相关论文: Integers and Fractions

The phase diagram of integer quantum Hall effect is numerically determined in the tight-binding model, which can account for overall features of recently obtained experimental phase diagram. In particular, the quantum Hall plateaus are…

We study theoretically the parallel quantum wires of the experiment by Auslaender et al. [Science 308, 88 (2005)] at low electron density. It is shown that a Hall effect as observed in two- or three-dimensional electron systems develops as…

A theory of integer quantum Hall effect(QHE) in realistic systems based on von Neumann lattice is presented. We show that the momentum representation is quite useful and that the quantum Hall regime(QHR), which is defined by the propagator…

The status of the ac quantum Hall effect is reviewed with emphasis on the theoretical development in recent years. In particular, the numerical approaches for the calculation of the frequency dependent Hall and longitudinal conductivities…

We propose an experiment to probe the unconventional quantum statistics of quasi-particles in fractional quantum Hall states by measurement of current noise. The geometry we consider is that of a Hall bar where two quantum point contacts…

We consider a collection of fermions in a strong magnetic field coupled by a purely three body repulsive interaction, and predict the formation of composite fermions, leading to a remarkably rich phase diagram containing a host of…

We construct a class of 2+1 dimensional relativistic quantum field theories which exhibit the Fractional Quantum Hall Effect in the infrared, both in the continuum and on the lattice. The UV completion consists of a perturbative $U(1)\times…

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…

Generalizing from previous work on the integer quantum Hall effect, we construct the effective action for the analog of Laughlin states for the fractional quantum Hall effect in higher dimensions. The formalism is a generalization of the…

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…

The present theory has investigated the FQHE without any quasi-particle. The electric field due to the Hall voltage is taken into consideration. We find the ground state where the electron configuration is uniquely determined so as to have…

Motivated by fractional quantum Hall effects, we introduce a universal space of statistics interpolating Bose-Einstein statistics and Fermi-Dirac statistics. We connect the interpolating statistics to umbral calculus and use it as a bridge…

A brief description of the work for which the first half of the Nobel prize for physics for the year 2002 is presented.

We present a Chern-Simons theory of the fractional quantum Hall effect in which flux attachment is followed by a transformation that effectively attaches the correlation holes. We extract the correlated wavefunctions, compute the drift and…

A novel model of complex quantum harmonic oscillator is found to account for the observed Fractional quantum Hall effect (FQHE). The sequences of the observed FQHE conductivity and charge are explained. The two sequences are found to…

A microscopic confirmation of the fractional statistics of the {\em quasiparticles} in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at $\nu=1/3$ and…

The fractional quantum Hall effect at $\nu=2+3/8$, which has been definitively observed, is one of the last fractions for which no viable explanation has so far been demonstrated. Our detailed study suggests that it belongs to a new class…

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…

Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. Here, we report the theoretical discovery of fractional quantum hall effect of…

One-dimensional (1D) quasicrystals exhibit physical phenomena associated with the 2D integer quantum Hall effect. Here, we transcend dimensions and show that a previously inaccessible phase of matter --- the 4D integer quantum Hall effect…