Related papers: Quantum Hall Physics in String Theory
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…
We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that irrespective of the interaction strength the Hall conductivity is given by the filling fraction of Landau levels averaged over…
Quantum Hall Dynamics is formulated on von Neumann lattice representation where electrons in Landau levels are defined on lattice sites and are treated systematically like lattice fermions. We give a proof of the integer Hall effect, namely…
We give a brief introduction to the phenomenon of the Fractional Quantum Hall effect, whose discovery was awarded the Nobel prize in 1998. We also explain the composite fermion picture which describes the fractional quantum Hall effect as…
We consider the geometric part of the effective action for Fractional Quantum Hall Effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to the obtain correct gravitational linear…
Exploring new Hall effect is always a fascinating research topic. The ordinary Hall effect and the quantum Hall effect, initially discovered in two-dimensional (2D) non-magnetic systems, are the phenomena that a transverse current is…
The discovery of the quantum Hall effect (QHE) in 1980 marked a turning point in condensed matter physics: given appropriate experimental conditions, the Hall conductivity {\sigma}_xy of a two-dimensional (2D) electron system is exactly…
We review the fermionic Chern-Simons field theory for the Fractional Quantum Hall Effect (FQHE). We show that in this field theoretic approach to the problem of interacting electrons moving in a plane in the presence of an external magnetic…
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…
It is demonstrated that all observed fractions at moderate Landau level fillings in the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
A natural generalization of the Heisenberg uncertainty principle inequality holding for non hermitian operators is presented and applied to the fractional quantum Hall effect (FQHE). This inequality was used in a previous paper to prove the…
In this paper, we develop a unified theory for describing Hall effect in various electronic systems based on a pure electron picture (without the hole concept). We argue that the Hall effect is the magnetic field induced symmetry breaking…
Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving…
The fractional quantum Hall effect remains a captivating area in condensed matter physics, characterized by strongly correlated topological order, which manifests as fractionalized excitations and anyonic statistics. Numerical simulations,…
We analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices [A. S{\o}rensen {\it et al.}, Phys. Rev. Lett. {\bf 94} 086803 (2005)]. Extending the previous work, we investigate…
The observed quantization of the Hall conductivity in graphene at high magnetic fields is explained as being due to the dynamically generated spatial modulation of either the electron spin or the density, as decided by the details of…
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…
We reanalyse theoretical considerations and experimental data, in an attempt to decide hether there is another scale in the fractional quantum Hall effect problem, in addition to the magnetic scale defined by the magnetic length $a_c$ or…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative…
We derive, from first principles, the complete Luttinger liquid theory of abelian quantum Hall edge states. This theory includes the effects of disorder and Coulomb interactions as well as the coupling to external electromagnetic fields. We…