Heat transport in nonuniform superconductors

Abstract

We calculate electronic energy transport in inhomogeneous superconductors using a fully self-consistent nonequilibrium quasiclassical Keldysh approach. We develop a general theory and apply it to a superconductor with an order parameter that forms domain walls of the type encountered in the Fulde-Ferrell-Larkin-Ovchinnikov state. The heat transport in the presence of a domain wall is inherently anisotropic and nonlocal. The bound states in the nonuniform region play a crucial role and control heat transport in several ways: (i) they modify the spectrum of quasiparticle states and result in Andreev reflection processes and (ii) they hybridize with the impurity band and produce a local transport environment with properties very different from those in a uniform superconductor. As a result of this interplay, heat transport becomes highly sensitive to temperature, magnetic field, and disorder. For strongly scattering impurities, we find that the transport across domain walls at low temperatures is considerably more efficient than in the uniform superconducting state.