Insensitivity of Quantized Hall Conductance to Disorder and Interactions
| dc.creator | Koma, Tohru | |
| dc.date | 1998-11-09 | |
| dc.date | 1999-12-27 | |
| dc.date.accessioned | 2026-07-07T03:11:55Z | |
| dc.date.available | 2026-07-07T03:11:55Z | |
| dc.description | A two-dimensional quantum Hall system is studied for a wide class of potentials including single-body random potentials and repulsive electron-electron interactions. We assume that there exists a non-zero 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 $σ_{xy}$ and the diagonal conductance $σ_{yy}$ satisfy $|σ_{xy}+e^2ν/h|\le{\rm const.}L^{-1/12}$ and $|σ_{yy}|\le{\rm const.}L^{-1/12}$. Here $e^2/h$ is the universal conductance with the charge $-e$ of electron and the Planck constant $h$; $ν$ is the filling factor of the Landau level, and $L$ is the linear dimension of the system. In the thermodymanic limit, our results show $σ_{xy}=-e^2ν/h$ and $σ_{yy}=0$. The former implies that integral and fractional filling factors $ν$ with a gap lead to, respectively, integral and fractional quantizations of the Hall conductance. | |
| dc.description | LaTeX, 62 pages, no figures, typos corrected, some references added, discussion on the standard time-dependent vector potential added, accepted for publication in J. Stat. Phys | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9811112 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9811112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/28759 | |
| dc.subject | Mesoscale and Nanoscale Physics | |
| dc.subject | Statistical Mechanics | |
| dc.title | Insensitivity of Quantized Hall Conductance to Disorder and Interactions | |
| dc.type | text |