The enigma of the quantum Hall effect in graphene

We apply Laughlin’s gauge argument to analyze the ν=0 quantum Hall effect observed in graphene when the Fermi energy lies near the Dirac point, and conclude that this necessarily leads to divergent bulk longitudinal resistivity in the zero temperature thermodynamic limit. We further predict that in a Corbino geometry measurement, where edge transport and other mesoscopic effects are unimportant, one should find the longitudinal conductivity vanishing in all graphene samples which have an underlying ν=0 quantized Hall effect. We argue that this ν=0 graphene quantum Hall state is qualitatively similar to the high field insulating phase (also known as the Hall insulator) in the lowest Landau level of ordinary semiconductor two-dimensional electron systems. We establish the necessity of having a high magnetic field and high mobility samples for the observation of the divergent resistivity as arising from the existence of disorder-induced density inhomogeneity at the graphene Dirac point.     

Generalization of the theory of three-dimensional quantum Hall effect of Fermi arcs in Weyl semimetal

The quantum Hall effect (QHE), which is usually observed in two-dimensional systems, was predicted theoretically and observed experimentally in three-dimensional (3D) topological semimetal. However, there are some inconsistencies between the theory and the experiments showing the theory is imperfect. Here, we generalize the theory of the 3D QHE of Fermi arcs in Weyl semimetal. Through calculating the sheet Hall conductivity of a Weyl semimetal slab, we show that the 3D QHE of Fermi arcs can occur in a large energy range and the thickness dependences of the QHE in different Fermi energies are distinct. When the Fermi energy is near the Weyl nodes, the Fermi arcs give rise to the QHE which is independent of the thickness of the slab. When the Fermi energy is not near the Weyl nodes, the two Fermi arcs form a complete Fermi loop with the assistance of bulk states giving rise to the QHE which is dependent on the sample thickness. We also demonstrate how the band anisotropic terms influence the QHE of Fermi arcs. Our theory complements the imperfections of the present theory of 3D QHE of Fermi arcs.     

Current distribution in the integer quantum Hall effect: The role of bulk states

The role of bulk and edge currents in a two-dimensional electron gas under the conditions of the integer quantum Hall effect (IQHE) was studied by means of an inductive coupling to Hall bar geometry. From this study we conclude that the extended states at the bulk of the sample below the Fermi energy are capable of carrying a substantial amount of Hall current. For Hall bar geometry sample with a back gate we demonstrated that injected current can be pushed from one edge to another by reversing the direction of the external magnetic field.     

Quantum spin Hall effect in a square-lattice model under a uniform magnetic field

We study a toy square-lattice model under a uniform magnetic field. Using the Landauer-Bttiker formula, we calculate the transport properties of the system on a two-terminal, a four-terminal and a six-terminal device. We find that the quantum spin Hall (QSH) effect appears in energy ranges where the spin-up and spin-down subsystems have different filling factors. We also study the robustness of the resulting QSH effect and find that it is robust when the Fermi levels of both spin subsystems are far away from the energy plateaus but is fragile when the Fermi level of any spin subsystem is near the energy plateaus. These results provide an example of the QSH effect with a physical origin other than time-reversal (TR) preserving spin-orbit coupling (SOC).     

Evolution of individual quantum Hall edge states in the presence of disorder

By using the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As demonstrated by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of the n = 1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions that are well localized at the system edge and independent of the Fermi energy. On the other hand, at fixed Fermi energy, the edge state from higher Landau levels exhibit larger expansion, which results in less stable quantum Hall states at high Fermi energies. By presenting the local current density distribution, the effect of disorder on eigenmode-resolved edge states is distinctly demonstrated.     

Spin-dependent resistivity and quantum Hall ferromagnetism in two-dimensional electrons confined to AlAs quantum wells

We observe a strong dependence of the amplitude and field position of longitudinal resistivity (ρ_xx) peaks in the spin-resolved integer quantum Hall regime on the spin orientation of the Landau level (LL) in which the Fermi energy resides. The amplitude of a given peak is maximal when the partially filled LL has the same spin as the lowest LL, and amplitude changes as large as an order of magnitude are observed as the sample is tilted in field. In addition, the field position of both the ρ_xx peaks and plateau–plateau transitions in the Hall resistance shift depending on the spin orientation of the LLs. The spin dependence of the resistivity points to a new explanation for resistivity spikes, associated with first-order quantum Hall ferromagnetic transitions, that occur at the edges of quantum Hall states.     

