Finite Length Effects and Coulomb Interaction in Ge Quantum Well-Based Josephson Junctions Probed with Microwave Spectroscopy

Proximitized Ge quantum wells have emerged as a novel platform for studying Andreev bound states (ABSs), due to their expected strong spin-orbit interaction and high mobility. Here, we used microwave spectroscopy techniques to investigate ABSs in Josephson junctions (JJs) realized in proximitized Ge quantum wells. Spectroscopic signatures observed in a 350 nm junction indicated the presence of multiple ABSs, and were reproduced with a model including finite-length effects. The ABS spectra measured for a $1.2~μ$m junction were explained by a model including three ABSs in two conduction channels and finite Coulomb interaction. Our work highlights the importance of interactions in JJs and serves as a basis for understanding and manipulating ABSs in Ge-based hybrid devices.