Orbital Response of Evanescent Cooper Pairs in Paramagnetically Limited Al Films

We report a detailed study of the pairing resonance via tunneling density of states in ultra-thin superconducting Al films in supercritical magnetic fields. Particular emphasis is placed on effects of the perpendicular component of the magnetic field on the resonance energy and magnitude. Though the resonance is broadened and attenuated by $H_\bot$ as expected, its energy is shifted upward linearly with $H_\bot$. Extension of the original theory of the resonance to include strong perpendicular fields shows that at sufficiently large $H_\bot$ the overlap of the broadened resonance tail with the underlying degenerate Fermi sea alters the spectral distribution of the resonance via the exclusion principle. This leads to the shift of the the resonance feature to higher energy.