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.

11 pages, 10 figures

References in corpus (8)

• Topological Crystalline Insulators
• Topological spin-current in non-centrosymmetric superconductors
• Anomalous Andreev bound state in non-centrosymmetric superconductors
• Surface density of states and topological edge states in non-centrosymmetric superconductors
• Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number
• Topologically protected flat zero-energy surface bands in non-centrosymmetric superconductors
• Andreev spectroscopy and surface density of states for a three-dimensional time-reversal invariant topological superconductor
• Dephasing-enabled triplet Andreev conductance

Cited by in corpus (5)

• Topological surface states in nodal superconductors
• Zero-bias conductance peak in detached flakes of superconducting 2H-TaS${}_2$ probed by scanning tunneling spectroscopy
• Helical spin texture of surface states in topological superconductors
• Phase-locked magnetoconductance oscillations as a probe of Majorana edge states
• Helical Majorana surface states of strongly disordered topological superconductors with time-reversal symmetry