Insensitivity of Quantized Hall Conductance to Disorder and Interactions
Abstract
A twodimensional quantum Hall system is studied for a wide class of potentials including singlebody random potentials and repulsive electronelectron interactions. We assume that there exists a nonzero excitation gap above the ground state(s), and then the conductance is derived from the linear perturbation theory with a sufficiently weak electric field. Under these two assumptions, we proved that the Hall conductance $\sigma_{xy}$ and the diagonal conductance $\sigma_{yy}$ satisfy $\sigma_{xy}+e^2\nu/h\le{\rm const.}L^{1/12}$ and $\sigma_{yy}\le{\rm const.}L^{1/12}$. Here $e^2/h$ is the universal conductance with the charge $e$ of electron and the Planck constant $h$; $\nu$ is the filling factor of the Landau level, and $L$ is the linear dimension of the system. In the thermodymanic limit, our results show $\sigma_{xy}=e^2\nu/h$ and $\sigma_{yy}=0$. The former implies that integral and fractional filling factors $\nu$ with a gap lead to, respectively, integral and fractional quantizations of the Hall conductance.
 Publication:

arXiv eprints
 Pub Date:
 November 1998
 DOI:
 10.48550/arXiv.condmat/9811112
 arXiv:
 arXiv:condmat/9811112
 Bibcode:
 1998cond.mat.11112K
 Keywords:

 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Condensed Matter  Statistical Mechanics
 EPrint:
 LaTeX, 62 pages, no figures, typos corrected, some references added, discussion on the standard timedependent vector potential added, accepted for publication in J. Stat. Phys