Related papers: Is There Another Scale in the Fractional Quantum H…
Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be…
A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave…
Recent developments in the scaling theory of the integer quantum Hall effect are discussed. In particular, the influence of electron-electron interactions on the critical behavior are studied. It is further argued that recent experiments on…
The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may…
The fractional quantum Hall (FQH) effect refers to the strongly-correlated phenomena and the associated quantum phases of matter realized in a two-dimensional gas of electrons placed in a large perpendicular magnetic field. In such systems,…
The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a new type of fractional quantum Hall system, which has the special property that it lives in…
We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Both effects…
In this letter, we discuss the recently proposed fractional quantum Hall effect in the absence of Landau levels. It is shown that the parton construction can explain all properties of 1/3 state, including the effective charge of…
Using a mapping of a layered three-dimensional system with significant inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong magnetic field limit is obtained in the semi-classical approximation. This phase diagram,…
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…
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…
We propose the two formalisms for obtaining the noncommutative spacetime in a magnetic field. One is the first-order formalism and the other is the second-order formalism. Although the noncommutative spacetime is realized manifestly in the…
The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of…
After more than three decades the fractional quantum Hall effect still poses challenges to contemporary physics. Recent experiments point toward a fractal scenario for the Hall resistivity as a function of the magnetic field. Here, we…
Edge states of the quantum Hall fluid provide an opportunity to study mesoscopic effects in a highly correlated electron system that is both experimentally accessible and theoretically tractable. In this paper we review recent work on the…
We introduce and study the Wannier functions for an electron moving in a plane under the influence of a perpendicular uniform and constant magnetic field. The relevance for the Fractional Quantum Hall Effect is discussed; in particular it…
Since the discovery of the Fractional Quantum Hall Effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing…
We derive a general scaling relation for the anomalous Hall effect in ferromagnetic metals involving multiple competing scattering mechanisms, described by a quadratic hypersurface in the space spanned by the partial resistivities. We also…
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 formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…