title: Gauge Physics of Spin Hall Effect.
abstract: Spin Hall effect (SHE) has been discussed in the context of Kubo formulation, geometric physics, spin orbit force, and numerous semi-classical treatments. It can be confusing if the different pictures have partial or overlapping claims of contribution to the SHE. In this article, we present a gauge-theoretic, time-momentum elucidation, which provides a general SHE equation of motion, that unifies under one theoretical framework, all contributions of SHE conductivity due to the kinetic, the spin orbit force (Yang-Mills), and the geometric (Murakami-Fujita) effects. Our work puts right an ambiguity surrounding previously partial treatments involving the Kubo, semiclassical, Berry curvatures, or the spin orbit force. Our full treatment shows the Rashba 2DEG SHE conductivity to be [formula in text] instead of [formula in text], and Rashba heavy hole [formula in text] instead of [formula in text]. This renewed treatment suggests a need to re-derive and re-calculate previously studied SHE conductivity.
authors.affiliation: Data Storage Institute, Agency for Science, Technology and Research (A*STAR) 2 Fusionopolis Way, #08-01 DSI, Innovis, Singapore 138634.|Computational Nanoelectronics and Nano-device Laboratory, Electrical and Computer Engineering Department, National University of Singapore, 4 Engineering Drive 3, Singapore 117576.
authors.forename: Seng Ghee
authors.initials: SG
authors.lastname: Tan
authors.affiliation: Computational Nanoelectronics and Nano-device Laboratory, Electrical and Computer Engineering Department, National University of Singapore, 4 Engineering Drive 3, Singapore 117576.|Information Storage Materials Laboratory, Electrical and Computer Engineering Department, National University of Singapore, 4 Engineering Drive 3, Singapore 117576.
authors.forename: Mansoor B A
authors.initials: MB
authors.lastname: Jalil
authors.affiliation: Computational Nanoelectronics and Nano-device Laboratory, Electrical and Computer Engineering Department, National University of Singapore, 4 Engineering Drive 3, Singapore 117576.
authors.forename: Cong Son
authors.initials: CS
authors.lastname: Ho
authors.affiliation: Computational Nanoelectronics and Nano-device Laboratory, Electrical and Computer Engineering Department, National University of Singapore, 4 Engineering Drive 3, Singapore 117576.
authors.forename: Zhuobin
authors.initials: Z
authors.lastname: Siu
authors.affiliation: Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan.
authors.forename: Shuichi
authors.initials: S
authors.lastname: Murakami