Scattering theory of topological invariants in nodal superconductors

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.