A prohibition of equilibrium spin currents in multi-terminal ballistic devices

TL;DR

This paper proves that multi-terminal ballistic devices with intrinsic spin-orbit interaction do not support equilibrium spin currents at any energy, and explores implications for spin polarization in various device configurations.

Contribution

It provides a rigorous proof that equilibrium spin currents are absent in such devices and analyzes the limitations on spin polarization in multi-terminal setups.

Findings

No equilibrium spin currents at any energy in multi-terminal ballistic devices.

Two-terminal devices cannot polarize transient current.

N-1 input terminals in parallel cannot produce spin polarization.

Abstract

We show that in the multi-terminal ballistic devices with intrinsic spin-orbit interaction connected to normal metal contacts there are no equilibrium spin currents present at any given electron energy. Obviously, this statement holds also after the integration over all occupied states. Based on the proof of this fact, a number of scenarios involving nonequilibrium spin currents is identified and further analyzed. In particular, it is shown that an arbitrary two-terminal device cannot polarize transient current. The same is true for the output terminal of an N-terminal device when all N-1 inputs are connected in parallel.