Piezoelectric coupling, phonons, and tunneling into a quantum Hall edge

TL;DR

This paper investigates how piezoelectric coupling to phonons affects electron tunneling into quantum Hall edges, revealing negative corrections to tunneling exponents consistent with experiments and exploring higher-order effects.

Contribution

It provides a theoretical analysis of piezoelectric phonon effects on tunneling exponents in quantum Hall systems, including higher-order corrections.

Findings

Piezoelectric coupling causes negative renormalization of tunneling exponents.

Corrections can reach a few percent depending on edge plasmon speed.

Higher-order effects influence the infrared behavior of tunneling.

Abstract

We show that the piezoelectric coupling to three-dimensional phonons in GaAs renormalizes the current-voltage exponent for tunneling of electrons into an incompressible quantum Hall edge. The leading correction is always negative, in agreement with experiments on the $\nu = 1/3$ state and, depending on the precise value of the edge plasmon speed, can be as large as a few percent. We also discuss higher-order corrections, which determine the effect of the piezoelectric coupling in the extreme infrared limit.