Onsager Relations in Coupled Electric, Thermoelectric and Spin Transport: The Ten-Fold Way

Abstract

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 a complete list of the Onsager reciprocity relations between transport coefficients for coupled electric, spin, thermoelectric and spin caloritronic effects. We apply these to all ten symmetry classes, paying special attention to specific additional relations that follow from the combination of symmetries, beyond microreversibility. We discuss these relations in several illustrative situations. We show the reciprocity between spin-Hall and inverse spin-Hall effects, and the reciprocity between spin-injection and magnetoelectric spin currents. We discuss the symmetry and reciprocity relations of Seebeck, Peltier, spin-Seebeck and spin-Peltier effects in systems with and without coupling to superconductors.

14 pages (4 figures) - typos corrected in v2

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• Classification of topological insulators and superconductors in three spatial dimensions
• Direct electronic measurement of the spin Hall effect
• Thermo-spin effects in a quantum dot connected to ferromagnetic leads
• Electron Transport Driven by Nonequilibrium Magnetic Textures
• Mesoscopic Spin Hall Effect in Multiprobe Ballistic Spin-Orbit Coupled Semiconductor Bridges
• Spin Pumping of Current in Non-Uniform Conducting Magnets
• Mesoscopic Spin Hall Effect
• Detection of current-induced spins by ferromagnetic contacts
• Intrinsic Coupling between Current and Domain Wall Motion in (Ga,Mn)As
• Quantitative measurements of the thermal resistance of Andreev interferometers
• Thermopower oscillations in mesoscopic Andreev interferometers

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