Andreev versus Tunneling Spectroscopy of Unconventional Flat Band Superconductors

STM experiments in the tunneling and Andreev regimes on graphene-based moire superconductors (SC) show two distinct energy scales whose origin is mysterious. We express the conductance of a normal-SC interface in terms of Green's functions, which allows us to sharpen the issues in two ways. First, we show that the two distinct energy scales cannot be understood in terms of a pseudogap in tunneling and a superconducting gap in the Andreev spectra. Second, the large Fermi velocity vF mismatch between the STM tip and the at band SC renormalizes a transparent interface towards the tunneling regime, and the ballistic Andreev regime cannot be realized in moire SCs. We also discuss self energy corrections to vF that determines the conductance. Finally, we offer a resolution to these problems by modeling the Andreev experiment as a circular metallic disc embedded in an unconventional SC. We show that with strong vF mismatch the low bias conductance is dominated by Andreev bound states induced by the tip at the interface with the unconventional SC. The ABS give rise to the low energy scale seen in Andreev experiments, smaller than the SC gap in tunneling spectroscopy.