Effects of disorder on modulated quantum Hall systems

The Hall conductivity and the localization length are calculated for weakly modulated two-dimensional systems within the lowest Landau level approximation. We find that the fractal character of the Hofstadter butterfly is reflected on the coincidence in the localization and the Hall conductivity among a series of fluxes φ+2n with integers n.     

Wave function multifractality and dephasing at metal–insulator and quantum Hall transitions

We analyze the critical behavior of the dephasing rate induced by short-range electron–electron interaction near an Anderson transition of metal–insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in 2 + ? dimensions) with numerical simulations on the Chalker–Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data.     

Self-assembled nanocrystalline CdSe thin films

The topic of this contribution is the investigation of quantum states and quantum Hall effect in electron gas subjected to a periodic potential of the lateral lattice. The potential is formed by triangular quantum antidots located on the sites of the square lattice. In such a system the inversion center and the four-fold rotation symmetry are absent. The topological invariants which characterize different magnetic subbands and their Hall conductances are calculated. It is shown that the details of the antidot geometry are crucial for the Hall conductance quantization rule. The critical values of lattice parameters defining the shape of triangular antidots at which the Hall conductance is changed drastically are determined. We demonstrate that the quantum states and Hall conductance quantization law for the triangular antidot lattice differ from the case of the square lattice with cylindrical antidots. As an example, the Hall conductances of magnetic subbands for different antidot geometries are calculated for the case when the number of magnetic flux quanta per unit cell is equal to three.     

Three-dimensional quantum Hall effect in Weyl and double-Weyl semimetals

The well-known quantum Hall effect (QHE) was usually studied in 2D systems. In this work, we investigate the integer QHE in 3D Weyl and double-Weyl semimetals. Based on the lattice models of Weyl and double-Weyl semimetals subjected to a uniform magnetic field, we derive the generalized 3D spinfull Hofstadter Hamiltonians and Harper equations for the two systems, and obtain their corresponding energy spectra. Furthermore, we show that for proper hopping parameters and rational magnetic fluxes, both systems exhibit the 3D QHE when the Fermi level lies in some band gaps. The 3D QHE is topologically characterized by three Chern numbers with one or two nonzero Chern values which are respectively defined for three crystal planes. The possible experimental realization and detection of the 3D QHE are also discussed.     

Anomalous quantum Hall effect induced by nearby quantum dots

Transport measurements in high magnetic fields have been performed on two-dimensional electron system (2DES) separated by a thin barrier layer from a layer of InAs self-assembled quantum dots (QDs). Clear feature of quantum Hall effect was observed in spite of presence of QDs nearby 2DES. However, both magnetoresistance, ρ_xx, and Hall resistance, ρ_xy, are suppressed significantly only in the magnetic field range of filling factor in 2DES ν<1 and voltage applied on a front gate . The results indicate that the electron state in QDs induces spin-flip process in 2DES.     

Electrostatic theory for imaging experiments on local charges in quantum Hall systems

We use a simple electrostatic treatment to model recent experiments on quantum Hall systems, in which charging of localised states by addition of integer or fractionally charged quasiparticles is observed. Treating the localised state as a compressible quantum dot or antidot embedded in an incompressible background, we calculate the electrostatic potential in its vicinity as a function of its charge, and the chemical potential values at which its charge changes. The results offer a quantitative framework for analysis of the observations.     

Thermodynamic properties of a quantum Hall anti-dot interferometer

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.     

Widths of the Hall Conductance Plateaus

We study the charge transport of the noninteracting electron gas in a two-dimensional quantum Hall system with Anderson-type impurities at zero temperature. We prove that there exist localized states of the bulk order in the disordered-broadened Landau bands whose energies are smaller than a certain value determined by the strength of the uniform magnetic field. We also prove that, when the Fermi level lies in the localization regime, the Hall conductance is quantized to the desired integer and shows the plateau of the bulk order for varying the filling factor of the electrons rather than the Fermi level.     

PLE studies of two-dimensional hole systems in the quantum Hall regime

We report a spectroscopic investigation of the densities of both occupied and unoccupied states of a high-quality two-dimensional hole system, in the regime of the quantum Hall effects (QHEs). Photoluminescence and photoluminescence excitation spectroscopies are used to elucidate the complicated valence band structure of the holes, and to establish their optical response to the QHEs.     

Screening model of magnetotransport hysteresis observed in bilayer quantum Hall systems

We report on theoretical and experimental investigations of a novel hysteresis effect that has been observed on the magnetoresistance of quantum Hall bilayer systems. Extending to these system a recent approach, based on the Thomas–Fermi–Poisson nonlinear screening theory and a local conductivity model, we are able to explain the hysteresis as being due to screening effects such as the formation of “incompressible strips”, which hinder the electron density in a layer within the quantum Hall regime to reach its equilibrium distribution.     

