Interaction of nonuniform elastic waves with two-dimensional electrons in AlGaAs-GaAs-AlGaAs heterostructures

TL;DR

This paper investigates how nonuniform elastic waves interact with a two-dimensional electron system in AlGaAs-GaAs-AlGaAs heterostructures, revealing the dependence of coupling on layer thickness and wave vector, and analyzing velocity renormalization in fractional quantum Hall states.

Contribution

It provides a detailed calculation of the coupling constant dependence on layer thickness and wave vector, and explores velocity renormalization in fractional quantum Hall regimes.

Findings

Maximum coupling occurs when wavelength is comparable to GaAs layer thickness.

Velocity of elastic modes is renormalized in fractional quantum Hall states.

Transition to Halperin wave function alters velocity shift dependence.

Abstract

An interaction of a double layer electron system realized in an AlGaAs-GaAs-AlGaAs heterostructure with nonuniform elastic modes localized in the GaAs layer is considered. The dependence of the coupling constant on the ratio between the thickness of the GaAs layer and the wavelength is calculated for the wave vector directed along the [110] axis, the displacement vector lying in the (1-10) plane and the interface boundaries parallel to the (001) plane. It is shown, that the coupling constant reaches the maximal value at the wavelength which is of order of the thickness of the GaAs layer. The renormalization of the velocity of the elastic modes is found for the case, when the electron system is in the fractional quantum Hall regime. It is shown, that for certain modes the dependence of the velocity shift on the wave vector is modified qualitatively under a transition of the electron system to the state, which corresponds to the Halperin wave function.