From charge to spin: Analogies and differences in quantum transport coefficients
Abstract
We review some recent results from the mathematical theory of transport of charge and spin in gapped crystalline quantum systems. The emphasis will be on transport coefficients, such as conductivities and conductances. As for the former, those are computed as appropriate expectations of current operators in a nonequilibrium almoststationary state (NEASS), which arises from the perturbation of an equilibrium state by an external electric field. While for charge transport the usual doublecommutator Kubo formula is recovered (also beyond linear response), we obtain formulas for appropriately defined spin conductivities, which are still explicit but more involved. Certain "Kubolike" terms in these formulas are also shown to agree with the corresponding contributions to the spin conductance. In addition to that, we employ similar techniques to show a new result, namely that even in systems with nonconserved spin, there is no generation of spin torque, that is, the spin torque operator has an expectation in the NEASS which vanishes faster than any power of the intensity of the perturbing field.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 July 2022
 DOI:
 10.1063/5.0089786
 arXiv:
 arXiv:2203.08044
 Bibcode:
 2022JMP....63g2102M
 Keywords:

 Mathematical Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 8106;
 81Q15;
 81V70
 EPrint:
 12 pages