Abstract
We consider a general problem of a Josephson contact between two multiband superconductors with coexisting superconducting and magnetic phases. As a particular example, we use the quasiclassical theory of superconductivity to study the properties of a Josephson contact between two disordered $s^{\pm}$-wave superconductors allowing for the coexistence between superconductivity and spin-density-wave orders. The intra- and inter-band scattering effects of disorder are treated within the self-consistent Born approximation. We calculate the spatial profile of the corresponding order parameters on both sides of the interface assuming that the interface has finite reflection coefficient and use our results to evaluate the local density of states at the interface as well as critical supercurrent through the junction as a function of phase or applied voltage. Our methods are particularly well suited for describing spatially inhomogeneous states of iron-based superconductors where controlled structural disorder can be created by an electron irradiation. We reveal the connection between our theory and the circuit-theory of Andreev reflection and extend it to superconducting junctions of arbitrary nature. Lastly, we outline directions for further developments in the context of proximity circuits of correlated electron systems.
Highlights
In many practical cases, superconductivity occurs in the form of a spatially inhomogeneous state [1,2]
We present the results of our analysis of the quasiclassical equations and use these results to compute the observables: local density of states and critical current
By solving the corresponding quasiclassical equations for the Eilenberger functions, we have found the variation of the superconducting and magnetic order parameters across the interface with arbitrary transparency
Summary
Superconductivity occurs in the form of a spatially inhomogeneous state [1,2]. Josephson junction is the example of the other kind, where inhomogeneity is created near the contact area when two superconductors are brought into proximity via a tunnel barrier or other type of the weak link [4,5] In both of these cases, and many other physical situations, the spatial inhomogeneity extends over the length scale of superconducting coherence length that is large as compared to electron Fermi wavelength. Under this condition, the semiclassical theory of superconductivity based on Eilenberger [6] and Usadel [7] equations become applicable. In Appendixes A, B, and C, we provide the details on the derivations of the expressions that we used to obtain the solution of the Eilenberger equations
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