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Register a new userNonequilibrium superconducting thin films with sub-gap and pair-breaking photon illumination
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We calculate nonequilibrium quasiparticle and phonon distributions for a number of widely-used low transition temperature thin-film superconductors under constant, uniform illumination by sub-gap probe and pair-breaking signal photons simultaneously. From these distributions we calculate material-characteristic parameters that allow rapid evaluation of an effective quasiparticle temperature using a simple analytical expression, for all materials studied (Mo, Al, Ta, Nb, and NbN) for all photon energies. We also explore the temperature and energy-dependence of the low-energy quasiparticle generation efficiency $eta$ by pair-breaking signal photons finding $eta approx 0.6$ in the limit of thick films at low bath temperatures that is material-independent. Taking the energy distribution of excess quasiparticles into account, we find $eta to 1$ as the bath temperature approaches the transition temperature in agreement with the assumption of the two-temperature model of the nonequilibrium response that is appropriate in that regime. The behaviour of $eta$ with signal frequency scaled by the superconducting energy gap is also shown to be material-independent, and is in qualitative agreement with recent experimental results. An enhancement of $eta$ in the presence of sub-gap (probe) photons is shown to be most significant at signal frequencies near the superconducting gap frequency and arises due to multiple photon absorption events that increase the average energy of excess quasiparticles above that in the absence of the probe.
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Understanding the detailed behaviour of superconducting pair breaking photon detectors such as Kinetic Inductance Detectors requires knowledge of the nonequilibrium quasiparticle energy distributions. We have previously calculated the steady state distributions resulting from uniform absorption of monochromatic sub gap and above gap frequency radiation by thin films. In this work, we use the same methods to calculate the effect of illumination by broadband sources, such as thermal radiation from astrophysical phenomena or from the readout system. Absorption of photons at multiple above gap frequencies is shown to not change the structure of the quasiparticle energy distribution close to the superconducting gap. Hence for typical absorbed powers, we find the effects of absorption of broadband pair breaking radiation can simply be considered as the sum of the effects of absorption of many monochromatic sources. Distribution averaged quantities, like quasiparticle generation effciency $eta$, match exactly a weighted average over the bandwidth of the source of calculations assuming a monochromatic source. For sub gap frequencies, however, distributing the absorbed power across multiple frequencies does change the low energy quasiparticle distribution. For moderate and high absorbed powers, this results in a significantly larger $eta$ - a higher number of excess quasiparticles for a broadband source compared to a monochromatic source of equal total absorbed power. Typically in KIDs the microwave power absorbed has a very narrow bandwidth, but in devices with broad resonance characteristics (low quality factors), this increase in $eta$ may be measurable.
We have fabricated planar amorphous Indium Oxide superconducting resonators ($T_csim2.8$ K) that are sensitive to frequency-selective radiation in the range of 7 to 10 GHz. Those values lay far below twice the superconducting gap that worths about 200 GHz. The photons detection consists in a shift of the fundamental resonance frequency. We show that the detected frequency can be adjusted by modulating the total length of the superconducting resonator. We attribute those observations to the excitation of higher-order resonance modes. The coupling between the fundamental lumped and the higher order distributed resonance is due to the kinetic inductance non-linearity with current. These devices, that we have called Sub-gap Kinetic Inductance Detectors (SKIDs), are to be distinguished from the standard Kinetic Inductance Detectors (KIDs) in which quasi-particles are generated when incident light breaks down Cooper pairs.
We analyze the influence of the surface passivation produced by oxides on the superconducting properties of $gamma$-Mo$_2$N ultra-thin films. The superconducting critical temperature of thin films grown directly on Si (100) with those using a buffer and a capping layer of AlN are compared. The results show that the cover layer avoids the presence of surface oxides, maximizing the superconducting critical temperature for films with thicknesses of a few nanometers. We characterize the flux-flow instability measuring current-voltage curves in a 6.4 nm thick Mo$_2$N film with a superconducting critical temperature of 6.4 K. The data is analyzed using the Larkin and Ovchinnikov model. Considering self-heating effects due to finite heat removal from the substrate, we determine a fast quasiparticle relaxation time $approx$ 45 ps. This value is promising for its applications in single-photon detectors.
Thin-film superconductors with thickness 30 to 500 nm are used as non-equilibrium quantum detectors for photons, phonons or more exotic particles. One of the most basic questions in determining their limiting sensitivity is the efficiency with which the quanta of interest couple to the detected quasiparticles. As low temperature superconducting resonators, thin-films are attractive candidates for producing quantum-sensitive arrayable sensors and the readout uses an additional microwave probe. We have calculated the quasiparticle generation efficiency eta_s for low energy photons in a representative, clean thin-film superconductor (Al) operating well-below its superconductingtransition temperature as a function of film thickness, within the framework of the coupled kineticequations described by Chang and Scalapino.[J. J. Chang and D. J. Scalapino, J. Low Temp. Phys. 31, 1 (1978)]. We have also included the effect of a lower frequency probe. We show that phonon loss from the thin-film reduces eta_s by as much as 40% compared to earlier models that considered relatively thick films or infinite volumes. We also show that the presence of the probe and signal enhances the generation efficiency slightly. We conclude that the ultimate limiting noise equivalent power of this class of detector is determined by the thin-film geometry.
We use both Eilenberger-Usadel and Ginzburg-Landau (GL) theory to calculate the superfluids temperature-dependent kinetic inductance for all currents up to the depairing current in thin and narrow superconducting films. The calculations apply to BCS weak-coupling superconductors with isotropic gaps and transport mean-free paths much less than the BCS coherence length. The kinetic inductance is calculated for the response to a small alternating current when the film is carrying a dc bias current. In the slow-experiment/fast-relaxation limit, in which the superconducting order parameter quasistatically follows the time-dependent current, the kinetic inductance diverges as the bias current approaches the depairing value. However, in the fast-experiment/slow-relaxiation limit, in which the the superconducting order parameter remains fixed at a value corresponding to the dc bias current, the kinetic inductance rises to a finite value at the depairing current. We then use time-dependent GL theory to calculate the kinetic impedance of the superfluid, which includes not only the kinetic reactance but also the kinetic resistance of the superfluid arising from dissipation due to order-parameter relaxation. The kinetic resistance is largest for angular frequencies $omega$ obeying $omega tau_s > 1$, where $tau_s$ is the order-parameter relaxation time, and for bias currents close to the depairing current. We also include the normal fluids contribution to dissipation in deriving an expression for the total kinetic impedance. The Appendices contain many details about the temperature-dependent behavior of superconductors carrying current up to the depairing value.
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