Transport between edge states in multilayer integer quantum Hall systems: exact treatment of Coulomb interactions and disorder

Abstract

A set of stacked two-dimensional electron systems in a perpendicular magnetic field exhibits a three-dimensional version of the quantum Hall effect if interlayer tunneling is not too strong. When such a sample is in a quantum Hall plateau, the edge states of each layer combine to form a chiral metal at the sample surface. We study the interplay of interactions and disorder in transport properties of the chiral metal, in the regime of weak interlayer tunneling. Our starting point is a system without interlayer tunneling, in which the only excitations are harmonic collective modes: surface magnetoplasmons. Using bosonization and working perturbatively in the interlayer tunneling amplitude, we express transport properties in terms of the spectrum for these collective modes, treating electron-electron interactions and impurity scattering exactly. We calculte the conductivity as a function of temperature, finding that it increases with increasing temperature as observed in recent experiments. We also calculate the autocorrelation function of mesoscopic conductance fluctuations induced by changes in a magnetic field component perpendicular to the sample surface, and its dependence on temperature. We show that conductance fluctuations are characterised by a dephasing length that varies inversely with temperature.Comment: 13 pages, 10 figures, minor changes made for publicatio