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Onsager relations in coupled electric, thermoelectric, and spin transport: The tenfold way

Onsager relations in coupled electric, thermoelectric, and spin transport: The tenfold way

Hamiltonian systems can be classified into ten classes, in terms of the presence or absence of time-reversal symmetry, particle-hole symmetry and sublattice/chiral symmetry. We construct a quantum coherent scattering theory of linear transport for coupled electric, heat and spin transport; including the effect of Andreev reflection from superconductors. We derive …