Spin-orbit interaction in symmetric wells with two subbands

TL;DR

This paper derives a new spin-orbit interaction term in symmetric quantum wells with two subbands, which affects spin transport phenomena like the spin-Hall effect and induces zitterbewegung without magnetic fields.

Contribution

It introduces a novel inter-subband-induced spin-orbit term in symmetric wells, derived from the Kane model, that was previously unrecognized.

Findings

New spin-orbit term exists in symmetric wells due to parity of states.

The new term is comparable in strength to Rashba coupling.

It leads to a non-zero spin-Hall conductivity and induces zitterbewegung.

Abstract

We investigate the spin-orbit (s-o) interaction in two-dimensional electron gases (2DEGs) in quantum wells with two subbands. From the $8\times 8$ Kane model, we derive a new inter-subband-induced s-o term which resembles the functional form of the Rashba s-o -- but is non-zero even in \emph{symmetric} structures. This follows from the distinct parity of the confined states (even/odd) which obliterates the need for asymmetric potentials. We self-consistently calculate the new s-o coupling strength for realistic wells and find it comparable to the usual Rashba constant. Our new s-o term gives rise to a non-zero ballistic spin-Hall conductivity, which changes sign as a function of the Fermi energy ($\epsilon_F$), and can induce an unusual \emph{zitterbewegung} with cycloidal trajectories \textit{without} magnetic fields.