Related papers: Scaling Behavior of Level Statistics in Quantum Ha…
We study the Landau level localization and scaling properties of a disordered two-dimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as random distributed scattering centers with…
The statistical properties of energy eigenvalues in the critical regime of the lowest Landau band are investigated. The nearest neighbour level spacing distribution $P(s)$ and the Mehta quantity $I_0$, from which the scaling exponent $\nu$…
Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this…
The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are…
Temperature dependence of the longitudinal and Hall resistance is studied in the regime of localization-delocalization transition. We carry out measurements of a scaling exponent $\kappa$ in the Landau level mixing region at several filling…
The statistical properties of the dynamics of energy levels are investigated in the case of two two-dimensional disordered quantum dot models with nearest neighbor hopping subjected to external time-dependent perturbations. While in the…
A numerical analysis is made of the breakdown of the quantum Hall effect caused by the Hall electric field in competition with disorder. It turns out that in the regime of dense impurities, in particular, the number of localized states…
We investigate the fate of the quantum Hall extended states within a continuum model with spatially correlated disorder potentials. The model can be projected onto a couple of the lowest Landau bands. Levitation of the $n=0$ critical states…
To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…
The shape analysis of the energy spacing distribution $P(s)$ obtained from numerical simulation of two dimensional disordered electron systems subject to strong magnetic fields is performed. In the present work we reanalyze the data…
We have measured the temperature dependence of the longitudinal resistivity $% \rho_{xx}$ of a two-dimensional electron system in the regime of the quantum Hall plateau transition. We extracted the quantitative form of scaling function for…
We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wavefunctions at the transition energy are obtained within the…
The statistics of the energy eigenvalues at the metal-insulator-transition of a two-dimensional disordered system with spin-orbit interaction is investigated numerically. The critical exponent $\nu$ is obtained from the finite-size scaling…
We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to…
This review is intended to give a pedagogical and unified view on the subject of the statistics and scaling of physical quantities in disordered electron systems at very low temperatures. Quantum coherence at low temperatures and randomness…
The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced.…
We present a simple classification of the different liquid and solid phases of quantum Hall systems in the limit where the Coulomb interaction between the electrons is significant, i.e. away from integral filling factors. This…
The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of…
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 level statistics in the two dimensional disordered electron systems in magnetic fields (unitary ensemble) or in the presence of strong spin-orbit scattering (symplectic ensemble) are investigated at the Anderson transition points. The…