Spin symmetry and spin current of helicity eigenstates of the Luttinger Hamiltonian

TL;DR

This paper uses symmetry arguments to show that the net spin current predicted in certain semiconductors cannot occur under the Luttinger Hamiltonian due to cancellation of contributions from degenerate helicity eigenstates, challenging previous predictions.

Contribution

It introduces a symmetry-based analysis demonstrating the absence of net spin current in the Luttinger model, and discusses mechanisms that could break this symmetry to produce spin currents.

Findings

Net spin current cancels out in the Luttinger Hamiltonian due to symmetry.

Degeneracy of eigenstates leads to exact cancellation of spin flux.

Symmetry breaking mechanisms are necessary to generate spin currents.

Abstract

A general spin symmetry argument is proposed for spin currents in semiconductors. In particular, due to the symmetry with respect to spin polarization of the helicity eigenstates of the Luttinger Hamiltonian for a hole-doped semiconductor, the spin polarized flux from a single helicity eigenstate induced by an external electric field, is canceled exactly when all such contributions from eigenstates that are degenerate in energy are summed. Thus, the net spin current predicted by Murakami et al, Science 301, 1348 (2003), cannot be produced by such a Hamiltonian. Possible symmetry breaking mechanisms which may generate a spin current are discussed.