Decoherence of high-energy electrons in weakly disordered quantum Hall edge states

Abstract

We investigate theoretically the phase coherence of electron transport in edge states of the integer quantum Hall effect at filling factor $\nu=2$, in the presence of disorder and inter-edge state Coulomb interaction. Within a Fokker-Planck approach, we calculate analytically the visibility of the Aharonov-Bohm oscillations of the current through an electronic Mach-Zehnder interferometer. In agreement with recent experiments, we find that the visibility is independent of the energy of the current-carrying electrons injected high above the Fermi sea. Instead, it is the amount of disorder at the edge that sets the phase space available for inter-edge state energy exchange and thereby controls the visibility suppression.