INCREASE OF QUANTUM HALL PLATEAU WIDTHS DUE TO ELECTRON-PHONON INTERACTION

Abstract

We calculate the conductivities for a model system of the integer quantum Hall effect including electron-phonon interactions, with a substrate potential chosen such that microscopic processes can be understood in detail. We find that in general the macroscopic Hall current is not only composed of velocities arising from the Schrödinger time evolution but also of velocities generated by electron-phonon interactions and that the latter can contribute to the formation of the quantized Hall plateaus. We show for typical quantum Hall systems the phonon induced contributions lead to Hall plateaus which are somewhat larger than the plateaus of the dissipative conductivity. Experimentally this difference has been known for a long time, but it seemed unexplained so far. In the case where the substrate potential has no spatial fluctuations in the direction of the macroscopic electric field, all states are conducting and the dissipative conductivity vanishes only near integer filling factors. Nevertheless, the calculated Hall conductivity shows broad quantized plateaus, which here are entirely generated by velocities arising from phonon induced relaxation processes. These results show that absence of dissipation is not indispensable for the existence of quantized Hall plateaus.