Imaging geometry- and phase-controlled spectra in a surface-state Andreev cavity

Andreev cavities provide a setting in which superconducting proximity spectra are shaped by phase-coherent electron-hole motion along extended trajectories. While such Andreev physics is well established in transport, local spectra in two-dimensional cavities remain largely unexplored in real space. Here we use scanning tunnelling spectroscopy to study confined Cu(111) surface states coupled to superconducting Nb(110). The in-plane magnetic-field scale for the collapse of the resolved low-energy spectrum is controlled by the transverse extent available to Andreev trajectories, while the zero-field excitation energy evolves with the characteristic trajectory length. These trends, together with spatial variations within individual islands and the response to vortex phase textures, are captured by a minimal semiclassical phase-accumulation picture. Our results identify geometry-defined Andreev trajectories as a design principle for phase-coherent superconducting cavities accessible by local spectroscopy.