Communications in Mathematical Sciences

Volume 12 (2014)

Number 3

Diffusion models for spin transport derived from the spinor Boltzmann equation

Pages: 565 – 592



Raymond El Hajj (Institut National des Sciences Appliquées de Rennes, France)


The aim of this paper is to derive and analyze diffusion models for semiconductor spintronics. We begin by presenting and studying the so called “spinor” Boltzmann equation. Starting then from a rescaled version of linear Boltzmann equation with different spin-flip and non spin-flip collision operators, different continuum (drift-diffusion) models are derived. By comparing the strength of the spin-orbit scattering with the scaled mean free paths, we explain how some models existing in the literature (like the two-component models) can be obtained from the spinor Boltzmann equation. A new spin-vector drift-diffusion model keeping spin relaxation and spin precession effects due to the spin-orbit coupling in semiconductor structures is derived and some of its mathematical properties are checked.


spinor Boltzmann equation, spin-orbit coupling, spin-flip interactions, diffusion limit, decoherence limit, two-component drift-diffusion model, spin-vector drift-diffusion model

2010 Mathematics Subject Classification

35Q20, 76R50, 81R25

Published 26 November 2013