Related papers: Localization structure of electronic states in the…
We present here a model of carrier distribution and transport in semiconductor alloys accounting for quantum localization effects in disordered materials. This model is based on the recent development of a mathematical theory of quantum…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative…
A field-theoretic formulation of a planar Hall-electron system with edges is presented and some fundamental aspects of the integer quantum Hall effect are studied with emphasis on clarifying general symmetry-based consequences of…
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.…
In this paper we present a modified localization landscape theory to calculate localized/confined electron and hole states and the corresponding energy eigenvalues without solving a (large) eigenvalue problem. We motivate and demonstrate…
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…
This paper introduces a novel method to account for quantum disorder effects into the classical drift-diffusion model of semiconductor transport through the localization landscape theory. Quantum confinement and quantum tunneling in the…
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…
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…
We investigate integer and fractional quantum Hall states in quantum point contacts (QPCs) of different geometries, defined in AlGaAs/GaAs heterostructures employing different doping and screening techniques. We find that, even in the…
An approximate analytic solution for the ground electron state are found to the Schroedinger equation for a combination of a uniform magnetic field and single attractive delta-potential. Effect of the magnetic field on this bound localized…
A model system is considered where two dimensional electrons are confined by a harmonic potential in one direction, and are free in the other direction. Ground state in strong magnetic fields is investigated through numerical…
Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with non-ergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body…
The localization of two interacting electrons in a coupled-quantum-dots semiconductor structure is demonstrated through numerical calculations of the time evolution of the two-electron wave function including the Coulomb interaction between…
We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…
We use a simple electrostatic treatment to model recent experiments on quantum Hall systems, in which charging of localised states by addition of integer or fractionally-charged quasiparticles is observed. Treating the localised state as a…
We study electron localization in disordered quantum systems, focusing on both individual eigenstates and thermal states. We employ complex polarization as a numerical indicator to characterize the system's localization length. Furthermore,…
At low energy, the dynamics of excitations of many physical systems are locally constrained. Examples include frustrated anti-ferromagnets, fractional quantum Hall fluids and Rydberg atoms in the blockaded regime. Can such locally…
Great progress has been made in the last several years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of…