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

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 Bc(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 two to three 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 ν =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 Bc(T ) phase observed in experiment.