. PMID:27517787
Topological phase transition and quantum spin Hall edge states of antimony few layers
NASA Astrophysics Data System (ADS)
Kim, Sung Hwan; Jin, Kyung-Hwan; Park, Joonbum; Kim, Jun Sung; Jhi, Seung-Hoon; Yeom, Han Woong
2016-09-01
While two-dimensional (2D) topological insulators (TI’s) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi2Te2Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition.
High-Temperature Quantum Anomalous Hall Effect in n -p Codoped Topological Insulators
NASA Astrophysics Data System (ADS)
Qi, Shifei; Qiao, Zhenhua; Deng, Xinzhou; Cubuk, Ekin D.; Chen, Hua; Zhu, Wenguang; Kaxiras, Efthimios; Zhang, S. B.; Xu, Xiaohong; Zhang, Zhenyu
2016-07-01
The quantum anomalous Hall effect (QAHE) is a fundamental quantum transport phenomenon that manifests as a quantized transverse conductance in response to a longitudinally applied electric field in the absence of an external magnetic field, and it promises to have immense application potential in future dissipationless quantum electronics. Here, we present a novel kinetic pathway to realize the QAHE at high temperatures by n -p codoping of three-dimensional topological insulators. We provide a proof-of-principle numerical demonstration of this approach using vanadium-iodine (V-I) codoped Sb2 Te3 and demonstrate that, strikingly, even at low concentrations of ˜2 % V and ˜1 % I, the system exhibits a quantized Hall conductance, the telltale hallmark of QAHE, at temperatures of at least ˜50 K , which is 3 orders of magnitude higher than the typical temperatures at which it has been realized to date. The underlying physical factor enabling this dramatic improvement is tied to the largely preserved intrinsic band gap of the host system upon compensated n -p codoping. The proposed approach is conceptually general and may shed new light in experimental realization of high-temperature QAHE.
Topological phase transition and quantum spin Hall edge states of antimony few layers.
Kim, Sung Hwan; Jin, Kyung-Hwan; Park, Joonbum; Kim, Jun Sung; Jhi, Seung-Hoon; Yeom, Han Woong
2016-01-01
While two-dimensional (2D) topological insulators (TI's) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi2Te2Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition. PMID:27624972
Dumbbell silicene: a strain-induced room temperature quantum spin Hall insulator
NASA Astrophysics Data System (ADS)
Zhang, Tian; Zeng, Zhao-Yi; Cheng, Yan; Chen, Xiang-Rong; Cai, Ling-Cang
2016-04-01
By the generalized gradient approximation in the framework of density functional theory, we find a new silicon allotrope (called dumbbell silicene) with high stability, which can turn a quantum spin Hall insulator with an inverted band gap through tuning external compression strain, just like in previous silicene. However, the obtained maximum topological nontrivial band gap about 12 meV under isotropic strain is much larger than that for previous silicene, and can be further improved to 36 meV by tuning extra anisotropic strain, which is sufficiently large to realize quantum spin Hall effect even at room-temperature, and thus is beneficial to the fabrication of high-speed spintronics devices. Furthermore, we confirm that the boron nitride sheet is an ideal substrate for the experimental realization of the dumbbell silicene under external strain, maintaining its nontrivial topology. These properties make the two-dimensional dumbbell silicene a good platform to study novel quantum states of matter, showing great potential for future applications in modern silicon-based microelectronics industry.
Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states
NASA Astrophysics Data System (ADS)
Fuji, Yohei; He, Yin-Chen; Bhattacharjee, Subhro; Pollmann, Frank
2016-05-01
We investigate a model of hard-core bosons with correlated hopping on the honeycomb lattice in an external magnetic field by means of a coupled-wire approach. It has been numerically shown that this model exhibits at half filling the bosonic integer quantum Hall (BIQH) state, which is a symmetry-protected topological phase protected by the U (1 ) particle conservation [Y.-C. He et al., Phys. Rev. Lett. 115, 116803 (2015), 10.1103/PhysRevLett.115.116803]. By combining the bosonization approach and a coupled-wire construction, we analytically confirm this finding and show that it even holds in the strongly anisotropic (quasi-one-dimensional) limit. We discuss the stability of the BIQH phase against tunnelings that break the separate particle conservations on different sublattices down to a global particle conservation. We further argue that a phase transition between two different BIQH phases is in a deconfined quantum critical point described by two copies of the (2 +1 ) -dimensional O (4 ) nonlinear sigma model with the topological θ term at θ =π . Finally, we predict a possible fractional quantum Hall state, the Halperin (221 ) state, at 1 /6 filling.
Valley-polarized metals and quantum anomalous Hall effect in silicene.
