Topological nature of the proper spin current and the spin-Hall torque

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Topological nature of the proper spin current and the spin-Hall torque

Authors

Hong Liu, James H. Cullen, Dimitrie Culcer

Abstract

Spin currents driven by spin-orbit coupling are key to spin torque devices, but determining the proper spin current is highly non-trivial. Here we derive a general quantum-mechanical formula for the intrinsic proper spin current showing that it is a topological quantity, and can be finite even in the gap. We determine the spin-Hall current due to the bulk states of topological insulators both deep in the bulk, where the system is unmagnetized, and near the interface, where a proximity-induced magnetization is present, as well as for low-dimensional spin-3/2 hole systems.

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