Proximity effect in normal-superconductor hybrids for quasiparticle traps

Coherent transport of charges in the form of Cooper pairs is the main feature of Josephson junctions which plays a central role in superconducting qubits. However, the presence of quasiparticles in superconducting devices may lead to incoherent charge transfer and limit the coherence time of superconducting qubits. A way around this so-called ''quasiparticle poisoning'' might be using a normal-metal island to trap quasiparticles; this has motivated us to revisit the proximity effect in normal-superconductor hybrids. Using the semiclassical Usadel equations, we study the density of states (DoS) both within and away from the trap. We find that in the superconducting layer the DoS quickly approaches the BCS form; this indicates that normal-metal traps should be effective at localizing quasiparticles.