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

Matthias Eschrig, Christian Iniotakis+1 more|arXiv (Cornell University)|Jan 14, 2010

Physics of Superconductivity and MagnetismPhysics and Astronomy2 references161 citations

TL;DR

This paper presents a theoretical framework for understanding Andreev and tunneling spectroscopy in non-centrosymmetric superconductors, focusing on spin-polarized bound states and their topological properties. It shows that triplet-dominated pairing induces helical edge modes carrying spin supercurrents, while equal singlet-triplet components trigger a quantum phase transition, with zero-bias conductance peaks serving as signatures of non-trivial pairing symmetry and spin-orbit coupling effects.

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.

Motivation & Objective

• To develop a theoretical framework for analyzing Andreev spectroscopy in non-centrosymmetric superconductors using quasiclassical Nambu-Gor'kov Green's functions.
• To investigate the interplay between spin-orbit coupling on the Fermi surface and the symmetry of the superconducting order parameter.
• To determine the conditions under which topologically protected helical edge modes—carrying spin supercurrents—emerge at interfaces.
• To analyze the tunneling conductance and point contact spectra, particularly the emergence of zero-bias conductance peaks as signatures of non-trivial pairing.
• To identify the quantum phase transition between topologically distinct superconducting states when singlet and triplet components are balanced.

Proposed method

• Employing the quasiclassical theory of superconductivity with Nambu-Gor'kov Green's functions to model Andreev bound states in non-centrosymmetric systems.
• Using the Bogoliubov wave function approach in the Andreev approximation to derive the energy spectrum of bound states near surfaces and interfaces.
• Applying the Blonder-Tinkham-Klapwijk (BTK) model to calculate tunneling conductance in normal metal-superconductor junctions.
• Introducing a spin-orbit vector field on the Fermi surface and analyzing its impact on the order parameter symmetry and bound state structure.
• Modeling the interface with a thin layer of suppressed order parameter to study its effect on conductance, assuming clean limit and perfect transmission.
• Analyzing different spin-orbit coupling types—Rashba, Dresselhaus, and cubic symmetry—via numerical solutions of coherence amplitudes and conductance spectra.

Experimental results

Research questions

• RQ1 How does spin-orbit coupling in non-centrosymmetric superconductors influence the formation and topology of Andreev bound states?
• RQ2 Under what conditions does a helical edge mode carrying a spin supercurrent emerge at the interface?
• RQ3 What is the role of the relative strength of singlet versus triplet components in the superconducting order parameter in determining the existence of zero-bias conductance peaks?
• RQ4 How does the tunneling conductance spectrum reflect the underlying pairing symmetry and spin-orbit vector structure?
• RQ5 What is the nature of the quantum phase transition when singlet and triplet components of the order parameter are equal?

Key findings

• Helical edge modes carrying spin supercurrents appear only when the triplet component of the order parameter dominates over the singlet component.
• A quantum phase transition occurs at equal singlet and triplet order parameter components, where the zero-energy Andreev bound state disappears and a new topological ground state emerges.
• Zero-bias conductance peaks in tunneling spectroscopy are robust signatures of non-trivial pairing symmetry and are directly linked to the presence of Andreev bound states at the Fermi surface.
• For Rashba spin-orbit coupling, the Andreev conductance shows a pronounced anisotropy and a zero-bias peak enhanced to twice the normal conductance, indicating strong spin-polarization effects.
• In the case of cubic symmetry, the conductance spectrum resembles that of an s-wave singlet superconductor, suggesting a suppression of spin-orbit-induced anisotropy.
• The suppression of the order parameter in a surface layer does not affect zero-bias conductance in the clean limit, as coherence amplitudes remain spatially constant at ε = 0.