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In this study, quantum Hall effect-like plateaus, exhibiting the behavior of single- and multi-graphene, are observed in ZYA-grade highly oriented pyrolytic graphite (HOPG). Massless Dirac carriers and massive normal carriers of the HOPG are distinguished from the analysis of Shubnikov-de Haas and de Haas van Alphen oscillations. The quantum Hall effect-like plateaus are diminished after proton-irradiation owing to increasing interlayer interaction along the c-axis that causes the change of two-dimensional massless carriers of the HOPG to three-dimensional massive carriers. Moreover, tight-binding calculations exhibit similar diminishing plateaus of the Hall conductivity of HOPG as the interlayer interaction increases. This observation of dimensional crossover of the Hall conductivity demonstrates that proton-irradiation would be a useful tool to control quantum transport in HOPG through manipulating its interlayer interaction.

The classical and quantum Hall effects are important subjects in condensed matter physics. The emergent 3D quantum Hall effects and nonlinear Hall effect have attracted considerable interest recently, with the former elevating the quantum Hall effect to a higher dimension and the latter extending the Hall effect to higher-order responses. In this perspective, we briefly introduce these two new members of the Hall family and discuss the open questions and future research directions.

The interplay of strong Coulomb interactions and of topology is currently under intense scrutiny in various condensed matter and atomic systems. One example of this interplay is the phase competition of fractional quantum Hall states and the Wigner solid in the two-dimensional electron gas. Here we report a Wigner solid at ν = 1.79 and its melting due to fractional correlations occurring at ν = 9/5. This Wigner solid, that we call the reentrant integer quantum Hall Wigner solid, develops in a range of Landau level filling factors that is related by particle-hole symmetry to the so called reentrant Wigner solid. We thus find that the Wigner solid in the GaAs/AlGaAs system straddles the partial filling factor 1/5 not only at the lowest filling factors, but also near ν = 9/5. Our results highlight the particle-hole symmetry as a fundamental symmetry of the extended family of Wigner solids and paint a complex picture of the competition of the Wigner solid with fractional quantum Hall states.

Using recently developed tools from space-adiabatic perturbation theory, in particular the construction of a non-equilibrium almost stationary state, we give a new proof that the Kubo formula for the Hall conductivity remains valid beyond the linear response regime. In particular, we prove that, in quantum Hall systems and Chern insulators, the transverse response current is quantized up to any order in the strength of the inducing electric field. The latter is introduced as a perturbation to a periodic, spectrally gapped equilibrium Hamiltonian by means of a linear potential; existing proofs of the exactness of Kubo formula rely instead on a time-dependent magnetic potential. The result applies to both continuum and discrete crystalline systems modelling the quantum (anomalous) Hall effect., Comment: 18 pages

The Hall effects comprise one of the oldest but most vital fields in condensed matter physics, and they persistently inspire new findings, such as quantum Hall effects and topological phases of matter. The recently discovered nonlinear Hall effect is a new member of the family of Hall effects. It is characterized as a transverse Hall voltage in response to two longitudinal currents in the Hall measurement, but it does not require time-reversal symmetry to be broken. It has deep connections to symmetry and topology and, thus, opens new avenues by which to probe the spectral, symmetry and topological properties of emergent quantum materials and phases of matter. In this Perspective, we present an overview of the recent progress regarding the nonlinear Hall effect. We discuss the open problems, the prospects of the use of the nonlinear Hall effect in spectroscopic and device applications, and generalizations to other nonlinear transport effects., A subscription-free version can be found at https://rdcu.be/cwqYd

The quantum Hall effect is the seminal example of topological protection, as charge carriers are transmitted through one-dimensional edge channels where backscattering is prohibited. Graphene has made its marks as an exceptional platform to reveal new facets of this remarkable property. However, in conventional Hall bar geometries, topological protection of graphene edge channels is found regrettably less robust than in high mobility semi-conductors. Here, we explore graphene quantum Hall regime at the local scale, using a scanning gate microscope. We reveal the detrimental influence of antidots along the graphene edges, mediating backscattering towards upstream edge channels, hence triggering topological breakdown. Combined with simulations, our experimental results provide further insights into graphene quantum Hall channels vulnerability. In turn, this may ease future developments towards precise manipulation of topologically protected edge channels hosted in various types of two-dimensional crystals., 6 pages, 4 figures

Exciting phenomena may emerge in non-centrosymmetric two-dimensional electronic systems when spin-orbit coupling (SOC)1 interplays dynamically with Coulomb interactions2,3, band topology4,5 and external modulating forces6-8. Here we report synergetic effects between SOC and the Stark effect in centrosymmetric few-layer black arsenic, which manifest as particle-hole asymmetric Rashba valley formation and exotic quantum Hall states that are reversibly controlled by electrostatic gating. The unusual findings are rooted in the puckering square lattice of black arsenic, in which heavy 4p orbitals form a Brillouin zone-centred Γ valley with pz symmetry, coexisting with doubly degenerate D valleys of px origin near the time-reversal-invariant momenta of the X points. When a perpendicular electric field breaks the structure inversion symmetry, strong Rashba SOC is activated for the px bands, which produces spin-valley-flavoured D± valleys paired by time-reversal symmetry, whereas Rashba splitting of the Γ valley is constrained by the pz symmetry. Intriguingly, the giant Stark effect shows the same px-orbital selectiveness, collectively shifting the valence band maximum of the D± Rashba valleys to exceed the Γ Rashba top. Such an orchestrating effect allows us to realize gate-tunable Rashba valley manipulations for two-dimensional hole gases, hallmarked by unconventional even-to-odd transitions in quantum Hall states due to the formation of a flavour-dependent Landau level spectrum. For two-dimensional electron gases, the quantization of the Γ Rashba valley is characterized by peculiar density-dependent transitions in the band topology from trivial parabolic pockets to helical Dirac fermions.

We fabricated a monolayer graphene transistor device in the shape of the Hall-bar structure, which produced an exactly symmetric signal following the sample geometry. During electrical characterization, the device showed the standard integer quantum Hall effect of monolayer graphene except for a broader range of several quantum Hall plateaus corresponding to small filling factors in the electron region. We investigated this anomaly on the basis of localized states owing to the presence of possible electron traps, whose energy levels were estimated to be near the Dirac point. In particular, the inequality between the filling of electrons and holes was ascribed to the requirement of excess electrons to fill the trap levels. The relations between the quantum Hall plateau, Landau level, and filling factor were carefully analyzed to reveal the details of the localized states in this graphene device.

Electron interferometry with quantum Hall edge channels holds promise for probing and harnessing exotic exchange statistics of non-Abelian anyons. In semiconductor heterostructures, however, quantum Hall interferometry has proven challenging and often obscured by charging effects. Here we show that high-mobility monolayer graphene equipped with a series of gate-tunable quantum point contacts that act as electron beam-splitters provides a model system to perform Fabry-P\'{e}rot quantum Hall interferometry. We observe high-visibility Aharonov-Bohm interference free of charging effects and widely tunable through electrostatic gating or magnetic field, in remarkable agreement with theory. A coherence length of $\mathbf{10 \,\mu m}$ at a temperature of $0.02$ K allows us to further achieve coherently-coupled double Fabry-P\'{e}rot interferometry. Our results open a new avenue for quantum Hall interferometry and the exploitation of topological excitations for quantum computation., Comment: Revised main text

Interferometers probe the wave-nature and exchange statistics of indistinguishable particles—for example, electrons in the chiral one-dimensional edge channels of the quantum Hall effect (QHE). Quantum point contacts can split and recombine these channels, enabling interference of charged particles. Such quantum Hall interferometers (QHIs) can unveil the exchange statistics of anyonic quasi-particles in the fractional quantum Hall effect (FQHE). Here, we present a fabrication technique for QHIs in van der Waals (vdW) materials and realize a tunable, graphene-based Fabry–Perot (FP) QHI. The graphite-encapsulated architecture allows observation of FQHE at a magnetic field of 3T and precise partitioning of integer and fractional edge modes. We measure pure Aharonov–Bohm interference in the integer QHE, a major technical challenge in small FP interferometers, and find that edge modes exhibit high-visibility interference due to large velocities. Our results establish vdW heterostructures as a versatile alternative to GaAs-based interferometers for future experiments targeting anyonic quasi-particles. Interferometers can probe the wave-nature and exchange statistics of indistinguishable particles. Quantum Hall interferometers from graphite-encapsulated graphene heterostructures now enable the observation of the Aharonov–Bohm effect and of robust fractional quantum Hall states.

The efforts toward the experimental realization of spin-polarized transports in ideal materials or platforms, such as the magnetized graphene or various quantum Hall states, is a research hotspot in spintronics. Magnetic van der Waals materials open the door for exploring various physical phenomena, technologies, and integrating novel spintronic devices seamlessly within the 2D limit. Here, we demonstrate magnetic proximity effect in chromium trichloride (CrCl3)/bilayer graphene (BLG) heterostructures by low-temperature transport measurements. An effective exchange field induced in BLG has been demonstrated by the Zeeman spin Hall effect via nonlocal measurements. Furthermore, the exchange field modulates the quantum Hall ground state of BLG and thus favors the formation of a canted antiferromagnetic (CAF) phase in an external perpendicular magnetic field (B⊥). Asymmetric nonlocal magneto-transport behaviors are also observed at opposite B⊥ directions, due to the asymmetric modulation on the exchange field by external B⊥ directions. Our work suggests that the 2D magnetic van der Waals materials and graphene hybrid systems offer a unique platform for quantum Hall ferromagnetism physics.

The thermodynamic stability of quantum Hall ferromagnets with filling factors ν = 1 and ν = 2 is studied via inelastic light scattering in strongly interacting two-dimensional electronic systems based on ZnO. For a ferromagnet with ν = 2, it is found that the Curie temperature is determined by the Coulomb energy of the formation of domain walls. For a ferromagnet with ν = 1, the thermodynamic stability is determined by the Zeeman splitting of the spin sublevels.

It is found that the thermalization of triplet spin-flip magneto-excitons in a quantum Hall dielectric is an unprecedentedly long process for translation-invariant nonequilibrium electronic systems. It is shown that a magneto-fermionic condensate, a state characterized by the ability to rapidly transfer spin over macroscopic distances, is formed by spin-flip excitons with generalized momenta on the order of the reciprocal magnetic length.

