Related papers: Models for the integer quantum Hall effect: the ne…
It is shown that the Jain mapping between states of integer and fractional quantum Hall systems can be described dynamically as a perturbative renormalization of an effective Chern-Simons field theory. The effects of mirror duality…
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…
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers $\mathcal{C}$ and $\mathcal{C}_{\text{spin}}$. We have only $\mathcal{C}_{\text{spin}}=0$ or $\pm \frac{1}{2}$ in conventional QH…
It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Fractional statistics can be extended to nonabelian statistics and examples can be constructed…
We study the anomalous quantum Hall effect exhibited by the relativistic particles living on two-sphere S^2 and submitted to a magnetic monopole. We start by establishing a direct connection between the Dirac and Landau operators through…
We demonstrate the emergence of the quantum Hall (QH) hierarchy in a 2D model of coupled quantum wires in a perpendicular magnetic field. At commensurate values of the magnetic field, the system can develop instabilities to appropriate…
Up to almost the last two decades all the experimental results concerning the quantum Hall effect (QHE), i.e., the observation of plateaux at integer (IQHE) or fractional (FQHE) values of the constant h/e2, were related to quantum-wells in…
We review the recently proposed Dirac composite fermion theory of the half-filled Landau level.
We investigate the quantum Hall effect in graphene. We argue that in graphene in presence of an external magnetic field there is dynamical generation of mass by a rearrangement of the Dirac sea. We show that the mechanism breaks the lattice…
We introduce a large N version of the spin quantum Hall transition problem. It is formulated as a problem of Dirac fermions coupled to disorder, whose Hamiltonian belong to the symmetry class C. The fermions carry spin degrees of freedom…
Topological aspects represent currently a boosting area in condensed matter physics. Yet there are very few suggestions for technical applications of topological phenomena. Still, the most important is the calibration of resistance…
We consider the quantum Hall effect in terms of an effective field theory formulation of the edge states, providing a natural common framework for the fractional and integral effects.
We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting…
A mapping is developed between the quantum Hall plateau transition and two-dimensional self-interacting lattice polymers. This mapping is exact in the classical percolation limit of the plateau transition, and diffusive behavior at the…
The Hamiltonian Theory of the fractional quantum Hall effect is an operator description that subsumes many properties of Composite Fermions, applies to gapped and gapless cases, and has been found to provide results in quantitative accord…
The dynamics responsible for lifting the degeneracy of the Landau levels in the quantum Hall (QH) effect in graphene is studied by utilizing a low-energy effective model with a contact interaction. A detailed analysis of the solutions of…
We construct an explicit duality between the interacting quantum Hall system in the lowest Landau level and a non-interacting Landau problem. This is done by absorbing the interaction into the gauge field in the form of an effective…
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…
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…
We show that any critical transition region between two adjacent Hall plateaus in either integer or fractional quantum Hall effect is characterized by a universal semi-circle relationship between the longitudinal and transverse…