Subgap transport in superconductor-semiconductor hybrid islands: Weak and strong coupling regimes

Superconductor-semiconductor hybrid systems play a crucial role in realizing nanoscale quantum devices, including hybrid qubits, Majorana bound states, and Kitaev chains. For such hybrid devices, subgap states play a prominent role in their operation. In this paper, we study these subgap states via Coulomb and tunneling spectroscopy through a superconducting island defined in a semiconductor nanowire fully coated by a superconductor. We systematically explore regimes ranging from an almost decoupled island to the open configuration. In the weak-coupling regime, the experimental observations are very similar in the absence of a magnetic field and when one flux quantum pierces the superconducting shell. Conversely, in the strong-coupling regime, significant distinctions emerge between the two cases. We attribute this distinct behavior to the existence of subgap states at one flux quantum, which become observable only for sufficiently strong coupling to the leads. We support our interpretation using a simple model to describe transport through the island. Our study highlights the importance of studying a broad range of tunnel couplings for understanding the rich physics of hybrid devices.