Andreev versus tunneling spectroscopy in unconventional flat band superconductors; a theoretical perspective

Andreev spectroscopy is a phase-sensitive experiment that can shed light on the pairing symmetry of superconductors (SCs). Its interpretation in moiré graphene SCs is, however, unclear as STM experiments in the Andreev and tunneling regimes show two very different energy scales whose origin is mysterious. We develop a Green’s function formulation that allows us to include self-energy effects and go beyond the standard Blonder-Tinkham-Klapwijk framework. We first show that the two energy scales cannot be understood as a SC gap in the Andreev spectra and a pseudogap in tunneling. We next show that the high transparency Andreev regime cannot be realized in moiré materials, as the large Fermi velocity (v_F) mismatch between the flat band SC and the STM tip renormalizes a transparent interface to the tunneling regime. We discuss the self-energy corrections to v_F that determines the conductance. Finally, we model the Andreev experiment as a circular metallic disc embedded in an unconventional SC and show that it leads to tip-induced Andreev bound states (ABS). In the regime of strong v_F mismatch, tunneling into the ABS gives rise to the observed low-energy sub-gap scale in the conductance. Such a low-energy scale would not exist in an s-wave SC, and thus the observed Andreev spectrum gives strong evidence for an unconventional sign-changing order parameter.