Umklapp scattering at reconstructed quantum Hall edges

We study the low-lying excitations of a quantum Hall sample that has undergone edge reconstruction such that there exist three branches of chiral edge excitations. Among the interaction processes that involve electrons close to the three Fermi points is a new type of Umklapp-scattering process which has not been discussed before. Using bosonization and a refermionization technique, we obtain exact results for electronic correlation functions and discuss the effect Umklapp scattering has on the Luttinger-liquid properties of quantum Hall edges.     

Current carrying states in the disordered quantum anomalous Hall effect

In a quantum Hall effect, flat Landau levels may be broadened by disorder. However, it has been found that in the thermodynamic limit, all extended (or current carrying) states shrink to one single energy value within each Landau level. On the other hand, a quantum anomalous Hall effect consists of dispersive bands with finite widths. We numerically investigate the picture of current carrying states in this case. With size scaling, the spectrum width of these states in each bulk band still shrinks to a single energy value in the thermodynamic limit, in a power law way. The magnitude of the scaling exponent at the intermediate disorder is close to that in the quantum Hall effects. The number of current carrying states obeys similar scaling rules, so that the density of states of current carrying states is finite. Other states in the bulk band are localized and may contribute to the formation of a topological Anderson insulator.     

The conductivity of a two-dimensional electronic system of finite width in the presence of a strong perpendicular magnetic field and a random potential

Starting from the Kubo formula the conductivity tensor of a two-dimensional electronic system in a perpendicular magnetic field is evaluated. It is shown that at zero temperature only the states at the Fermi level contribute. The Hall conductivity of a purely periodic system of finite width is calculated and compared with earlier suggestions by Thouless et al. For a system described by a periodic and a random potential the Hall conductivity is calculated as a function of the electron density. The results emphasize the importance of disorder independent current carrying states for the Quantum Hall effect which extend along the boundaries of the system. The plateaux values of the Hall conductivity are related to the number of these states, and are independent of the existence of extended bulk states below the Fermi energy.     

Spin and spin-valley Hall effects in a honeycomb lattice with antiferromagnetism and spin-orbit couplings

We study linear response to a longitudinal electric field on an antiferromagnetic honeycomb lattice with intrinsic and Rashba spin-orbit couplings (SOCs). It is found that the spin-valley Hall effect could emerge alone or coexist with the spin Hall effect. The spin and spin-valley Hall conductivities exhibit some peculiarities that depend on the distinct topological states of the graphene lattice. Furthermore, the spin and spin-valley Hall conductivities could be remarkably modulated by changing the Fermi level. Our findings suggest that the antiferromagnetic honeycomb lattice with SOCs is an excellent platform for potential applications of spintronics and valleytronics.     

Hall resistance and the diamagnetic moment of periodically modulated two-dimensional systems

It is argued that the Hall resistance of macroscopic samples can be directly obtained by ensemble averaged transport properties of mesoscopic systems. The resulting formula relates the Hall current to the part of the magnetic moment of Fermi electrons, which originates in macroscopic currents only. As one of the possible application the Hall resistance of the periodically modulated two-dimensional electron system in the strong magnetic field is briefly discussed.     

Pressure tuning of the anomalous Hall effect in the kagome superconductor CsV3Sb5

Controlling the anomalous Hall effect(AHE)inspires potential applications of quantum materials in the next generation of electronics.The recently discovered quasi-2D kagome superconductor CsV₃Sb₅ exhibits large AHE accompanying with the charge-density-wave(CDW)order which provides us an ideal platform to study the interplay among nontrivial band topology,CDW,and unconventional superconductivity.Here,we systematically investigated the pressure effect of the AHE in CsV₃Sb₅.Our high-pressure transport measurements confirm the concurrence of AHE and CDW in the compressed CsV₃Sb₅.Remarkably,distinct from the negative AHE at ambient pressure,a positive anomalous Hall resistivity sets in below 35 K with pressure around 0.75 GPa,which can be attributed to the Fermi surface reconstruction and/or Fermi energy shift in the new CDW phase under pressure.Our work indicates that the anomalous Hall effect in CsV₃Sb₅ is tunable and highly related to the band structure.     

Two-dimensional transport and strong spin-orbit interaction in SrMnSb_2

We have carried out magneto-transport measurements for single crystal SrMnSb_2. Clear Shubnikov-de Haas oscillations were resolved at relatively low magnetic field around 4 T, revealing a quasi-2D Fermi surface. We observed a development of quantized plateaus in Hall resistance(R_(xy)) at high pulsed fields up to 60 T. Due to the strong 2D confinement and layered properties of the samples, we interpreted the observation as bulk quantum Hall effect that is contributed by the parallel 2D conduction channels. Moreover, the spin degeneracy was lifted leading to Landau level splitting. The presence of anisotropic g factor and the formation of the oscillation beating pattern reveal a strong spin-orbit interaction in the SrMnSb_2 system.     

