Abstract
We consider hybrid systems consisting of a hole-doped semiconductor coupled to electronic states of finite-size superconductors, where the opposite sign of the masses in the two subsystems give rise to insulating gaps at subband anticrossings. Consequently, increasing the coupling strength to the superconductor can paradoxically suppress the proximity-induced superconductivity in the semiconductor by enhancing these insulating gaps. We demonstrate that the presence of such induced insulating gaps leads to a characteristic anomalous behavior of the critical supercurrent in Josephson junctions based on these hybrid structures. Our findings provide important insights for the design of robust quantum computing platforms utilizing hybrid superconductor-hole systems.