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

2010/03/31 by Cosimo Gorini, C. Gorini, P. Schwab +3
Physics and Astronomy · #Magnetic properties of thin films #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.82.195316

published as Phys.Rev.B82:195316,2010 · 11 pages, 1 figure; some corrections and updated/extended references

openalex publication_date 2010/11/15 · arxiv created 2010/11/16 · arxiv updated 2011/04/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We present a microscopic derivation of the generalized Boltzmann and Eilenberger equations in the presence of non-Abelian gauges for the case of a nonrelativistic 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 gives 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.

Citations

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