Observation of a subgap density of states in superconductor-normal metal bilayers in the Cooper limit

We present transport and tunneling measurements of Pb-Ag bilayers with thicknesses, $d_{Pb}$ and $d_{Ag}$, that are much less than the superconducting coherence length. The transition temperature, $T_c$, and energy gap, $\Delta$, in the tunneling Density of States (DOS) decrease exponentially with $d_{Ag}$ at fixed $d_{Pb}$. Simultaneously, a DOS that increases linearly from the Fermi energy grows and fills nearly 40% of the gap as $T_c$ is 1/10 of $T_c$ of bulk Pb. This behavior suggests that a growing fraction of quasiparticles decouple from the superconductor as $T_c$ goes to 0. The linear dependence is consistent with the quasiparticles becoming trapped on integrable trajectories in the metal layer.