Theory of superconducting proximity effect in hole-based Ge hybrid semiconductor-superconductor devices

Hybrid superconductor-semiconductor systems have received great attention in the last few years due to their potential for the development of hybrid qubits and topological devices. By putting semiconductor devices in contact with superconductors, superconducting correlations are induced in the electrons of the semiconductor device. Furthermore, by a competing effect between magnetic and spin-orbit terms, it is possible to induce unconventional types of superconductivity in the semiconductor device.



Recently, the induction of superconductivity in hole-based Ge devices has been achieved experimentally. In contrast with electrons in group IV semiconductors, hole spins exhibit a more complex, strong spin-orbit interaction with largely anisotropic responses to electric and magnetic fields. Hence, it is of great importance to understand the interplay between the induced superconducting correlations and the anisotropic behavior of Ge holes. In this work, we analyze the different types of superconducting correlations that are induced in Ge hole spins considering the different contributions from all the bands. We develop an effective theory that allows us to identify the different superconducting terms and their dependence on electric and magnetic fields. This work opens new avenues in the development of hybrid devices and topological quantum computation.