Related papers: Dynamical mobility edge for various random Landau …
We prove the existence of dynamical delocalization for random Landau Hamiltonians near each Landau level. Since typically there is dynamical localization at the edges of each disordered-broadened Landau band, this implies the existence of…
In this note we prove the existence of a localization/delocalization transition for Landau Hamiltonians randomly perturbed by an electric potential with unbounded amplitude. In particular, with probability one, no Landau gaps survive as the…
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…
The integer quantum Hall effect features a paradigmatic quantum phase transition. Despite decades of work, experimental, numerical, and analytical studies have yet to agree on a unified understanding of the critical behavior. Based on a…
Quantum transport properties in quantum Hall wires in the presence of spatially correlated random potential are investigated numerically. It is found that the potential correlation reduces the localization length associated with the edge…
We investigate new properties of the Dirac electrons in the finite graphene sample under perpendicular magnetic field that emerge when an in-plane electric bias is also applied. The numerical analysis of the Hofstadter spectrum and of the…
We investigate the emergence of long-range electron hopping mediated by cavity vacuum fields in disordered quantum Hall systems. We show that the counter-rotating (anti-resonant) light-matter interaction produces an effective hopping…
Transport in a two-dimensional electron gas subject to an external magnetic field is analyzed in the presence of a \textit{longitudinal barrier.} We show that \textit{quantum interference of the edge states} bound by the longitudinal…
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 explore the two-dimensional motion of relativistic electrons when they are trapped in magnetic fields having spatial power-law variation. Its impacts include lifting of degeneracy that emerged in the case of the constant magnetic field,…
The low-field quantum Hall effect is investigated on a two-dimensional electron system in an AlGaAs/GaAs heterostructure. Magneto-oscillations following the semiclassical Shubnikov-de Haas formula are observed even when the emergence of the…
Quantum electron transport in side-gated graphene Hall bars is investigated in the presence of quantizing external magnetic fields. The asymmetric potential of four side-gates distorts the otherwise flat bands of the relativistic Landau…
Low-energy transport in quantum Hall states is carried through edge modes, and is dictated by bulk topological invariants and possibly microscopic Boltzmann kinetics at the edge. Here we show how the presence or breaking of symmetries of…
Landau level bending near the edge of graphene, described using 2d Dirac equation, provides a microscopic framework for understanding the quantum Hall Effect (QHE) in this material. We review properties of the QHE edge states in graphene,…
Searching for Anderson localization of light in three dimensions has challenged experimental and theoretical research for the last decades. Here the problem is analyzed through large scale numerical simulations, using a radiative…
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…
Dynamical Hall conductivity {\sigma}_H({\omega}) of a 2D electron gas with impurities in the perpendicular magnetic field is analyzed. Plateau-like behavior at low frequencies as well as at high frequencies provided the complete filling of…
Quantum Hall states can be characterized by their chiral edge modes. Upon softening the edge potential, the edge has long been known to undergo spontaneous reconstruction driven by charging effects. In this paper we demonstrate a…
In this note we consider a Landau Hamiltonian perturbed by a random magnetic potential of Anderson type. For a given number of bands, we prove the existence of both strongly localized states at the edges of the spectrum and dynamical…
We report on recent experimental results from transport measurements with large Hall bars made of high mobility GaAs/AlGaAs heterostructures. Thermally activated conductivities and hopping transport were investigated in the integer quantum…