Odd-parity pairing correlations in a d-wave superconductor

Abstract

We theoretically study the effects of spin-orbit interactions on the symmetry of a Cooper pair in a spin-singlet d-wave superconductor and on the chiral property of the surface Andreev bound states at zero energy. The pairing symmetry is analyzed by using the anomalous Green's function, which is obtained by solving the Gor'kov equation analytically. The chiral property of surface bound states is discussed by using an index that represents a number of zero-energy states in the presence of potential disorder at a surface. A spin-orbit interaction induces a spatially uniform spin-triplet p-wave pairing correlation in a superconductor and an odd-frequency spin-triplet s-wave pairing correlation at a surface. The spin-orbit interaction splits the Fermi surface into two depending on the spin configuration. As a result of splitting, the index can be a nontrivial nonzero value. On the basis of the close relationship among the odd-frequency s-wave pairing correlation at a surface, the nonzero index of surface bound states, and the anomalous proximity effect, we provide a design of a superconductor that causes the strong anomalous proximity effect.

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