Reconciling Kubo and Keldysh Approaches to Fermi-Sea-Dependent Nonequilibrium Observables: Application to Spin Hall Current and Spin-Orbit Torque in Spintronics

Simao M. Joao, Marko D. Petrovic, J. M. Viana Parente Lopes +2

Quantum transport studies of spin-dependent phenomena in solids commonly employ the Kubo or Keldysh formulas for the nonequilibrium density operator in the steady-state linear-resp…