Charge and spin diffusion on the metallic side of the metal-insulator transition: a self-consistent approach

TL;DR

This paper presents a self-consistent theoretical framework for understanding spin and electron diffusion in doped semiconductors near the metal-insulator transition, accounting for spin-orbit effects and aligning with numerical simulations.

Contribution

It introduces a novel self-consistent approach to describe spin and electron diffusion, improving upon phenomenological models and matching numerical results for zinc-blende semiconductors.

Findings

Qualitative reproduction of previous phenomenological models

More elaborate calculations align with numerical simulations

Universal applicability to zinc-blende semiconductors

Abstract

We develop a self-consistent theory describing the spin and spatial electron diffusion in the impurity band of doped semiconductors under the effect of a weak spin-orbit coupling. The resulting low-temperature spin-relaxation time and diffusion coefficient are calculated within different schemes of the self-consistent framework. The simplest of these schemes qualitatively reproduces previous phenomenological developments, while more elaborate calculations provide corrections that approach the values obtained in numerical simulations. The results are universal for zinc-blende semiconductors with electron conductance in the impurity band, and thus they are able to account for the measured spin-relaxation times of materials with very different physical parameters. From a general point of view, our theory opens a new perspective for describing the hopping dynamics in random quantum networks.