Related papers: A Four Dimensional Generalization of the Quantum H…
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…
We show the inconsistency of the argument linking the integral quantum Hall effect to gauge invariance. The inconsistency mainly consists of equating gauge and real vector potential transformations for a particular system geometry. Correct…
We give an overview of the Integer Quantum Hall Effect. We propose a mathematical framework using Non-Commutative Geometry as defined by A. Connes. Within this framework, it is proved that the Hall conductivity is quantized and that…
We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly.…
The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas. Given its technological relevance, it is important to understand its development in realistic nanoscale devices. In this work we…
We study the Quantum Hall phases that appear in the dilute limit of rotating Bose-Einstein condensates. By exact diagonalization in a spherical geometry we obtain the ground-state and low-lying excited states of a small number of bosons as…
In this work we investigate an unusual transport phenomenon observed in two-dimensional electron gas under integer quantum Hall effect conditions. Our calculations are based on the screening theory, using a semi-analytical model. The…
In a two-dimensional electron gas, the quantized Hall conductance can be induced by a strong magnetic field, known as the quantum Hall effect, and it can also result from the strong exchange coupling of magnetic ions, dubbed as the "quantum…
In search of states with non-Abelian statistics, we explore the fractional quantum Hall effect in a system of two-dimensional charge carrier holes. We propose a new method of mapping states of holes confined to a finite width quantum well…
The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past thirty years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of…
Using scanning tunneling spectroscopy in ultra-high vacuum at low temperature (T = 0.3 K) and high magnetic fields (B < 12 T), we directly probe electronic wave functions across an integer quantum Hall transition. In accordance with…
Recently, generalizations of quantum Hall effects (QHE) have been made from 2D to 4D and 8D by considering their mathematical frameworks within complex (C), quaternion (H) and octonion (O) compact (gauge) Lie algebra domains. Just as QHE in…
We present a drop model for integer and fractional quantum Hall effects (FQHE). We show that the two-dimensional electron gas breaks up into regions with filling factors {\nu} = 1 and {\nu} = 0 in disk geometry, and the formation of drops…
It is shown, that a spectrum generating algebras and wave functions for the integral and fractional quantum Hall effect are related by the non-unitary similarity transformation. This transformation corresponds to the introduction of the…
We study the quantum Hall states in the lowest Landau level for a single wide quantum well. Due to a separation of charges to opposite sides of the well, a single wide well can be modelled as an effective two level system. We provide…
The effects of the generalized uncertainty principle (GUP) on the low-energy stationary states of a particle moving in a cavity with no sharp boundaries are determined by means of the perturbation expansion in the framework of…
We consider four dimensional quantum field theories which have a continuous manifold of inequivalent exact ground states -- a moduli space of vacua. Classically, the singular points on the moduli space are associated with extra massless…
We study theoretically the dispersion of a single quasiparticle or quasihole of the fractional quantum Hall effect, obtained by injecting or removing a composite fermion. By comparing to a free fermion system, we estimate the regime of…
Most of the fractions observed to date belong to the sequences $\nu=n/(2pn\pm 1)$ and $\nu=1-n/(2pn\pm 1)$, $n$ and $p$ integers, understood as the familiar {\em integral} quantum Hall effect of composite fermions. These sequences fail to…
In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed…