Envelope function approach to superconducting proximity effect in Ge-superconductor heterostructures

The appropriate theoretical model for coupling a Ge quantum well to a superconductor is not obvious due to the presence of multiple bands near the valence-band edge of Ge. Here, we address this question by considering the superconductor as a free-electron gas with uniform s-wave superconductivity and modeling the Ge within an empirical pseudopotential framework. By analyzing the model using an envelope function approach and group theory principles, we show that the heavy-hole and light-hole states of Ge have essentially independent induced superconducting gaps, where the light-hole gap is roughly twice as large as the heavy-hole gap.