D'yakonov-Perel' spin relaxation for degenerate electrons in the electron-hole liquid

TL;DR

This paper provides an analytical model for D'yakonov-Perel' spin relaxation in degenerate electron-hole liquids, highlighting the dominant role of electron-hole scattering and the effects of density on relaxation times.

Contribution

It derives simple expressions for scattering rates affecting spin relaxation and analyzes how electron-hole density influences relaxation dynamics in semiconductors.

Findings

Electron-hole scattering rates are comparable to impurity scattering rates.

Decreasing electron-hole density enhances scattering and slows spin relaxation.

At high densities, the model breaks down and free precession dominates.

Abstract

We present an analytical study of the D'yakonov-Perel' spin relaxation time for degenerate electrons in a photo-excited electron-hole liquid in intrinsic semiconductors exhibiting a spin-split band structure. The D'yakonov-Perel' spin relaxation of electrons in these materials is controlled by electron-hole scattering, with small corrections from electron-electron scattering and virtually none from electron-impurity scattering. We derive simple expressions (one-dimensional and two-dimensional integrals respectively) for the effective electron-hole and electron-electron scattering rates which enter the spin relaxation time calculation. The electron-hole scattering rate is found to be comparable to the scattering rates from impurities in the electron liquid - a common model for n-type doped semiconductors. As the density of electron-hole pairs decreases (within the degenerate regime), a strong enhancement of the scattering rates and a corresponding slowing down of spin relaxation is predicted due to exchange and correlation effects in the electron-hole liquid. In the opposite limit of high density, the original D'yakonov-Perel' model fails due to decreasing scattering rates and is eventually superseded by free precession of individual quasiparticle spins.