Abstract
We present a theoretical study of diffusive superconducting systems with extrinsic spin-orbit coupling and arbitrarily strong impurity potential. We derive from a microscopic Hamiltonian a diffusion equation for the quasi-classical Green function, and demonstrate that all mechanisms related to the spin-orbit coupling are expressed in terms of three kinetic coefficients: the spin Hall angle, the spin current swapping coefficient, and the spin relaxation rate due to Elliott-Yafet mechanism. The derived diffusion equation contains a hitherto unknown term describing a spin-orbit torque that appears exclusively in the superconducting state. As an example, we provide a qualitative description of a magnetic vortex in a superconductor with triplet correlations, and show that the novel term describes a spin torque proportional to the vector product between the spectral angular momentum of the condensate and the triplet vector. Our equation opens up the possibility to explore spintronic effects in superconductors with no counterparts in the normal metallic state.
Highlights
Exotic phenomena can occur when two or more materials with different properties are merged into a single hybrid structure
We derive from a microscopic Hamiltonian a diffusion equation for the quasi-classical Green function, and demonstrate that all mechanisms related to the spin-orbit coupling are expressed in terms of three kinetic coefficients: the spin Hall angle, the spin current swapping coefficient, and the spin relaxation rate due to Elliott-Yafet mechanism
Note the extrinsic spin-orbit coupling (SOC) that leads to Mott scattering starts at power λ2pF2, this is different from a uniform SOC in electron gas where impurities
Summary
Exotic phenomena can occur when two or more materials with different properties are merged into a single hybrid structure. The quasiclassical kinetic equation provides a unified description of realistic hybrid structures, including disorder, interfaces, and out-of-equilibrium situations. This approach becomes particular relevant when the hybrid structure is in the diffusive limit. The Usadel equation has been extended to discuss spin-relaxation induced by spin-orbit coupling (SOC) and/or a magnetic exchange field. Besides spin-relaxation [17], SOC can lead to fascinating spin-charge coupling phenomena that have spurred intensive research activities in the field of spintronics. Notable spincharge coupling phenomena like the anomalous Hall effect [18], the spin Hall effect [19] (SHE), and the spin-galvanic effect [20,21,22,23] have been discussed extensively in metallic systems
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