Critical conductivity of the quantum Hall system at higher Landau levels

Abstract

The two-particle spectral function S(q,\ensuremath{\omega}) is studied at the mobility edge on the quantum Hall system, in the lowest and higher Landau level. The profile and its scaling properties of S(q,\ensuremath{\omega}) are numerically clarified. Our result shows that, in higher Landau level with the long-range random potential, the critical dissipative conductivity ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{xx}}^{\mathrm{c}}$ is approximately equal to the universal value 0.${5\mathrm{e}}^{2}$/h. This suggests that the critical conductivity ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{xx}}^{\mathrm{c}}$ on the quantum Hall system with the long-range potential is independent of the Landau-level index N.