Non-Abelian gauge fields in the gradient expansion: generalized Boltzmann and Eilenberger equations

Details Non-Abelian gauge fields in the gradient expansion: generalized Boltzmann and Eilenberger equations Non-Abelian gauge fields in the gradient expansion: generalized Boltzmann and Eilenberger equations

2010-03-30

arxiv.org/abs/1003.5763v3

Phys.Rev.B82:195316,2010

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

11 pages, 1 figure; some corrections and updated/extended references

Scientific paper

10.1103/PhysRevB.82.195316

We present a microscopic derivation of the generalized Boltzmann and Eilenberger equations in the presence of non-Abelian gauges, for the case of a non-relativistic disordered Fermi gas. A unified and symmetric treatment of the charge $[U(1)]$ and spin $[SU(2)]$ degrees of freedom is achieved. Within this framework, just as the $U(1)$ Lorentz force generates the Hall effect, so does its $SU(2)$ counterpart give rise to the spin Hall effect. Considering elastic and spin-independent disorder we obtain diffusion equations for charge and spin densities and show how the interplay between an in-plane magnetic field and a time dependent Rashba term generates in-plane charge currents.

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