Theoretical aspects of Andreev spectroscopy and tunneling spectroscopy in non-centrosymmetric superconductors: a topical review

TL;DR

This paper reviews theoretical insights into Andreev and tunneling spectroscopy in non-centrosymmetric superconductors, focusing on surface states, topological edge modes, and the effects of mixed singlet-triplet pairing on conductance signatures.

Contribution

It introduces a theoretical framework for calculating Andreev bound states and explores the topological nature of edge modes influenced by order parameter components.

Findings

Presence of zero bias conductance peaks indicating non-trivial pairing

Existence of helical edge modes when triplet pairing dominates

Quantum phase transition at equal singlet and triplet components

Abstract

Tunneling spectroscopy at surfaces of unconventional superconductors has proven an invaluable tool for obtaining information about the pairing symmetry. It is known that mid gap Andreev bound states manifest itself as a zero bias conductance peak in tunneling spectroscopy. The zero bias conductance peak is a signature for a non-trivial pair potential that exhibits different signs on different regions of the Fermi surface. Here, we review recent theoretical results on the spectrum of Andreev bound states near interfaces and surfaces in non-centrosymmetric superconductors. We introduce a theoretical scheme to calculate the energy spectrum of a non-centrosymmetric superconductor. Then, we discuss the interplay between the spin orbit vector field on the Fermi surface and the order parameter symmetry. The Andreev states carry a spin supercurrent and represent a helical edge mode along the interface. We study the topological nature of the resulting edge currents. If the triplet component of the order parameter dominates, then the helical edge mode exists. If, on the other hand, the singlet component dominates, the helical edge mode is absent. A quantum phase transition occurs for equal spin singlet and triplet order parameter components. We discuss the tunneling conductance and the Andreev point contact conductance between a normal metal and a non-centrosymmetric superconductor.