Crystalline superconductor-semiconductor Josephson junctions for compact superconducting qubits

The narrow bandgap of semiconductors allows for thick, uniform Josephson junction barriers, potentially enabling reproducible, stable, and compact superconducting qubits. We study vertically stacked van der Waals Josephson junctions with semiconducting weak links, whose crystalline structures and clean interfaces offer a promising platform for quantum devices. We observe robust Josephson coupling across 2--12 nm (3--18 atomic layers) of semiconducting WSe$_2$ and, notably, a crossover from proximity- to tunneling-type behavior with increasing weak link thickness. Building on these results, we fabricate a prototype all-crystalline merged-element transmon qubit with transmon frequency and anharmonicity closely matching design parameters. We demonstrate dispersive coupling between this transmon and a microwave resonator, highlighting the potential of crystalline superconductor-semiconductor structures for compact, tailored superconducting quantum devices.