Related papers: Renormalization Group Derivation of the Localizati…
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…
I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic…
The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and…
We study the localization transition in the integer quantum Hall effect as described by the network model of quantum percolation. Starting from a path integral representation of transport Green's functions for the network model, which…
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 perform the two loop level renormalization of quantum gravity in $2+\epsilon$ dimensions. We work in the background gauge whose manifest covariance enables us to use the short distance expansion of the Green's functions. We explicitly…
The recent discovery of the 3D quantum Hall effect in $\mathrm{HfTe_5}$ has also revealed puzzling signatures of possible 3D fractionalization. Beyond the first plateau associated with the lowest Landau band, Hall conductivity exhibits a…
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…
We extend the real-space renormalization group (RG) approach to the study of the energy level statistics at the integer quantum Hall (QH) transition. Previously it was demonstrated that the RG approach reproduces the critical distribution…
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…
Generic classical electron motion in a strong perpendicular magnetic field and random potential reduces to the bond percolation on a square lattice. Here we point out that for certain smooth 2D potentials with 120 degrees rotational…
We consider the localization of independent electron orbitals in double-layer two-dimensional electron systems in the strong magnetic field limit. Our study is based on numerical Thouless number calculations for realistic microscopic models…
We propose a general mechanism for renormalization of the tunneling exponents in edge states of the fractional quantum Hall effect. Mutual effects of the coupling with out-of-equilibrium 1/f noise and dissipation are considered both for the…
The effect of inter-Landau-band mixing on electron localization in an integer quantum Hall system is studied. We find that mixing of localized states with {\it opposite chirality} tends to delocalize the states. This delocalization effect…
We report a magnetotransport study of the termination of the spin-resolved integer quantum Hall effect by controlled disorder in a gated GaAs/AlGaAs heterostructure. We have found that, for a given N^{th} Landau level, the difference in…
The scaling property of level statistics in the quantum Hall regime, i.e. 2D disordered electron systems subject to strong magnetic fields, is analyzed numerically in the light of the random matrix theory. The energy dependences of the…
We investigate the localization of electronic states in the integer quantum Hall effect using a magnetic localization landscape (MLL) approach. By studying a continuum Schr\"odinger model with disordered electrostatic potential, we…
We explore the consequences of introducing a complex conductivity into the quantum Hall effect. This leads naturally to an action of the modular group on the upper-half complex conductivity plane. Assuming that the action of a certain…
We prove quantization of the Hall conductance for continuous ergodic Landau Hamiltonians under a condition on the decay of the Fermi projections. This condition and continuity of the integrated density of states are shown to imply…
A theory of integer quantum Hall effect(QHE) in realistic systems based on von Neumann lattice is presented. We show that the momentum representation is quite useful and that the quantum Hall regime(QHR), which is defined by the propagator…