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We report on numerical studies into the interplay of disorder and electron-electron interactions within the integer quantum Hall regime, where the presence of a strong magnetic field and two-dimensional confinement of the electronic system profoundly affects thermodynamic and transport properties. We emphasise the behaviour of the electronic compressibility, the local density of states, and the Kubo conductivity. Our treatment of the electron-electron interactions relies on the Hartree-Fock approximation so as to achieve system sizes comparable to experimental situations. Our results clearly exhibit manifestations of various interaction-mediated features, such as non-linear screening, local charging, and g-factor enhancement, implying the inadequacy of independent-particle models for comparison with experimental results.
Conductivity of Integer Quantum Hall Effect (IQHE) may be expressed as the topological invariant composed of the two - point Green function. Such a topological invariant is known both for the case of homogeneous systems with intrinsic Anomalous Quant
We study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We then establ
The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but is sensiti
Electron pairing is a rare phenomenon appearing only in a few unique physical systems; e.g., superconductors and Kondo-correlated quantum dots. Here, we report on an unexpected, but robust, electron pairing in the integer quantum Hall effect (IQHE) r
In recent interference experiments with an electronic Fabry-Perot interferometer (FPI), implemented in the integer quantum Hall effect regime, a flux periodicity of $h/2e$ was observed at bulk fillings $ u_B>2.5$. The halved periodicity was accompani