Related papers: Quantum Hall Effects
The fractional quantum Hall effect in 2D electron gases submitted to large magnetic fields remains one of the most striking phenomena in condensed matter physics. Historically, the first observed signature is a Hall resistance quantized to…
The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons…
There are compelling reasons to seek a new coherent description of the Quantum Hall Effects (QHE). The theories of the `Integer' (IQHE) and the `Fractional' (FQHE) quantum Hall effects are very different at present, despite their remarkable…
In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties of the material are the charge carriers two-dimensional and relativistic character. The first experimental evidence of the two-dimensional…
The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective…
Integer and fractional quantum Hall effects were studied with different physics models and explained by different physical mechanisms. In this paper, the common physical mechanism for integer and fractional quantum Hall effects is studied,…
Strongly correlated electron liquids which occur in quantizing magnetic fields reveal a cornucopia of fascinating quantum phenomena such as fractionally charged quasiparticles, anyonic statistics, topological order, and many others. Probing…
We discuss in many details two quantum mechanical models of planar electrons which are very much related to the Fractional Quantum Hall Effect. In particular, we discuss the localization properties of the trial ground states of the models…
We study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We…
On the basis of our previous studies on energy levels and wave functions of single electrons in a strong magnetic field, the energy levels and wave functions of non-interacting electron gas system, electron gas Hall surface density and Hall…
The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting…
A two-dimensional array of quantum dots in a magnetic field is considered. The electrons in the quantum dots are described as unitary random matrix ensembles. The strength of the magnetic field is such that there is half a flux quantum per…
The quantum Hall effect is observed in a two-dimensional electron gas formed in millimeter-scale hydrogenated graphene, with a mobility less than 10 $\mathrm{cm^{2}/V\cdot s}$ and corresponding Ioffe-Regel disorder parameter…
The quantum Hall effect in a 2D electron system expresses a topological invariant, leading to a quantized conductivity. The thermal Hall and thermoelectric Nernst conductances in two dimensions are also reported to be quantized in specific…
The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall…
We address two fundamental issues in the physics of the quantum Hall effect: a unified description of scaling behavior of conductances in the integral and fractional regimes, and a quasi-particle formulation of the chiral Luttinger Liquids…
We study Faraday rotation in the quantum relativistic limit. Starting from the photon self-energy in the presence of a constant magnetic field the rotation of the polarization vector of a plane electromagnetic wave which travel along the…
Recent theoretical results on magnetotransport of electrons in a 2D system in the range of moderately strong transverse magnetic fields are reviewed. The phenomena discussed include: quasiclassical memory effects in systems with various…
We quantum mechanically analyze the fractional quantum Hall effect in graphene. This will be done by building the corresponding states in terms of a potential governing the interactions and discussing other issues. More precisely, we…
Contrary to common belief, the current emitted by a contact embedded in a two-dimensional electron gas (2DEG) is quantized in the presence of electric and magnetic fields. This observation suggests a simple, clearly defined model for the…