Ezawa, Motohiko
2012-08-01
Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low-energy structure of silicene is described by Dirac electrons with relatively large spin-orbit interactions due to its buckled structure. The key observation is that the band structure is controllable by applying electric field to silicene. We explore the phase diagram of silicene together with exchange field M and by applying electric field E(z). A quantum anomalous Hall (QAH) insulator, valley polarized metal (VPM), marginal valley polarized metal (M-VPM), quantum spin Hall insulator, and band insulator appear. They are characterized by the Chern numbers and/or by the edge modes of a nanoribbon. It is intriguing that electrons have been moved from a conduction band at the K point to a valence band at the K' point for E(z) > 0 in the VPM. We find in the QAH phase that almost flat gapless edge modes emerge and that spins form a momentum-space Skyrmion to yield the Chern number. It is remarkable that a topological quantum phase transition can be induced simply by changing electric field in a single silicene sheet.
Room temperature quantum spin Hall insulators with a buckled square lattice.
Luo, Wei; Xiang, Hongjun
2015-05-13
Two-dimensional (2D) topological insulators (TIs), also known as quantum spin Hall (QSH) insulators, are excellent candidates for coherent spin transport related applications because the edge states of 2D TIs are robust against nonmagnetic impurities since the only available backscattering channel is forbidden. Currently, most known 2D TIs are based on a hexagonal (specifically, honeycomb) lattice. Here, we propose that there exists the quantum spin Hall effect (QSHE) in a buckled square lattice. Through performing global structure optimization, we predict a new three-layer quasi-2D (Q2D) structure, which has the lowest energy among all structures with the thickness less than 6.0 Å for the BiF system. It is identified to be a Q2D TI with a large band gap (0.69 eV). The electronic states of the Q2D BiF system near the Fermi level are mainly contributed by the middle Bi square lattice, which are sandwiched by two inert BiF2 layers. This is beneficial since the interaction between a substrate and the Q2D material may not change the topological properties of the system, as we demonstrate in the case of the NaF substrate. Finally, we come up with a new tight-binding model for a two-orbital system with the buckled square lattice to explain the low-energy physics of the Q2D BiF material. Our study not only predicts a QSH insulator for realistic room temperature applications but also provides a new lattice system for engineering topological states such as quantum anomalous Hall effect.
Phase diagram and edge excitations of the ν = 0 quantum Hall state in graphene
NASA Astrophysics Data System (ADS)
Kharitonov, Maxim
2013-03-01
The interaction-induced broken-symmetry incompressible quantum Hall states in graphene at integer and fractional filling factors have by now been firmly established in transport and compressibility measurements. However, identifying their precise nature (e.g., how the symmetry is broken) still remains a tough challenge: on the experimental side, transport and compressibility probes do not provide direct information about the physical order; on the theoretical side, the presence of additional to spin discrete degrees of freedom, valleys, results in a variety of competing phases in this multicomponent system. As the prime example of this rich behavior, I will present a generic phase diagram for the intriguing ν = 0 state, obtained within the framework of quantum Hall ``ferromagnetism.'' The diagram consists of the canted antiferromagnetic, ferromagnetic, charge-density-wave (charge-layer-polarized), and Kekulé (interlayer-coherent) phases in monolayer (bilayer). I will then discuss the edge excitations of the ν = 0 state. Remarkably, the edge excitations are nonuniversal (e.g., can be gapped or gapless) and crucially depend on which phase is realized in the bulk of the system. Besides being of considerable theoretical interest, these unprecedented properties simultaneously allow one to infer about the nature of the phases from the transport experiments. I will present arguments based on this analysis and existing data why the insulating ν = 0 state realized in real bilayer (and possibly, monolayer) graphene is likely to be canted antiferromagnetic. Finally, I will mention how this theoretical framework can be generalized to fractional quantum Hall states in graphene, which could shed light on some of the puzzling features of the recent experiments. This research was supported by the U.S. DOE under contracts No. DE-FG02-99ER45790 and No. DE- AC02-06CH11357.
