Ghee Tan
title: Gauge field in systems with spin orbit interactions and additional discrete degrees of freedom to real spin 
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Introduction
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In the Spin Hall Effect (SHE) [@SHE1; @SHE2; @SHE3; @SHE4; @SHE5], the passage of an in-plane electric field in a two-dimensional electron gas (2DEG) with spin orbit interactions (SOIs) leads to the appearance of an out of plane spin accumulation.

Murakami [@Murakami] and Fujita [@Grp1; @Grp2; @Grp3; @Grp4; @SGTSciRep], and their respective coauthors, had independently studied the SHE. They showed that the out of plane spin accumulation can be understood as the response of the charge carriers as their spins align adiabatically with the momentum dependent SOI field. The direction of the SOI field changes in time due to the change in the momentum of the charge carriers as they accelerate under the electric field. Mathematically, the electric field gives to an effective magnetization term in the Hamiltonian which we shall, for short, call the Murakami-Fujita (MF) potential.

Many emerging material systems in interest in spintronics, for example silicene [@Sil1; @Sil2; @Sil3; @Sil4] and [@Mo1; @Mo2; @Mo3], possess discrete degrees of freedom (DoFs) such as the pseudospin and / or valley degrees of freedom, in addition to 