Gauge Covariance and Spin Current Conservation in the Gauge Field Formulation of Systems with Spin-Orbit Coupling

Abstract

The question of gauge-covariance in the non-Abelian gauge-field formulation of two space-dimensional systems with spin-orbit coupling relevant to spintronics is investigated. Although, these are generally gauge-fixed models, it is found that for the class of gauge fields that are space-time independent and satisfy a U(1) algebra, thus having a vanishing field strength, there is a residual gauge freedom in the Hamiltonian. The gauge transformations assume the form of a space-dependent rotation of the transformed wave functions with rotation angles and axes determined by the specific form of the gauge-field, i.e., the spin-orbit coupling. The fields can be gauged away, reducing the Hamiltonian to one which is isospectral to the free-particle Hamiltonian, and giving rise to the phenomenon of persistent spin helix reported first by B.~A.~Bernevig \emph{et al.} [Phys.~Rev.~Lett. \textbf{97}, 236601 (2006)]. The investigation of the global gauge transformations leads to the derivation of a continuity equation where the component of the spin-density along given directions, again fixed by the specific form of the gauge field, is conserved.

11 pages, no figures

References in corpus (7)

• An Exact SU(2) Symmetry and Persistent Spin Helix in a Spin-Orbit Coupled System
• On A Proper Definition of Spin Current
• Non-Abelian hydrodynamics and the flow of spin in spin-orbit coupled substances
• Non-Abelian spin-orbit gauge: Persistent spin helix and quantum square ring
• Gauge symmetry breaking and topological quantization for the Pauli Hamiltonian
• Understanding spin transport from the motion in SU(2)$\times$U(1) fields
• Understanding spin Hall effects from the motion in SU(2)XU(1) fields

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• Pure Gauge Spin-Orbit Couplings