A study is preformed of the relationship between the spectrum of low-energy collective excitations in two-dimensional Fermi liquids and the paramagnet/ferromagnet phase transition in the quantum Hall state with filling factor v = 2. It is shown theoretically and experimentally that the softening of the energy of collective spin–flip excitations accompanies the spontaneous switching of the spin configuration of the system from the paramagnetic to the ferromagnetic phase.

In bilayer graphene rotationally faulted to theta=1.1 degrees, interlayer tunneling and rotational misalignment conspire to create a pair of low energy flat band that have been found to host various correlated phenomena at partial filling. Most work to date has focused on the zero magnetic field phase diagram, with magnetic field (B) used as a probe of the B=0 band structure. Here, we show that twisted bilayer graphene (tBLG) in a B as low as 2T hosts a cascade of ferromagnetic Chern insulators with Chern number |C|=1,2 and 3. We argue that the emergence of the Chern insulators is driven by the interplay of the moire superlattice with the B, which endow the flat bands with a substructure of topologically nontrivial subbands characteristic of the Hofstadter butterfly. The new phases can be accounted for in a Stoner picture in which exchange interactions favor polarization into one or more spin- and valley-isospin flavors; in contrast to conventional quantum Hall ferromagnets, however, electrons polarize into between one and four copies of a single Hofstadter subband with Chern number C=-1. In the case of the C=\pm3 insulators in particular, B catalyzes a first order phase transition from the spin- and valley-unpolarized B=0 state into the ferromagnetic state. Distinct from other moire heterostructures, tBLG realizes the strong-lattice limit of the Hofstadter problem and hosts Coulomb interactions that are comparable to the full bandwidth W and are consequently much stronger than the width of the individual Hofstadter subbands. In our experimental data, the dominance of Coulomb interactions manifests through the appearance of Chern insulating states with spontaneously broken superlattice symmetry at half filling of a C=-2 subband. Our experiments show that that tBLG may be an ideal venue to explore the strong interaction limit within partially filled Hofstadter bands., 17 pages, 15 figures

van der Waals heterostructures of two-dimensional materials are naturally endowed with the nanoscale moire pattern, which has become a versatile platform for studying novel quantum phenomena during the past few decades. Here, we discussed the moire superlattice combining graphene and hexagonal boron nitride (h-BN) which led to the observation of electronic minibands, superlattice Dirac points and anomalous physical phenomena such as the quantum Hall effect and the Hofstadter butterfly pattern. The twist bilayer graphene (TBG) system has witnessed the appearance of angle-dependent van Hove singularities. Moreover, in the magic-angle twisted bilayer graphene (MATBG), there is a superconductor–insulator transition due to the enhancement of van der Waals forces by interlayer resonant conditions. Besides, owing to the moire superlattice constant being comparable to the Bohr radius of excitons, exciton physics dominated by the moire potential for the heterojunction based on transition metal dichalcogenide (TMD) monolayers has attracted extensive attention. This review mainly covers the exotic physical properties, ranging from electronic structures to excitonic properties of graphene-based and TMD-based van der Waals-coupled twistronic materials, and discusses the remaining unsolved strongly correlated questions and possible expected semiconductor device applications in the quantum matter world.

Quantum point contacts (QPC) are a primary component in mesoscopic physics and have come to serve various purposes in modern quantum devices. However, fabricating a QPC that operates robustly under extreme conditions, such as high bias or magnetic fields, still remains an important challenge. As a solution, we have analyzed the trench-gated QPC (t-QPC) that has a central gate in addition to the split-gate structure used in conventional QPCs (c-QPC). From simulation and modelling, we predicted that the t-QPC has larger and more even subband spacings over a wider range of transmission when compared to the c-QPC. After an experimental verification, the two QPCs were investigated in the quantum Hall regimes as well. At high fields, the maximally available conductance was achievable in the t-QPC due to the local carrier density modulation by the trench gate. Furthermore, the t-QPC presented less anomalies in its DC bias dependence, indicating a possible suppression of impurity effects.

Anyons are quasiparticles that, unlike fermions and bosons, show fractional statistics when two of them are exchanged. Here, we report the experimental observation of anyonic braiding statistics for the ν = 1/3 fractional quantum Hall state by using an electronic Fabry–Perot interferometer. Strong Aharonov–Bohm interference of the edge mode is punctuated by discrete phase slips that indicate an anyonic phase θanyon = 2π/3. Our results are consistent with a recent theory that describes an interferometer operated in a regime in which device charging energy is small compared to the energy of formation of charged quasiparticles, which indicates that we have observed anyonic braiding. An interferometer device is used to detect the quantum-mechanical phase that is gained when two anyons are braided around each other. The fractional value of the phase proves that these quasiparticles are neither bosons nor fermions.

We present a study of Shubnikov–de Haas (SdH) oscillations at temperatures of (2.2–10) K in magnetic fields up to 2.5 T in the HgCdTe/HgTe/HgCdTe heterostructure for a wide (20.3 nm) HgTe quantum well with an inverted energy band structure. The analysis of the temperature dependence of SdH amplitude in weak fields, in a region of doubly degenerate magnetoresistance peaks, led us to the value of effective electron mass mc/m0 = (0.022 ± 0.002) which is about half the theoretical estimates. But in a region of higher magnetic fields, for nondegenerate magnetoresistance peaks, we confidently have mc/m0 = (0.034 ± 0.003) in good agreement both with the theoretical estimation and with our experimental results on the analysis of activation transport under quantum Hall effect regime. The reasons for this discrepancy are discussed.

