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The fate of the current carrying states of a quantum Hall system is considered in the situation when the disorder strength is increased and the transition from the quantum Hall liquid to the Hall insulator takes place. We investigate a…
The disorder driven quantum Hall to insulator transition is investigated for a two-dimensional lattice model. The Hall conductivity and the localization length are calculated numerically near the transition. For uncorrelated and weakly…
The disorder driven quantum Hall to insulator transition is investigated for a two-dimensional lattice system. We consider a Gaussian correlated random potential, study the behaviour of the current carrying states and trace their…
Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically…
Understanding scattering mechanisms in semiconductor heterostructures is crucial to reducing sources of disorder and ensuring high yield and uniformity in large spin qubit arrays. Disorder of the parent two-dimensional electron or hole gas…
Quantum Hall Dynamics is formulated on von Neumann lattice representation where electrons in Landau levels are defined on lattice sites and are treated systematically like lattice fermions. We give a proof of the integer Hall effect, namely…
A quantum Hall system which is divided into two laterally coupled subsystems by means of a tunneling barrier exhibits a complex Landau level dispersion. Magnetotunneling spectroscopy is employed to investigate the small energy gaps which…
The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong perpendicular magnetic field and was later generalized to Chern insulators without net magnetization. Here,…
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…
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…
We discuss the relationship between the quantum Hall conductance and a fractal energy band structure, Hofstadter's butterfly, on a square lattice under a magnetic field. At first, we calculate the Hall conductance of Hofstadter's butterfly…
Two-dimensional electron gas in the integer quantum Hall regime is investigated numerically by studying the dynamics of an electron hopping on a square lattice subject to a perpendicular magnetic field and random on-site energy with white…
We report results of numerical studies of the integer quantum Hall effect in a tight binding model on a two-dimensional square lattice with non-interacting electrons, in the presence of a random potential as well as a uniform magnetic field…
We present a class of states with both topological and conventional Landau order that arise out of strongly interacting spinless fermions in fractionally filled and topologically non-trivial bands with Chern number $C=\pm 1$. These quantum…
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 2D system of electron confined to the lowest Landau level is described using a representation of the density matrix depending both on electron and hole coordinates. Condensation of the electron system into a fractional quantum Hall…
In this report we summarize a recent progress in exploration of correlated two-dimensional electron states in partially filled high Landau levels. At a mean-field Hartree-Fock level they can be described as charge-density waves, either…
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…
A two-layer system coupled via tunneling and with different carrier masses in each layer is investigated in the integer quantum Hall regime. Striking deviations of the one-layer Hall conductivity from the usual quantization are found, if…
We propose a geometric mechanism for fractional quantum Hall states based on impurity-induced correlations within a Landau level. A correlated distribution of ionized impurities partially modifies the Landau-level degeneracy through…