相关论文: Localization and exact current compensation in the…
An effective Hamiltonian for the study of the quantum Hall effect is proposed. This Hamiltonian, which includes a ``current-current" interaction has the form of a Hamiltonian for a conformal field theory in the large $N$ limit. An order…
The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it…
We discuss a model for the integer quantum Hall effect which is based on a Schroedinger-Chern-Simons-action functional for a non-interacting system of electrons in an electromagnetic field on a mutiply connected manifold. In this model the…
The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall…
Scaling of the anomalous Hall conductivity to longitudinal conductivity, has been observed in the dirty regime of two-dimensional weak and strong localization regions in ultrathin, polycrystalline, chemically disordered, ferromagnetic FePt…
We numerically investigate the effect of electron correlation on the integer quantum Hall effect in a square lattice. Increasing the correlation strength via the effective onsite repulsion parameter $U$ degrades the quantization of $\nu =…
The concept of the electron localization function (ELF) is extended to two-dimensional (2D) electron systems. We show that the topological properties of the ELF in 2D are considerably simpler than in molecules studied previously. We compute…
We extend the quantum Hall matrix model to include couplings to external electric and magnetic fields. The associated current suffers from matrix ordering ambiguities even at the classical level. We calculate the linear response at low…
Opposite spin Landau levels in a quantum well can be brought into coincidence by tilting the magnetic field away from normal orientation. We demonstrate that the magnetotransport anomaly at integer filling factors that was recently…
We construct the states of maximal localization taking into account a modification of the commutation relation between position and momentum operators to all orders of the minimum length parameter. To first order, the algebra we use…
The dynamical Hall response in a correlated electronic system is analysed within the linear response theory for tight binding models. At $T=0$ the d.c. Hall constant for a single quasiparticle is expressed explicitly via the charge…
We demonstrate a new method for locally probing the edge states in the quantum Hall regime utilizing a side coupled quantum dot positioned at an edge of a Hall bar. By measuring the tunneling of electrons from the edge states into the dot,…
The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…
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 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…
The creation of topologically non-trivial matter across electronic, mechanical, cold-atom, and photonic platforms is advancing rapidly, yet understanding the breakdown of topological protection remains a major challenge. In this work, we…
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…
We study the quantum Hall effect inside a gravitational field. First, we review the influence of the gravitational field of the Earth on the quantum Hall effect. Taking the gravitational field of the Earth to be uniform along the vertical…