The Raman study of strongly interacting two-dimensional electron systems based on ZnO/MgZnO has revealed an anomalously intense spectral line of the anti-Stokes component of the spin exciton. This line is manifested near the filling factor v = 2 at the ferromagnetic ordering of the spin subsystem, whereas it is not observed at the paramagnetic ordering. It has been shown that this line can be attributed to the formation of an ensemble of long-lived collective excitations in the ferromagnetic phase at a filling factor of v = 2.

We present in this paper the results from a recent study on the stability of the quantum Hall skyrmions state at a Landau level filling factor (ν) close to ν = 1 in a narrow GaAs quantum well. Consistent with previous work, a resonant behavior is observed in the resistively detected NMR measurements. In the subsequent current-voltage (I-V) measurements to examine its breakdown behavior under radio frequency radiations, we observe that the critical current assumes the largest value right at the 75As nuclear resonant frequency. We discuss possible origin for this unexpectedly enhanced stability.

application/pdf, 論文(Article), We introduced a liquid helium-free cryostat for studying quantum mechanical electron transports in semiconductors or topological insulators. This cryostat can cool the samples down to 1.5 K and is equipped with 14 T superconducting magnet. The resistance standard originating from the conductance quantization was accurately measured by the quantum Hall effect measurement in a Si-modulation-doped AlGaAs/GaAs single heterostructure, in which high-mobility two-dimensional electron channel was formed. In addition, diamagnetic levitation of bismuth was successively observed. Further enhancement of our study is expected using this cryostat system.

We summarize and discuss a self-consistent screening and magneto-transport theory, developed to understand the results of scanning-force-microscope experiments on the current distribution in a two-dimensional electron system (2DES), located in a narrow Hall bar under the conditions of the integer quantum Hall effect (IQHE) and its breakdown. The theory explains why, at low temperatures, at certain intervals of the applied perpendicular magnetic field, the current density is confined to “incompressible stripes” (ISs), in which a fixed number of Landau levels is occupied, and the longitudinal and Hall resistivity assume quantized values. The theory also explains, how the position and shape of these ISs depend on magnetic field and temperature, and why the confinement of the current density on these ISs leads to precisely quantized values of the macroscopic longitudinal and Hall resistance. The theory, which leads, at high temperatures, to the well known Drude results for current density and resistance, shows that the IQHE is a consequence of the peculiar screening properties of a 2DES in a strong magnetic field at low temperatures, and that it can be understood without assumptions about special localization effects.

Coulomb diamonds are the archetypal signatures of Coulomb blockade, a well-known charging effect mainly observed in nanometer-sized "electronic islands" tunnel-coupled with charge reservoirs. Here, we identify apparent Coulomb diamond features in the scanning gate spectroscopy of a quantum point contact carved out of a semiconductor heterostructure, in the quantum Hall regime. Varying the scanning gate parameters and the magnetic field, the diamonds are found to smoothly evolve to checkerboard patterns. To explain this surprising behavior, we put forward a model which relies on the presence of a nanometer-sized Fabry-P\'erot quantum Hall interferometer at the center of the constriction with tunable tunneling paths coupling the central part of the interferometer to the quantum Hall channels running along the device edges. Both types of signatures, diamonds and checkerboards, and the observed transition, are reproduced by simply varying the interferometer size and the transmission probabilities at the tunneling paths. The new proposed interpretation of diamond phenomenology will likely lead to revisit previous data, and opens the way towards engineering more complex interferometric devices with nanoscale dimensions., Comment: 8 pages, 4 figures

Partially filled Landau levels host competing electronic orders. For example, electron solids may prevail close to integer filling of the Landau levels before giving way to fractional quantum Hall liquids at higher carrier density1,2. Here, we report the observation of an electron solid with non-collinear spin texture in monolayer graphene, consistent with solidification of skyrmions3—topological spin textures characterized by quantized electrical charge4,5. We probe the spin texture of the solids using a modified Corbino geometry that allows ferromagnetic magnons to be launched and detected6,7. We find that magnon transport is highly efficient when one Landau level is filled ($$\nu =1$$), consistent with quantum Hall ferromagnetic spin polarization. However, even minimal doping immediately quenches the magnon signal while leaving the vanishing low-temperature charge conductivity unchanged. Our results can be understood by the formation of a solid of charged skyrmions near $$\nu =1$$, whose non-collinear spin texture leads to rapid magnon decay. Data near fractional fillings show evidence of several fractional skyrmion solids, suggesting that graphene hosts a highly tunable landscape of coupled spin and charge orders. The authors use spin waves to demonstrate that charged quantum Hall skyrmions exist away from integer filling. They also see evidence of several fractional skyrmion states.

The theory of the two-dimensional (2D) magnetoexcitons was enlarged in two aspects. One of them takes into account the electron-hole (e–h) exchange Coulomb interaction, which appears when the conduction and the valence electrons belong partially to both bands. The exchange Coulomb interaction gives rise to the Dirac cone dispersion law in the range of small in-plane wave vectors k|| obeying to the condition |k|||l0 < 1, where l0 is the magnetic length. Such dispersion law may change essentially the properties of the high density magnetoexcitons opening the possibility of their Bose-Einstein condensation at different from zero temperatures [1]. Another aspect concerns the high density magnetoexcitons with fractional filling factors in conditions of fractional quantum Hall effects. The Chern-Simons gauge field was introduced into the Hamiltonian of the 2D coplanar e–h system by the unitary transformation. It gives rise to the additional gauge vector potential, the influence of which leads to the anisotropic corrections to the magnetoexciton magnetic mass [2].

