Andreev reflection spectroscopy in strongly paired superconductors

Motivated by recent experiments on low-carrier-density superconductors, including twisted multilayer graphene, we study signatures of the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) evolution in Andreev reflection spectroscopy. We establish that in a standard quantum point contact geometry, Andreev reflection in a BEC superconductor is unable to mediate a zero-bias conductance beyond e^2/h per lead channel. This bound is shown to result from a duality that links the sub-gap conductance of BCS and BEC superconductors. We then demonstrate that sharp signatures of BEC superconductivity, including perfect Andreev reflection, can be recovered by tunneling through a suitably designed potential well. We propose various tunneling spectroscopy setups to experimentally probe this recovery.