Integer quantum Hall effect in a PbTe quantum well

Transport measurements have been carried out on a 10 nm n-type PbTe/Pb_0.9Eu_0.1Te quantum well at millikelvin temperatures. The Hall and longitudinal resistances are measured in a Van der Pauw geometry under high magnetic fields up to 23 T. A robust signature of the integer quantum Hall effect is observed without any sign of parasitic parallel conduction. The unconventional sequence of filling factors associated with the integer quantum Hall effect is discussed in terms of the occupancy of multiple valleys.     

Ballistic transport under quantum Hall effect conditions

The paper addresses details of the single-particle electron spectrum ?_l(p)${?}_l(p)$ in narrow Coulomb channels (l is the transverse spectrum part discrete index and p   is the continuous longitudinal electron momentum). The channel is said to be narrow if differences between transverse spectrum branches ?_l(p)${?}_l(p)$ are larger than temperature. Considered are two extreme cases with respect to magnetic field. For the first case where ?_F≥?ω_c${?}_F\ge \mathit{?}{\omega }_c$, the spectrum ?_l(p)${?}_l(p)$ first calculated by Stern et al. numerically is obtained with approximate analytical analysis (here ?_F${?}_F$ is the Fermi energy of the 2D electron system ?ω_c$\mathit{?}{\omega }_c$ is the cyclotron frequency). In the second case the proposed formalism is extended to high magnetic fields satisfying the inequality ?_F≤?ω_c${?}_F\le \mathit{?}{\omega }_c$. Calculated results are compared with available experimental data.     

Anyons and the quantum Hall effect—A pedagogical review

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.     

Intrinsic spin Hall effect in silicene: transition from spin Hall to normal insulator

An intrinsic contribution to the spin Hall effect in two‐dimensional silicene is considered theoretically within the linear response theory and Green's function formalism. When an external voltage normal to the silicene plane is applied, the spin Hall conductivity is shown to reveal a transition from the spin Hall insulator phase at low bias to the conventional insulator phase at higher voltages. This transition resembles the recently reported phase transition in bilayer graphene. The spin–orbit interaction responsible for this transition in silicene is much stronger than in graphene, which should make the transition observable experimentally. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental probes of emergent symmetries in the quantum Hall system

Experiments studying renormalization group flows in the quantum Hall system provide significant evidence for the existence of an emergent holomorphic modular symmetry Γ₀(2)${\Gamma }_0(2)$. We briefly review this evidence and show that, for the lowest temperatures, the experimental determination of the position of the quantum critical points agrees to the parts per mille   level with the prediction from Γ₀(2)${\Gamma }_0(2)$. We present evidence that experiments giving results that deviate substantially from the symmetry predictions are not cold enough to be in the quantum critical domain. We show how the modular symmetry extended by a non-holomorphic particle–hole duality leads to an extensive web of dualities related to those in plateau–insulator transitions, and we derive a formula relating dual pairs (B,Bd)$(B,B_d)$ of magnetic field strengths across any transition. The experimental data obtained for the transition studied so far is in excellent agreement with the duality relations following from this emergent symmetry, and rule out the duality rule derived from the “law of corresponding states”. Comparing these generalized duality predictions with future experiments on other transitions should provide stringent tests of modular duality deep in the non-linear domain far from the quantum critical points.     

Detection of hidden localized states by the quantum Hall effect in graphene

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.     

Nuclear-spin-lattice relaxation in a bilayer quantum Hall system

We examined the electron spin degree of freedom around the total Landau-level filling factor ν=1 in a bilayer system via nuclear spins. In a balanced bilayer system, nuclear-spin-lattice relaxation rate 1/T₁, which probes low-energy electron spin fluctuations, increases gradually as the system is driven from the quantum Hall (QH) state through a phase transition to the compressible state. This result demonstrates that the electron spin degree of freedom is not frozen either in the QH or compressible states. Furthermore, as the density difference between the two layers is increased from balanced bilayer to monolayer configurations, 1/T₁ around ν=1 shows a rapid yet smooth increase. This suggests that pseudospin textures around the bilayer ν=1 system evolves continuously into the spin texture for the monolayer system.     

Electron–hole states in the fractional quantum Hall regime probed by photoluminescence

The electron–hole states in the fractional quantum Hall regime is investigated with a back-gated undoped quantum well by photoluminesccence in magnetic fields. The evolution of the photoluminescence spectra is discussed depending on the electron density. We find anomalies of the photoluminescence at the integer as well as the fractional filling factors.     

From magnetically doped topological insulator to the quantum anomalous Hall effect

Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landau levels so that neither external magnetic field nor high sample mobility is required for its study and application, Such a QHE free of Landau levels, can appear in topological insulators （TIs） with ferromagnetism as the quantized version of the anomalous Hall effect, i.e., quantum anomalous Hall （QAH） effect. Here we review our recent work on experimental realization of the QAH effect in magnetically doped TIs. With molecular beam epitaxy, we prepare thin films of Cr-doped （Bi,Sb）2Te3 TIs with well- controlled chemical potential and long-range ferromagnetic order that can survive the insulating phase. In such thin films, we eventually observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect provides a foundation for many other novel quantum phenomena predicted in TIs, and opens a route to practical applications of quantum Hall physics in low-power-consumption electronics.     

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.