Gauge field in systems with spin orbit interactions and additional discrete degrees of freedom to real spin

TL;DR

This paper extends the spin gauge field formalism to systems with additional discrete degrees of freedom like pseudospin and valley, demonstrating its applicability to materials such as molybdenum sulphide, silicene, and topological insulators.

Contribution

It generalizes the effective magnetization concept in gauge field formalism to include pseudospin and valley degrees of freedom in spin orbit systems.

Findings

The generalized magnetization recovers key results from Sundaram-Niu and Kubo formalisms.

Application to topological insulator thin films shows the formalism's relevance.

Extension to materials with multiple discrete degrees of freedom.

Abstract

The spin gauge field formalism has been used to explain the emergence of out of plane spin accumulation in two-dimensional spin orbit interaction (SOI) systems in the presence of an in-plane electric field. The adiabatic alignment of the charge carrier spins to the momentum dependent SOI field, which changes in time due to the electric field, can be mathematically captured by the addition of a gauge term in the Hamiltonian. This gauge term acts like an effective, electric field dependent magnetization. In this work we show that this effective magnetization can be generalized to systems which include additional discrete degrees of freedom to real spin, such as the pseudospin and/or valley degrees of freedom in emerging materials like molybdenum sulphide and silicene. We show that the generalized magnetization recovers key results from the Sundaram-Niu formalism as well as from the Kubo formula. We then use the generalized magnetization to study the exemplary system of a topological insulator thin film system where the presence of both a top as well as a bottom surface provides an additional discrete degree of freedom in addition to the real spin.