Correlated Electrons in Two Dimensions: The Fractional Quantum Hall Effect and More
NASA Astrophysics Data System (ADS)
Eisenstein, James
2014-03-01
A collection of electrons confined to move on a plane surface is surely one of the simplest many-body systems imaginable. But in spite of this apparent simplicity, a strong magnetic field applied perpendicular to the plane opens a door to a complex and beautiful world filled with many-body exotica. The magnetic field quenches the kinetic energy, leaving Coulomb interactions in control of the physics. The result has been a revolution in many-body physics comparable to that created by the discovery of superconductivity. Incompressible liquid ground states with fractionally charged quasiparticle excitations exhibit the quantized Hall effect at numerous discrete partial fillings of the lowest and first excited Landau level. The first examples of topological condensed matter, these many-body bulk insulators possess complex families of both conducting and neutral edge states at their boundaries. Highly correlated compressible phases of composite fermions also exist and may be viewed as progenitors of the various families of incompressible states. Multi-component two-dimensional systems with active discrete internal degrees of freedom (spin, layer, valley, etc.) display a wide array of broken symmetry states including ferromagnetism and exciton condensation. Now thirty years old, the field generically dubbed ``the fractional quantum Hall effect,'' remains extraordinarily vibrant. Once confined largely to GaAs/AlGaAs heterostructures, the fractional quantum Hall effect and its many relatives and offspring are now pursued in graphene, various oxide interfaces, and other materials. Some of the most fundamental aspects, including the exotic non-abelian quasiparticle statistics expected of some of the more subtle phases, have hardly been touched experimentally even as their potential for applications to quantum computation is alluring. In this talk, I will try to give a flavor of this enormous field, emphasizing current topics and possible future directions.
NASA Astrophysics Data System (ADS)
Mihajlović, Goran; Xiong, Peng; von Molnár, Stephan; Ohtani, Keita; Ohno, Hideo; Field, Mark; Sullivan, Gerard J.
2005-09-01
Room-temperature detection of a single commercial superparamagnetic bead (1.2μm in diameter) suitable for biological applications has been realized using an InAs quantum-well micro-Hall sensor. The detection was demonstrated using phase-sensitive detection on a single Hall cross as well as in a Hall gradiometry setup. The high signal to noise ratio, obtained in both configurations, promises detection of single nanometer-size particles by further miniaturization of the device to submicron dimensions.
Strain-induced quantum spin Hall effect in methyl-substituted germanane GeCH3
Ma, Yandong; Dai, Ying; Wei, Wei; Huang, Baibiao; Whangbo, Myung-Hwan
2014-01-01
Quantum spin Hall (QSH) insulators exhibit a bulk insulting gap and metallic edge states characterized by nontrivial topology. We investigated the electronic structure of an isolated layer of methyl substituted germanane GeCH3 by density functional calculations (DFT), and its dynamic stability by phonon dispersion calculations. Our results show that an isolated GeCH3 layer has no dynamic instability, and is a QSH insulator under reasonable strain. This QSH insulator has a large enough band gap (up to 108 meV) at 12% strain. The advantageous features of this QSH insulator for practical room-temperature applications are discussed. PMID:25465887
Theory of High-Energy Features in the Tunneling Spectra of Quantum-Hall Systems
NASA Astrophysics Data System (ADS)
MacDonald, A. H.
2010-11-01
We show that the low-temperature sash features in lowest Landau-level (LLL) tunneling spectra recently discovered by Dial and Ashoori are intimately related to the discrete Haldane-pseudopotential interaction energy scales that govern fractional quantum-Hall physics. Our analysis is based on expressions for the tunneling density of states which become exact at filling factors close to ν=0 and ν=1, where the sash structure is most prominent. We comment on other aspects of LLL correlation physics that can be revealed by accurate temperature-dependent tunneling data.
Theory of high-energy features in the tunneling spectra of quantum-Hall systems.
MacDonald, A H
2010-11-12
We show that the low-temperature sash features in lowest Landau-level (LLL) tunneling spectra recently discovered by Dial and Ashoori are intimately related to the discrete Haldane-pseudopotential interaction energy scales that govern fractional quantum-Hall physics. Our analysis is based on expressions for the tunneling density of states which become exact at filling factors close to ν=0 and ν=1, where the sash structure is most prominent. We comment on other aspects of LLL correlation physics that can be revealed by accurate temperature-dependent tunneling data. PMID:21231254
Hydrodynamic study of edge spin-vortex excitations of fractional quantum Hall fluid
NASA Astrophysics Data System (ADS)
Rabiu, M.; Mensah, S. Y.; Seini, I. Y.; Abukari, S. S.
2016-07-01
We undertake a theoretical study of edge spin-vortex excitations in fractional quantum Hall fluid. This is done in view of quantised Euler hydrodynamics theory. The dispersions of true excitations for fractions within 0 ≤ ν ≤ 1 are simulated which exhibit universal similarities and differences in behaviour. The differences arise from different edge smoothness and spin (pseudo-spin) polarisations, in addition to spin-charge competition. In particular, tuning the spin-charge factor causes coherent spin flipping associated with partial and total polarisations of edge spin-vortices. This observation is tipped as an ideal mechanism for realisation of functional spintronic devices.