Andreev versus tunneling spectroscopy of unconventional flat-band superconductors

Andreev spectroscopy is one of the few phase-sensitive experiments done on moiré graphene superconductors (SC) that can shed light on the pairing symmetry. Its interpretation however is unclear, as Scanning tunneling microscopy (STM) experiments in the Andreev and tunneling regimes show two distinct energy scales whose origin is mysterious. We show using a Green’s function formulation that the two energy scales cannot be understood as a SC gap in the Andreev spectra and a pseudogap in tunneling. We also show that the ballistic Andreev regime can never be realized in moire SCs as the large mismatch in the Fermi velocity v F of the flat-band SC and the STM tip renormalizes a transparent interface toward the tunneling regime. We discuss 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. With strong v F mismatch the low bias conductance is dominated by tip-induced Andreev bound states, responsible for the low energy scale distinct from the SC gap seen in tunneling.