Crystalline defects can modify quantum interactions in solids, causing unintuitive, even favourable, properties such as quantum Hall effect or superconducting vortex pinning. Here we present another example of this notion - an unexpected unidirectional Kondo scattering in single crystals of 2H-NbS2. This manifests as a pronounced low-temperature enhancement in the out-of-plane resistivity and thermopower below 40 K, hidden for the in-plane charge transport. The anomaly can be suppressed by the c-axis-oriented magnetic field, but is unaffected by field applied along the planes. The magnetic moments originate from layers of 1T-NbS2, which inevitably form during the growth, undergoing a charge-density-wave reconstruction with each superlattice cell (David-star-shaped cluster of Nb atoms) hosting a localised spin. Our results demonstrate the unique and highly anisotropic response of a spontaneously formed Kondo lattice heterostructure, intercalated in a layered conductor., 44 pages, including the article, 5 figures, and Supplementary Information (6 notes, 9 figures, and 1 table)

Two-dimensional electron systems in a quantizing magnetic field are regarded as of exceptional interest, considering the possible role of anyons—quasiparticles with non-boson and non-fermion statistics—in applied physics. To this day, essentially none but the fractional states of the quantum Hall effect (FQHE) have been experimentally realized as a system with anyonic statistics. In determining the thermodynamic properties of anyon matter, it is crucial to gain insight into the physics of its neutral excitations. We form a macroscopic quasi-equilibrium ensemble of neutral excitations - spin one anyon complexes in the Laughlin state ν = 1/3, experimentally, where ν is the electron filling factor. The ensemble is found to have such a long lifetime that it can be considered the new state of anyon matter. The properties of this state are investigated by optical techniques to reveal its Bose properties., The microscopic nature of neutral collective excitation of the fractional quantum Hall state is still debated. Here the authors show that a macroscopic ensemble of neutral excitations in the 1/3 state exhibits properties of a Bose system with an exceptionally long coherence time.

In ZnO-based two-dimensional electron systems with strong Coulomb interaction, the anomalous spin-exciton branch is revealed. As probed by inelastic light scattering, in a ferromagnetic quantum-Hall state with the filling factor $\ensuremath{\nu}=2$, a spin exciton has a negative momentum dispersion with steepness dependent on the electron density. The negative dispersion of the spin exciton is associated with its interaction with higher-energy spin-flip modes that exist near $\ensuremath{\nu}=2$. Surprisingly, the anti-Stokes light scattering on spin excitons at ferromagnetic state $\ensuremath{\nu}=2$ is amplified by orders of magnitude, indicating the macroscopic accumulation of these excitations. The experimental findings are confirmed by the exact diagonalization method---these calculations show a magnetoroton minimum in the dispersion of spin excitons and also the attractive interaction between magnetoroton spin excitations.

Detection and characterization of a different type of topological excitations, namely the domain wall (DW) skyrmion, has received increasing attention because the DW is ubiquitous from condensed matter to particle physics and cosmology. Here we present experimental evidence for the DW skyrmion as the ground state stabilized by long-range Coulomb interactions in a quantum Hall ferromagnet. We develop an alternative approach using nonlocal resistance measurements together with a local NMR probe to measure the effect of low current-induced dynamic nuclear polarization and thus to characterize the DW under equilibrium conditions. The dependence of nuclear spin relaxation in the DW on temperature, filling factor, quasiparticle localization, and effective magnetic fields allows us to interpret this ground state and its possible phase transitions in terms of Wigner solids of the DW skyrmion. These results demonstrate the importance of studying the intrinsic properties of quantum states that has been largely overlooked., Skyrmions, a topological spin texture, have been found in a variety of magnetic systems, including quantum hall ferromagnets. Here, Yang et al demonstrate the existence of skyrmions in domain walls in a quantum Hall ferromagnet, and suggest that these skyrmions form a 1D Wigner crystal.

Mixing of Landau levels has been understood to be essential in governing the nature of the ground state for the even-denominator fractional quantum Hall effect. The incompressibility of the ground state at filling factor $5/2$ in the strong Landau-level-mixed systems, such as the ZnO quantum well, is not always stable. Here we present an approach to generally deal with this kind of system and satisfactorily explain the recent experiments [Falson et al., Sci. Adv. 4, eaat8742 (2018)] by implementing the screening plus the thickness effect. Further, the phase diagrams of the incompressibility of the ground state indicate that the phase transitions can be explicitly extracted by observing the lowest gap of the collective modes when the magnetic field and the width of the quantum well are tuned. We also predict the incompressibility of the two-dimensional electron gas in higher Landau levels in another strong Landau-level-mixed system, viz., the black phosphorene, by considering the screening effect where the relevant even-denominator fractional quantum Hall effects can possibly be observed.

