Scattering theory of topological invariants in nodal superconductors

TL;DR

This paper introduces a new way to determine topological invariants in nodal superconductors using Andreev reflection matrices, linking them to measurable conductance even at boundaries where states merge with the continuum.

Contribution

It provides an alternative formulation of topological invariants based on the Andreev reflection matrix, applicable across various symmetry classes and boundary conditions.

Findings

Derived conditions for conductance quantization in different symmetry classes.

Linked topological invariants to angle-resolved Andreev conductance.

Validated the approach on models with spin-singlet and triplet pairing with spin-orbit interaction.

Abstract

Time-reversal invariant superconductors having nodes of vanishing excitation gap support zero-energy boundary states with topological protection. Existing expressions for the topological invariant are given in terms of the Hamiltonian of an infinite system. We give an alternative formulation in terms of the Andreev reflection matrix of a normal-metal-superconductor interface. This allows to relate the topological invariant to the angle-resolved Andreev conductance, also when the boundary state in the superconductor has merged with the continuum of states in the normal metal. A variety of symmetry classes is obtained, depending on additional unitary symmetries of the reflection matrix. We derive conditions for the quantization of the conductance in each symmetry class and test these on a model for a 2D or 3D superconductor with spin-singlet and spin-triplet pairing, mixed by Rashba spin-orbit interaction.