Generation of odd-frequency surface superconductivity with spontaneous spin current due to the zero-energy Andreev bound state

TL;DR

This paper predicts the emergence of odd-frequency surface superconductivity with a spontaneous spin current at the edge of d-wave superconductors, driven by surface spin fluctuations and zero-energy Andreev bound states, and validates the Hermite odd-frequency gap concept.

Contribution

It introduces a mechanism for odd-frequency s-wave superconductivity at superconductor edges, linking it to surface states and spin currents, and confirms the Hermite odd-frequency gap function.

Findings

Odd-frequency s-wave gap emerges at superconductor edges.

Surface spin fluctuation pairing induces spin currents.

Edge s-wave gap can be detected via proximity effect.

Abstract

We propose that the odd-frequency $s$ wave ($s^{\rm{odd}}$ wave) superconducting gap function, which is usually unstable in the bulk, naturally emerges at the edge of $d$ wave superconductors. This prediction is based on the surface spin fluctuation pairing mechanism owing to the zero-energy surface Andreev bound state. The interference between bulk and edge gap functions triggers the $d+s^{\rm{odd}}$ state, and the generated spin current is a useful signal uncovering the ``hidden'' odd-frequency gap. In addition, the edge $s^{\rm{odd}}$ gap can be determined via the proximity effect on the diffusive normal metal. Furthermore, this study provides a decisive validation of the ``Hermite odd-frequency gap function,'' which has been an open fundamental challenge to this field.