Topological superconductivity and Majorana fermions in hybrid structures involving cuprate high-T_c superconductors

TL;DR

This paper explores how topological superconductivity and Majorana fermions can be induced in heterostructures involving cuprate high-T_c superconductors, revealing different induced pairing symmetries depending on the interface orientation and nanowire alignment.

Contribution

It provides a detailed theoretical analysis of induced triplet superconductivity and Majorana fermions in heterostructures with cuprate superconductors, considering various interface orientations and nanowire configurations.

Findings

Triplet p-wave superconductivity is induced on (100) facets.

Induced gap on (110) facets has even orbital symmetry and odd energy dependence.

Majorana fermions are predicted at the ends of appropriately oriented nanowires.

Abstract

The possibility of inducing topological superconductivity with cuprate high-temperature superconductors (HTSC) is studied for various heterostructures. We first consider a ballistic planar junction between a HTSC and a metallic ferromagnet. We assume that inversion symmetry breaking at the tunnel barrier gives rise to Rashba spin-orbit coupling in the barrier and allows equal-spin triplet superconductivity to exist in the ferromagnet. Bogoliubov-de Gennes equations are obtained by explicitly modeling the barrier, and taking account of the transport anisotropy in the HTSC. By making use of the self-consistent boundary conditions and solutions for the barrier and HTSC regions, an effective equation of motion for the ferromagnet is obtained where Andreev scattering at the barrier is incorporated as a boundary condition for the ferromagnetic region. For a ferromagnet layer deposited on a (100) facet of the HTSC, triplet p-wave superconductivity is induced. For the layer deposited on a (110) facet, the induced gap does not have the p-wave orbital character, but has an even orbital symmetry and an odd dependence on energy. For the layer on the (001) facet, an exotic f-wave superconductivity is induced. We also consider the induced triplet gap in a one-dimensional half-metallic nanowire deposited on a (001) facet of a HTSC. We find that for a wire axis along the a-axis, a robust triplet p-wave gap is induced. For a wire oriented 45 degrees away from the a-axis the induced triplet p-wave gap vanishes. For the appropriately oriented wire, the induced p-wave gap should give rise to Majorana fermions at the ends of the half-metallic wire. Based on our result, topological superconductivity in a semi-conductor nanowire may also be possible given that it is oriented along the a-axis of the HTSC.