Universal Prefactor of Activated Conductivity in the Quantum Hall Effect

TL;DR

This paper demonstrates that the prefactor of activated conductivity in the quantum Hall effect is universal, depending only on the filling factor, and explains this through electron-phonon interactions and percolation cluster dynamics.

Contribution

It introduces a universal value for the prefactor of activated conductivity in the quantum Hall effect based on long-range potential and percolation theory, extending understanding of dissipation mechanisms.

Findings

Prefactor equals 2e^2/h at integer filling factors.

Prefactor equals 2e^2/q^2h at fractional filling factors.

Long-range potential allows phonons to maintain quasi-equilibrium inside clusters.

Abstract

The prefactor of the activated dissipative conductivity in a plateau range of the quantum Hall effect is studied in the case of a long-range random potential. It is shown that due to long time it takes for an electron to drift along the perimeter of a large percolation cluster, phonons are able to maintain quasi-equilibrium inside the cluster. The saddle points separating such clusters may then be viewed as ballistic point contacts between electron reservoirs with different electrochemical potentials. The prefactor is universal and equal to 2$e^2/h$ at an integer filling factor $\nu$ and to 2$e^2/q^{2}h$ at $\nu=p/q$.