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We investigate the integer quantum Hall system in a two dimensional lattice model with spatially correlated disorder by using the efficient method to calculate the Chern number proposed by Fukui \textit{et al}. Distribution of charge…
Statistics of level spacing and magnetization are studied for the phase diagram of the integer quantum Hall effect in a 2D finite lattice model with Anderson disorder.
We report on results of systematic numerical studies of two-dimensional electron gas systems subject to a perpendicular magnetic field, with a high Landau level partially filled by electrons. Our results are strongly suggestive of a…
The spectrum and the eigenstates of a finite 2D tight-binding electronic system, with Dirichlet boundary conditions, in magnetic field and external linear potential are studied. The eigenstates show an equipotential character and may cross…
We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry…
The helical edge states in a quantum spin Hall insulator are presumably protected by time- reversal symmetry. However, even in the presence of magnetic field which breaks time-reversal symmetry, the helical edge conduction can still exist,…
We investigate the phenomenon of integer quantum Hall effect in a square lattice, subjected to a perpendicular magnetic field, through Landauer-B\"uttiker formalism within the tight-binding framework. The oscillating nature of longitudinal…
I give a brief review of higher dimensional quantum Hall effect (QHE) and how one can use a general framework to describe the lowest Landau level dynamics as a noncommutative field theory whose semiclassical limit leads to anomaly free…
We study the plateaux of the integer quantum Hall resistance in a bilayer electron system in tilted magnetic fields. In a narrow range of tilt angles and at certain magnetic fields, the plateau level deviates appreciably from the quantized…
We report experimental studies of disorder-induced transitions between quantum-Hall, metallic, and insulating states in a very dilute two-dimensional electron system in silicon at a magnetic field corresponding to Landau level filling…
We have introduced a controllable nano-scale incursion into a potential barrier imposed across a two-dimensional electron gas, and report on the phenomena that we observe as the incursion develops. In the quantum Hall regime, the…
In the quantum Hall regime, electronic correlations in double-layer two-dimensional electron systems are strong because the kinetic energy is quenched by Landau quantization. In this article we point out that these correlations are…
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…
The quantum Hall conductance of a disordered two-dimensional gas of non-interacting electrons is re-examined for its integrity against disorder in the limit of no mixing between different Landau levels. The exact one-electron eigenstates of…
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…
Computer modelling of the integer quantum Hall effect based on self-consistent Hartee-Fock calculations has now reached an astonishing level of maturity. Spatially-resolved studies of the electron density at near macroscopic system sizes of…
The quantum Hall effect is studied in the topological insulator BiSbTeSe$_2$. By employing top- and back-gate electric fields at high magnetic field, the Landau levels of the Dirac cones in the top and bottom topological surface states can…
The electronic structure of InAs/AlSb/GaSb quantum wells embedded in AlSb barriers and in the presence of a perpendicular magnetic field is studied theoretically within the $14$-band ${\bf k}\cdot{\bf p}$ approach without making the axial…
At total Landau level filling factor $\nu_{tot}=1$ a double layer two-dimensional electron system with small interlayer separation supports a collective state possessing spontaneous interlayer phase coherence. This state exhibits the…
We investigate a gapped two-dimensional nodal-line semimetal subjected to a perpendicular magnetic field. We identify an unusual pattern for Landau levels, where the energy of Landau levels first decreases and then starts increasing versus…