A microscopic model for the magnetic field driven breakdown of the dissipationless state in the integer and fractional quantum Hall effect

TL;DR

This paper presents a microscopic thermal activation model explaining the magnetic field-driven breakdown of the dissipationless state in quantum Hall systems, aligning well with experimental phase diagrams across various samples.

Contribution

It introduces a detailed Landau level broadening model with Lorentzian tails, linking localized and delocalized states to the breakdown mechanism in quantum Hall effects.

Findings

Good agreement with experimental phase diagrams over wide temperature and magnetic field ranges

Landau level width is independent of magnetic field

Composite Fermion Landau levels have the same width as electron Landau levels

Abstract

Intra Landau level thermal activation, from localized states in the tail, to delocalized states above the mobility edge in the same Landau level, explains the $B_c(T)$ (half width of the dissipationless state) phase diagram for a number of different quantum Hall samples with widely ranging carrier density, mobility and disorder. Good agreement is achieved over $2-3$ orders of magnitude in temperature and magnetic field for a wide range of filling factors. The Landau level width is found to be independent of magnetic field. The mobility edge moves, in the case of changing Landau level overlap to maintain a sample dependent critical density of states at that energy. An analysis of filling factor $\nu=2/3$ shows that the composite Fermion Landau levels have exactly the same width as their electron counterparts. An important ingredient of the model is the Lorentzian broadening with long tails which provide localized states deep in the gap which are essential in order to reproduce the robust high temperature $B_c(T)$ phase observed in experiment.