We study the low frequency admittance of a quantum Hall bar of size much larger than the electronic coherence length. We find that this macroscopic conductor behaves as an ideal quantum conductor with vanishing longitudinal resistance and purely inductive behavior up to f, 4 pages article with 4 figures, submitted to Physical Review B Letters, concatenated with 12 pages supplementary information (having 15 figures) in a 17 pages article with concantenated bibliography

Hybrid superconductor/graphene (SC/g) junctions are excellent candidates for investigating correlations between Cooper pairs and quantum Hall (QH) edge modes. Experimental studies are challenging as Andreev reflections are extremely sensitive to junction disorder and high magnetic fields are required to form QH edge states. We fabricated low-resistance SC/g interfaces, composed of graphene edge contacted with NbN with a barrier strength of $Z\approx 0.4$, that remain superconducting under magnetic fields larger than $18$ T. We establish the role of graphene's Dirac band structure on zero-field Andreev reflections and demonstrate dynamic tunability of the Andreev reflection spectrum by moving the boundary between specular and retro Andreev reflections with parallel magnetic fields. Through the application of perpendicular magnetic fields, we observe an oscillatory suppression of the 2-probe conductance in the $\nu = 4$ Landau level attributed to the reduced efficiency of Andreev processes at the NbN/g interface, consistent with theoretical predictions.

We propose an exact model of anyon ground states including higher Landau levels, and use it to obtain fractionally quantized Hall states at filling fractions $\nu=p/(p(m-1)+1)$ with $m$ odd, from integer Hall states at $\nu=p$ through adiabatic localization of magnetic flux. For appropriately chosen two-body potential interactions, the energy gap remains intact during the process. The construction hence establishes the existence of incompressible states at these fillings., Comment: 12pages

We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For interacting electrons, the statistical transmutation from anyons to bosons allows us to explicitly derive the microscopic statistical interaction between the anyons, in the form of the effective two-body and few-body interactions. This also leads to a number of unexpected topological phases of the single component bosonic fractional quantum Hall effect that may be experimentally accessible. Numerical analysis of the energy spectrum and ground state entanglement properties are carried out for simple examples., 4+ pages, 2 figures, comments very welcome

The integer quantum Hall state occurs when the Landau levels are fully occupied by the fermions, while the fractional quantum Hall state usually emerges when the Landau level is partially filled by the strongly correlated fermions or bosons. Here, we report two fractional Chern insulating states of the hard-core bosons in a multi-band lattice model hosting topological flat bands with high Chern number. The previously proposed $\nu=1/3$ fractional Chern insulating state inherited from the high Chern number $C=2$ of the lowest topological flat band is revisited by the infinite density matrix renormalization group algorithm. In particular, we numerically identify a bosonic $1/2$-Laughlin-like fractional Chern insulating state at the integer fillings. We show two lower topological flat bands jointly generate an effective $C=1$ Chern band with half-filling. Furthermore, we find a strictly particle-hole-like symmetry between the $\nu$ and $3-\nu$ filling in our model. These findings extend our understanding of quantum Hall states and offer a new route to realize the novel fractional states in the system with multi-bands and high-Chern numbers., Comment: 9 pages, 7 figures

The discrepancy between the theoretically calculated and experimentally measured activation gaps in quantum Hall effect has long been a puzzle. We revisit this issue in the context of the $\ensuremath{\nu}=1$ quantum Hall state, while also incorporating the skyrmion physics. We find that the finite width and the Landau level mixing effects are not sufficient to explain the observed activation gap. We further show that the presence of charged impurities located adjacent to the quantum well can cause a significant reduction in the activation gap, while also causing a suppression of the skyrmion size.

The quantum Hall effect, a quantum phenomenon that appears in macroscopic length scale, is one of the most important topics in condensed matter physics, is. It has long been expected that the quantum Hall effect may occur without Landau levels so that no external magnetic field nor high sample mobility is required for its studies and applications. Such a quantum Hall effect free of Landau levels can be realized in a topological insulator with its time-reversal symmetry broken by ferromagnetism as the quantized version of the anomalous Hall effect, i.e. the quantum anomalous Hall effect (see Figure 1 for the schematics of the quantum Hall effect and quantum anomalous Hall effect). Combing molecular beam epitaxy, scanning tunneling microscopy and angle-resolved photoemission spectroscopy, we prepared high quality thin films of magnetically doped (Bi, Sb)2Te3 topological insulator with well-controlled composition, thickness and chemical potential and systematically studied their transport properties. In 5 quintuple layer thick Cr-doped (Bi, Sb)2Te3 films we experimentally observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable reduction in the dissipation of electron transport. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value (see Figure 2). The observations unambiguously demonstrate the occurrence of the quantum anomalous Hall effect. The temperature, thickness and magnetic-doping-concentration dependences of the quantum anomalous Hall effect were systematically studied, which clarifies the roles of the band structure, electron localization and magnetic order in the effect and provides clues for obtaining the effect at a higher temperature. The experimental progresses in the quantum anomalous Hall effect pave the ways for applications of dissipationless quantum Hall edge states in low-energy-consuming devices and for realizations of other novel quantum phenomena such as chiral topological superconductivity and axion electrodynamics.