Axion response in gapless systems

The strong topological insulator in 3D is expected to realize a quantized magnetoelectric response, the so-called axion response. However, many of the materials predicted to be topological insulators have turned out to be metallic, with bulk Fermi surfaces. Following the result of Bergman and Refael [Phys. Rev. B 82, 195417 (2010)] that the surface states of the topological insulator persist even when the band structure gap is closed, we explore the fate of the magnetoelectric response in such systems. We find that a nonquantized magnetoelectric coupling remains once a bulk Fermi surface opens. More generally, we find higher-dimensional analogs of the intrinsic anomalous Hall effect for all Chern forms-quantized transport coefficients in the gapped case become nonquantized when the gap is closed. In particular, the nonquantized magnetoelectric response in 3D descends from the intrinsic anomalous Hall effect analog in 4D.     

THz imaging of cyclotron emission in quantum Hall conductors

Recent studies of cyclotron emission microscopy on quantum Hall related states are reported. The topics include non-equilibrium between edge and bulk states, current-induced breakdown of the quantum Hall effect, and the emission threshold at hot spots. Experimental method of scanning-type terahertz microscopes developed towards photon-counting level sensitivity is also described.     

Indications of an electronic phase transition in two-dimensional superconducting YBa2Cu3O(7-x) thin films induced by electrostatic doping

We successfully tuned an underdoped ultrathin YBa2Cu3O(7-x) film into the overdoped regime by means of electrostatic doping using an ionic liquid as a dielectric material. This process proved to be reversible. Transport measurements showed a series of anomalous features compared to chemically doped bulk samples and a different two-step doping mechanism for electrostatic doping was revealed. The normal resistance increased with carrier concentration on the overdoped side and the high temperature (180 K) Hall number peaked at a doping level of p～0.15. These anomalous behaviors suggest that there is an electronic phase transition in the Fermi surface around the optimal doping level.     

Current breakdown of the integer and fractional quantum Hall effects detected by torque magnetometry

We have developed a novel technique that enables measurements of the breakdown of both the integer and fractional quantum Hall effects in a two-dimensional electron system without the need to contact the sample. The critical Hall electric fields that we measure are significantly higher than those reported by other workers, and support the quasi-elastic inter-Landau-level tunnelling model of breakdown. Comparison of the fractional quantum Hall effect results with those obtained on the integer quantum Hall effect allows the fractional quantum Hall effect energy gap to be determined and provides a test of the composite-fermion theory. The temperature dependence of the critical current gives an insight into the mechanism by which momentum may be conserved during the breakdown process.     

Edge state propagation direction in the fractional quantum Hall regime: multi-terminal magnetocapacitance experiment

The propagation direction of fractional quantum Hall effect (FQHE) edge states has been investigated experimentally via the symmetry properties of the multi-terminal capacitances of a two-dimensional electron gas. Although strong asymmetries with respect to zero magnetic field appear, no asymmetries with respect to even denominator Landau level filling factor ν are seen. This indicates that current-carrying FQHE edge states propagate in the same direction as integer QHE edge states. In addition, anomalous capacitance features, indicative of enhanced bulk conduction, are observed at and .     

Interplay of Rashba effect and spin Hall effect in perpendicular Pt/Co/MgO magnetic multilayers

The interplay of the Rashba effect and the spin Hall effect originating from current induced spin–orbit coupling was investigated in the as-deposited and annealed Pt/Co/MgO stacks with perpendicular magnetic anisotropy. The above two effects were analyzed based on Hall measurements under external magnetic fields longitudinal and vertical to dc current,respectively. The coercive field as a function of dc current in vertical mode with only the Rashba effect involved decreases due to thermal annealing. Meanwhile, spin orbit torques calculated from Hall resistance with only the spin Hall effect involved in the longitudinal mode decrease in the annealed sample. The experimental results prove that the bottom Pt/Co interface rather than the Co/MgO top one plays a more critical role in both Rashba effect and spin Hall effect.     

Valley Hall effect and Nernst effect in strain engineered graphene

We theoretically predict the existence of tunneling valley Hall effect and Nernst effect in the normal/strain/normal graphene junctions, where a strained graphene is sandwiched by two normal graphene electrodes. By applying an electric bias a pure transverse valley Hall current with longitudinal charge current is generated. If the system is driven by a temperature bias, a valley Nernst effect is observed, where a pure transverse valley current without charge current propagates. Furthermore, the transverse valley current can be modulated by the Fermi energy and crystallographic orientation. When the magnetic field is further considered, we obtain a fully valley-polarized current. It is expected these features may be helpful in the design of the controllable valleytronic devices.