Robustness of quantum Hall interferometry

TL;DR

This paper addresses the robustness of quantum Hall interferometry by relating the interference phase to total charge, overcoming challenges posed by finite edge width and localized anyons, and analyzing effects of interactions, disorder, and multiple modes.

Contribution

It demonstrates that the interference phase can be directly linked to total charge in certain quantum Hall states, providing a robust interpretation despite edge complexities.

Findings

Interference phase relates to total charge in Laughlin and integer states.

The relation holds for arbitrary electron-electron interactions.

Charge-phase relation remains valid with disorder and soft confinement.

Abstract

Fabry-P\'{e}rot interferometry has emerged as a tool to probe anyon statistics in the quantum Hall effect. The interference phase is interpreted as a combination of a quantized statistical phase and an Aharonov-Bohm phase, proportional to the device area and the charge of the anyons propagating along the device edge. This interpretation faces two challenges. First, the edge states have a finite width and hence the device area is ill-defined. Second, multiple localized anyons may be present in states that overlap with the edge, and it may not be clear whether a second anyon traveling along the edge will go inside or outside the region with a localized anyon and therefore whether or not it should pick up a statistical phase. We show how one may overcome both challenges. In a case where only one chiral edge mode passes through the constrictions defining the interferometer, as when electrons in a constriction are in a Laughlin state with $\nu=1/(2n+1)$ or the integer state at $\nu=1$, we show that the interference phase can be directly related to the total electron charge contained in the interferometer. This holds for arbitrary electron-electron interactions and holds even if the bulk of the interferometer has a higher electron density than the region of the constrictions. In contrast to the device area or to the number of anyons inside a propagating edge channel, the total charge is well-defined. We examine, at the microscopic level, how the relation between charge and phase is maintained when there is a soft confining potential and disorder near the edge of the interferometer, and we discuss briefly the complications that can occur when multiple chiral modes can pass through the constriction.