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

TL;DR

This paper theoretically analyzes how disorder affects electron phase coherence in quantum Hall edge states, showing that edge disorder, not electron energy, governs the suppression of interference visibility.

Contribution

It provides an analytical Fokker-Planck model demonstrating the dominant role of edge disorder over electron energy in phase coherence loss.

Findings

Visibility is independent of electron energy at high injection energies.

Edge disorder determines the phase space for energy exchange.

The model agrees with recent experimental observations.

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.