Heat instability of quantum Hall conductors

Breakdown of the integer quantum Hall effect (IQHE) is discussed based on the consideration of heat stability of a two-dimensional electron gas (2DEG). First, the 2DEG system in the IQHE state is suggested to become thermally unstable when the Hall electric field E-y reaches a threshold value E-b. Above E-b, a small number of excited electrons in the higher Landau level, which are initially present in the conductor as fluctuation, are accelerated by E-y, and the 2DEG thereby undergoes a transition to a warm dissipative state. This abrupt transition is referred to as the bootstrap-type electron heating (BSEH). Second, the critical field, E-b, for BSEH is theoretically derived and compared with the experimental values of the IQHE breakdown reported earlier by different groups. The agreement is satisfactory, suggesting that BSEH is the basic mechanism behind the IQHE breakdown. Third, dynamical aspects of BSEH are discussed. It is argued that the BSEH is a process of the avalanche-type electron-hole pair multiplication, in which a small number of nonequilibrium. carriers gains kinetic energy within a Landau level and excites other electron-hole pairs via the inter-landau-level impact ionization. Electrons travel a macroscopic distance during the process of electron-hole multiplication. This feature is confirmed by experiments. Experiments indicate that E-y does not locally influence the longitudinal conductivity when the IQHE breaks down, providing definite proof of BSEH. Finally, a variety of characteristics of the IQHE, reported in earlier works, is reviewed and suggested to be consistent with the BSEH model.