Generalized Kubo formula for spin transport: A theory of linear response to non-Abelian fields

Abstract

The traditional Kubo formula is generalized to describe the linear response with respect to non-Abelian fields. To fulfil the demand for studying spin transport, the SU(2) Kubo formulae are derived by two conventional approaches with different gauge fixings. Those two approaches are shown to be equivalent where the non-conservation of the SU(2) current plays an essential role in guaranteeing the consistency. Some concrete examples relating Spin Hall Effect are considered. The dc spin conductivity vanishes in the system with parabolic unperturbed dispersion relation. By applying a time-dependent Rashba field, the spin conductivity can be measured directly. Our formula is also applied to the high-dimensional representation for the interests of some important models, such as Luttinger model and bilayer spin Hall system.

Revtex, 10 pages, 2 tables, typos corrected and ref added

References in corpus (7)

• Dissipationless Quantum Spin Current at Room Temperature
• Spin current and polarization in impure 2D electron systems with spin-orbit coupling
• Current induced electron spin polarization in strained semiconductors
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with Rashba Interaction in a Perpendicular Magnetic Field
• Dissipation effects in spin-Hall transport of electrons and holes
• DC Spin Current Generation in a Rashba-type Quantum Channel

Cited by in corpus (8)

• Generation of spin currents and spin densities in systems with reduced symmetry
• Magnetoelectric effects in Josephson junctions
• On the nature of steady states of spin distributions in the presence of spin-orbit interactions
• Spin polarization in biased Rashba-Dresselhaus two-dimensional electron systems
• Topological nature of the proper spin current and the spin-Hall torque
• Spin-Hall effect due to the bulk states of topological insulators: Extrinsic contribution to the conserved spin current
• Understanding spin Hall effects from the motion in SU(2)XU(1) fields
• Understanding spin transport from the motion in SU(2)$\times$U(1) fields