Adiabatically exchanging anyons gives rise to topologically protected operations on the quantum state of the system, but the desired result is only achieved if the anyons are well separated, which requires a sufficiently large area. Being able to reduce the area needed for the exchange, however, would have several advantages, such as enabling a larger number of operations per area and allowing anyon exchange to be studied in smaller systems that are easier to handle. Here, we use optimization techniques to squeeze the charge distribution of Abelian anyons in lattice fractional quantum Hall models, and we show that the squeezed anyons can be exchanged within a smaller area with a close to ideal outcome. We first use a toy model consisting of a modified Laughlin trial state to show that one can shape the anyons without altering the exchange statistics under certain conditions. We then squeeze and braid anyons in the Kapit-Mueller model and an interacting Hofstadter model by adding suitable potentials. We consider a fixed system size, for which the charge distributions of the normal anyons overlap, and we find that the outcome of the exchange process is closer to the ideal value for the squeezed anyons. The time needed for the exchange is also important, and for a particular example we find that the duration needed for the process to be close to the adiabatic limit is about five times longer for the squeezed anyons when the path length is the same. Finally we show that the exchange outcome is robust with respect to small modifications of the potential away from the optimized value., Comment: 9 pages, 4 figures, 1 movie

We study the transport properties of silicene in a perpendicular magnetic field by evaluating the Hall and longitudinal conductivities and resistivities when the acoustic phonon correction to the Landau level (LL) energy is taken into account. The acoustic phonons are considered by three modes: the transverse (TA), longitudinal, and out-of-plane ones. Under the influence of the acoustic phonon correction, the quantum Hall effect plateaus occur at higher values of the magnetic field, where the TA phonon displays the strongest effect. The combined effects of the strong spin-orbit coupling in silicene, the external electric field, and the Zeeman field on the transport parameters are investigated. These combined effects lift the spin and valley degeneracy of the LLs, leading to the additional plateaus in the Hall conductivity with the sequence being found as ${\ensuremath{\sigma}}_{yx}=(4{e}^{2}/h)(n/4+1/2)$. The temperature has a significant effect on the width of the Hall conductivity plateaus. We also appraise the longitudinal conductivity ${\ensuremath{\sigma}}_{xx}$ and the Hall, ${\ensuremath{\rho}}_{xy}$, and longitudinal, ${\ensuremath{\rho}}_{xx}$, resistivities and show the difference between the present results and those for graphene as well as for silicene without the Zeeman field effect. The combined effects of the electric and Zeeman fields lead to the quadrupled peaks of ${\ensuremath{\rho}}_{xx}$ and the sequence of $(h/{e}^{2})/(n+2)$ in the height of the plateaus in ${\ensuremath{\rho}}_{xy}$.

The electron spin resonance (ESR) of two-dimensional electrons with large effective mass was studied experimentally near even filling factors of the integer quantum Hall effect. Surprisingly, the electron spin resonance did not vanish at the exact even fillings even in the case of large electron densities, where the ground state of the system was previously reported to be paramagnetic. Furthermore, the ESR amplitude was comparable between even and odd fillings. Such anomalous behavior suggests a substantial degree of spin polarization of the even fillings and was observed in two different material systems, namely AlAs quantum wells and ZnO/MgZnO heterojunctions. In AlAs quantum wells, spin resonance tended to split into two well-resolved lines near even fillings whereas it remained a single peak near odd ones. The evolution of ESR with varying filling factor around even fillings is studied in detail. The reported nontrivial findings suggest the modification of the ground state around even filling factors with the aid of strong $e\text{\ensuremath{-}}e$ interaction and may be viewed as a precursor for the Stoner instability.

It is now well established that the peculiar linear-in-momentum dependence of the Rashba (and of the Dresselhaus) spin-orbit coupling leads to the vanishing of the spin Hall conductivity in the bulk of a two-dimensional electron gas (2DEG). In this paper we discuss how generic magnetic couplings change this behaviour providing then a potential handle on the spin Hall effect. In particular we examine the influence of magnetic impurities and an in-plane magnetic field. We find that in both cases there is a finite spin Hall effect and we provide explicit expressions for the spin Hall conductivity. The results can be obtained by means of the quasiclassical Green function approach, that we have recently extended to spin-orbit coupled electron systems.

Anomalous nematic states, recently discovered in ultraclean two-dimensional electron gas, emerge from quantum Hall stripe phases upon further cooling. These states are hallmarked by a local minimum (maximum) in the hard (easy) longitudinal resistance and by an incipient plateau in the Hall resistance in nearly half-filled Landau levels. Here, we demonstrate that a modest in-plane magnetic field, applied either along $\left < 110 \right >$ or $\left < 1\bar10 \right >$ crystal axis of GaAs, destroys anomalous nematic states and restores quantum Hall stripe phases aligned along their native $\left < 110 \right >$ direction. These findings confirm that anomalous nematic states are distinct from other ground states and will assist future theories to identify their origin., 5 pages, 4 figures

Parafermions or Fibonacci anyons leading to universal quantum computing, require strongly interacting systems. A leading contender is the fractional quantum Hall effect, where helical channels can arise from counter- propagating chiral modes. These modes have been considered weakly interacting. However, experiments on transport in helical channels in the fractional quantum Hall effect at a 2/3 filling shows current passing through helical channels on the boundary between polarized and unpolarized quantum Hall liquids nine-fold smaller than expected. This current can increase three-fold when nuclei near the boundary are spin polarized. We develop a microscopic theory of strongly interacting helical states and show that emerging helical Luttinger liquid manifests itself as unequally populated charge, spin and neutral modes in polarized and unpolarized fractional quantum Hall liquids. We show that at strong coupling counter-propagating modes of opposite spin polarization emerge at the sample edges, providing a viable path for generating proximity topological superconductivity and parafermions. Current, calculated in strongly interacting picture is in agreement with the experimental data.

