Spin current and spin Hall effects

Abstract

In terms of SU(2) Yang-Mills field formulism, we give a nature definition of spin current for the systems with Rashba or Dresselhaus spin-orbit couplings etc., and we obtain a covariant form of continuity equations for the corresponding spin current [1]. The traditional Kubo formula is generalized to describe the linear response with respect to non-Abelian fields. We find that the covariant form we proposed plays an essential role in guaranteeing the consistency of SU(2) Kubo formula [2]. We also derive the classical counterpart of quantum mechanical covariant “continuity-like” equation for the spin current, and present an intuitive picture for elucidating the non-conservation of the spin current [3]. We discuss the spin-relaxation time for two-dimensional systems with a hierarchy of spin-orbit couplings, and found that the spin-relaxation time can be infinite if the coupling strengths certain condition which correspond to the vanishing Yang-Mills “magnetic” field [4].