# Usadel equation in the presence of intrinsic spin-orbit coupling: A unified theory of magnetoelectric effects in normal and superconducting systems

Usadel equation in the presence of intrinsic spin-orbit coupling: A unified theory of... The Usadel equation is the standard theoretical tool for the description of superconducting structures in the diffusive limit. Here, I derive the Usadel equation for gyrotropic materials with a generic linear in momentum spin-orbit coupling. It accounts for the spin-charge/singlet-triplet coupling and in the normal state reduces to the system of spin-charge diffusion equations describing various magnetoelectric effects, such as the spin Hall effect (SHE), the spin-galvanic effect (SGE), and their inverses. Therefore the derived Usadel equation establishes a direct connection of these effects to their superconducting counterparts. The working power of the present formalism is illustrated on the example of the bulk SGE. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

# Usadel equation in the presence of intrinsic spin-orbit coupling: A unified theory of magnetoelectric effects in normal and superconducting systems

, Volume 96 (6) – Aug 2, 2017

## Usadel equation in the presence of intrinsic spin-orbit coupling: A unified theory of magnetoelectric effects in normal and superconducting systems

Abstract

The Usadel equation is the standard theoretical tool for the description of superconducting structures in the diffusive limit. Here, I derive the Usadel equation for gyrotropic materials with a generic linear in momentum spin-orbit coupling. It accounts for the spin-charge/singlet-triplet coupling and in the normal state reduces to the system of spin-charge diffusion equations describing various magnetoelectric effects, such as the spin Hall effect (SHE), the spin-galvanic effect (SGE), and their inverses. Therefore the derived Usadel equation establishes a direct connection of these effects to their superconducting counterparts. The working power of the present formalism is illustrated on the example of the bulk SGE.

Publisher
American Physical Society (APS)
ISSN
1098-0121
eISSN
1550-235X
D.O.I.
10.1103/PhysRevB.96.060502
Publisher site
See Article on Publisher Site

### Abstract

The Usadel equation is the standard theoretical tool for the description of superconducting structures in the diffusive limit. Here, I derive the Usadel equation for gyrotropic materials with a generic linear in momentum spin-orbit coupling. It accounts for the spin-charge/singlet-triplet coupling and in the normal state reduces to the system of spin-charge diffusion equations describing various magnetoelectric effects, such as the spin Hall effect (SHE), the spin-galvanic effect (SGE), and their inverses. Therefore the derived Usadel equation establishes a direct connection of these effects to their superconducting counterparts. The working power of the present formalism is illustrated on the example of the bulk SGE.

### Journal

Physical Review BAmerican Physical Society (APS)

Published: Aug 2, 2017

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