2024/08/29 by S. M. João, Joao, Simao M., Marko D. Petrović +7 · 2 citations
Materials Science · Physics and Astronomy · #Applied Physics (physics.app-ph) #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Magnetic and transport properties of perovskites and related materials #Magnetic properties of thin films #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum and electron transport phenomena
paper · doi:10.48550/arxiv.2408.16611
openalex publication_date 2024/08/29 · openalex created_date 2024/09/22 · openalex updated_date 2026/07/28
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-response regime. Its trace with operators of interest, such as the spin density, spin current density, etc., gives expectation values of experimentally accessible observables. For local quantities, these formulas require summing over the manifolds of \em both Fermi-surface and Fermi-sea states. However, debates have been raging in the literature about the vastly different physics the two formulations can apparently produce, even when applied to the same system. Here, we revisit this problem using infinite-size graphene with proximity-induced spin-orbit and magnetic exchange effects as a testbed. By splitting this system into semi-infinite leads and central active region, in the spirit of Landauer formulation of quantum transport, we prove the \em numerically exact equivalence of the Kubo and Keldysh approaches via the computation of spin Hall current density and spin-orbit torque in both clean and disordered limits. The key to reconciling the two approaches are the numerical frameworks we develop for: (\em i) evaluation of Kubo(-Bastin) formula for a system attached to semi-infinite leads, which ensures continuous energy spectrum and evades the need for commonly used phenomenological broadening introducing ambiguity; and (\em ii) proper evaluation of Fermi-sea term in the Keldysh approach, which \em must include the voltage drop across the central active region even if it is disorder free.