Sound and Heat Absorption by a 2D Electron Gas in an Odd-Integer Quantized-Hall Regime

TL;DR

This paper investigates how a 2D electron gas in an odd-integer quantum Hall state absorbs sound and heat via phonons, revealing different behaviors of spin-related absorption channels at low temperatures.

Contribution

It identifies two phonon absorption channels in a 2D electron gas in the quantum Hall regime, highlighting the role of spin-orbit coupling and temperature dependence.

Findings

Spin-orbit related absorption remains finite at zero temperature.

Non-spin-related absorption vanishes as temperature approaches zero.

Both channels influence phonon propagation and heat absorption in the 2DEG.

Abstract

The absorption of bulk acoustic phonons in a two-dimensional (2D) GaAs/AlGaAs heterostructure is studied (in the clean limit) where the 2D electron-gas (2DEG), being in an odd-integer quantum-Hall state, is in fact a spin dielectric. Of the two channels of phonon absorption associated with excitation of spin waves, one, which is due to the spin-orbit (SO) coupling of electrons, involves a change of the spin state of the system and the other does not. We show that the phonon-absorption rate corresponding to the former channel (in the paper designated as the second absorption channel) is finite at zero temperature ($T$), whereas that corresponding to the latter (designated as the first channel) vanishes for $T\to 0$. The long-wavelength limit, being the special case of the first absorption channel, corresponds to sound (bulk and surface) attenuation by the 2DEG. At the same time, the ballistic phonon propagation and heat absorption are determined by both channels. The 2DEG overheat and the attendant spin-state change are found under the conditions of permanent nonequilibrium phonon pumping.