1998/11/09 by Tohru Koma, Koma, Tohru
Engineering · Physics and Astronomy · #FOS: Physical sciences #Magnetic Field Sensors Techniques #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum and electron transport phenomena #Statistical Mechanics (cond-mat.stat-mech) #Surface and Thin Film Phenomena #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/9811112
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
openalex publication_date 1998/11/09 · arxiv created 1999/12/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 σxy and the diagonal conductance σyy satisfy |σxy+e2ν/h|≤\rm const.L-1/12 and |σyy|≤\rm const.L-1/12. Here e2/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 σxy=-e2ν/h and σyy=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.