Enhanced quasiparticle lifetime in a superconductor by selective blocking of recombination phonons with a phononic crystal

Abstract

When quasiparticles in a BCS superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at 2$\Delta$. We show that a phonon bandgap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon bandgap can be realized and matched to the recombination energy with a phononic crystal, a periodically-patterned dielectric membrane. We discuss in detail the non-equilibrium quasiparticle and phonon distributions that arise in a superconductor due to a phonon bandgap and a pair-breaking photon signal. Although intrinsically a non-equilibrium effect, the lifetime enhancement in the small-signal regime is remarkably similar to an estimate from an equilibrium formulation. The equilibrium estimate closely follows $\exp ({\Omega }_{bg}/k_B{T}_b)$, where ${\Omega }_{bg}$ is the phonon bandgap energy bandwidth above 2$\Delta$, and $T_b$ is the phonon bath temperature of the coupled electron-phonon system. We discuss the impact of a phononic bandgap on the performance of superconducting devices, and propose a superconducting microwave resonator circuit to measure the enhancement in the quasiparticle lifetime.

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• A Composite Phononic Crystal Design for Quasiparticle Lifetime Enhancement in Kinetic Inductance Detectors
• Properties of Shape-Engineered Phoxonic Crystals: Brillouin-Mandelstam Spectroscopy and Ellipsometry Study
• Strong Reduction of Quasiparticle Fluctuations in a Superconductor due to Decoupling of the Quasiparticle Number and Lifetime