Theory of Andreev spectroscopy of strongly correlated unconventional superconductors: applications to moiré graphene

Andreev spectroscopy is a powerful phase-sensitive probe of superconductivity that can reveal the pairing symmetry. Motivated by experiments on strongly correlated superconductors (SCs) like moiré graphene, we go beyond the standard Blonder–Tinkham–Klapwijk (BTK) theory and develop a Green’s-function approach using the Schwinger–Keldysh technique. We derive a general expression for the metal–SC interface conductance, valid to all orders in interfacial coupling, and use it to analyze self-energy effects such as signatures of superconductivity emerging from a pseudo-gapped normal state as well as the influence of Fermi velocity mismatch on interface transparency [1]. For unconventional SCs, we show that one cannot use bulk Green’s functions in this analysis, as they fail to capture Andreev bound states (ABS) at the metal-SC interface. We introduce a general method to construct half-space Green’s functions, providing a systematic framework to analyze Andreev spectra for arbitrary pairing symmetries. Applying this to d-wave SCs, we show that ABS are pinned to zero energy on suitably oriented smooth surfaces. We discuss the topological constraints underlying this result as well as perturbations such as surface roughness or magnetic fields that shift the ABS away from zero energy.

[1] S. Biswas, S. Suman, M. Randeria, R. Sensarma, arXiv:2503.07744, PNAS (to appear).