We show the low-lying excitations at filling factor $\ensuremath{\nu}=n+1/3$ with realistic interactions can be understood as quantum fluids with ``Gaffnian quasiholes'' as the proper elementary degrees of freedom. Each Laughlin quasihole can thus be understood as a bound state of two Gaffnian quasiholes, which in the lowest Landau level (LLL) behaves like ``partons'' with ``asymptotic freedom'' mediated by neutral excitations acting as ``gluons.'' Near the experimentally observed nematic FQH phase in higher LLs, quasiholes become weakly bound and can fractionalize with rich dynamical properties. By studying the effective interactions between quasiholes, we predict a finite temperature phase transition of the Laughlin quasiholes even when the Laughlin ground state remains incompressible, and derive relevant experimental conditions for its possible observations.

We report complex magnetotransport patterns of the $\ensuremath{\nu}=1$ integer quantum Hall state in a GaAs/AlGaAs sample from the newest generation with a record high electron mobility. The reentrant integer quantum Hall effect in the flanks of the $\ensuremath{\nu}=1$ plateau indicates the formation of the integer quantum Hall Wigner solid, a collective insulator. Moreover, at a fixed filling factor, the longitudinal resistance versus temperature in the region of the integer quantum Hall Wigner solid exhibits a sharp peak. Such sharp peaks in the longitudinal resistance versus temperature so far were only detected for bubble phases forming in high Landau levels but were absent in the region of the Anderson insulator. We suggest that in samples of sufficiently low disorder, sharp peaks in the longitudinal resistance versus temperature traces are universal transport signatures of all isotropic electron solids that form in the flanks of integer quantum Hall plateaus. We discuss possible origins of these sharp resistance peaks and we draw a stability diagram for the insulating phases in the $\ensuremath{\nu}\ensuremath{-}T$ phase space.

Motivated by recent transport experiments, we theoretically study the quantum Hall effect in topological semimetal films. Owing to the confinement effect, the bulk subbands originating from the chiral Landau levels establish energy gaps that have quantized Hall conductance and can be observed in relatively thick films. We find that the quantum Hall state is strongly anisotropic for different confinement directions not only due to the presence of the surface states but also because of the bulk chiral Landau levels. As a result, we re-examine the quantum Hall effect from the surface Fermi arcs and chiral modes in Weyl semimetals and give a more general view into this problem. Besides, we also find that when a topological Dirac semimetal is confined in its rotational symmetry axis, it hosts both quantum Hall and quantum spin Hall states, in which the helical edge states are protected by the conservation of the spin-$z$ component., Comment: 13 pages, 7 figures

Spin-valley locking in monolayer transition metal dichalcogenides has attracted enormous interest, since it offers potential for valleytronic and optoelectronic applications. Such an exotic electronic state has sparsely been seen in bulk materials. Here, we report spin-valley locking in a Dirac semimetal BaMnSb2. This is revealed by comprehensive studies using first principles calculations, tight-binding and effective model analyses, angle-resolved photoemission spectroscopy measurements. Moreover, this material also exhibits a stacked quantum Hall effect (QHE). The spin-valley degeneracy extracted from the QHE is close to 2. This result, together with the Landau level spin splitting, further confirms the spin-valley locking picture. In the extreme quantum limit, we also observed a plateau in the z-axis resistance, suggestive of a two-dimensional chiral surface state present in the quantum Hall state. These findings establish BaMnSb2 as a rare platform for exploring coupled spin and valley physics in bulk single crystals and accessing 3D interacting topological states., Valley dependent spin polarization called spin-valley locking appears in absence of magnetism but it is limited to rare examples of transition metal dichalcogenides. Here, the authors report evidence of spin-valley locking and stacked quantum Hall effect in a bulk Dirac semimetal BaMnSb2.

An adiabatic approach put forward by Greiter and Wilczek interpolates between the integer quantum Hall effects of electrons and composite fermions by varying the statistical flux bound to electrons continuously from zero to an even integer number of flux quanta, such that the intermediate states represent anyons in an external magnetic field with the same "effective" integer filling factor. We consider such anyons on a torus, and construct representative wave functions for their ground as well as excited states. These wave functions involve higher Landau levels in general, but can be explicitly projected into the lowest Landau level for many parameters. We calculate the variational energy gap between the first excited state and ground state and find that it remains open as the statistical phase is varied. Finally, we obtain from these wave functions, both analytically and numerically, various topological quantities, such as ground-state degeneracy, the Chern number, and the Hall viscosity., 14 pages, 5 figures

A seminal gedankenexperiment by Laughlin describes the charge transport in quantum Hall systems via the pumping of flux. Here, we propose an optical scheme which probes and manipulates quantum Hall systems in a similar way: When light containing orbital angular momentum interacts with electronic Landau levels, it acts as a flux pump which radially moves the electrons through the sample. We investigate this effect for a graphene system with Corbino geometry, and calculate the radial current in the absence of any electric potential bias. Remarkably, the current is robust against the disorder which is consistent with the lattice symmetry, and in the weak excitation limit, the current shows a power-law scaling with intensity characterized by the novel exponent 2/3.