Kinetic impedance and depairing in thin and narrow superconducting films

Abstract

We use both Eilenberger-Usadel and Ginzburg-Landau (GL) theory to calculate the superfluid's 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 fluid's 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.Comment: 17 pages, 14 figures, many changes made following referee suggestions, new material added regarding normal-fluid dissipatio

Single-photon imager based on a superconducting nanowire delay line

“…1b and Cm are the inductance and capacitance per unit length) 23 . In the SNSPI, as the thickness of superconducting nanowire is much less than the London penetration depth, the kinetic inductance of the nanowire is higher than the geometric inductance by about two orders of magnitude (see Methods for the calculation of kinetic inductance and geometric inductance) 21,26 .…”

Nonlinear high-temperature superconducting terahertz metamaterials

“…This has been extensively studied in static fields as the nonlinear Meissner effect (NLME) and at microwave frequencies where it results in intermodulation effects. Much of the theoretical work considering the ac nonlinearity assume a small perturbing ac field probing a nonlinearity due to a high dc bias [12, 19, 21-26, 28, 32, 37, 39], which may not describe the present experiment where only a strong ac field is applied [24,39]. There are two directions from which a more detailed picture of the mechanism responsible the depairing current (or NLME) is generally arrived at.…”

“…In a d-wave superconductor, the vanishing superconducting gap at the nodes both dramatically increases the magnitude of this effect, allows it to persist down to T = 0 K, and introduces a dependence on the inplane field orientation [12,19,[23][24][25]. However, it is important to keep in mind that because these theories may be inadequate to describe THz nonlinearities because they are derived in the quasistatic limit and therefore neglect mechanisms that only occur at high frequencies [24,39]. For example, for fast pulses comparable to the order parameter relaxation time, order parameter relaxation has been predicted to give rise to an additional dissipative term, kinetic resistance, separate from that due to the normal carriers [39].…”

“…Studying both types of superconductors is critical for developing a fundamental understanding of the THz field induced nonlinear effects because the presence of nodes in the superconducting gap can dramatically alter the behaviour [25,27,[35][36][37][38] while observation of similar effects in both types of superconductors points towards a physical mechanism that does not require the presence of nodes. Further, the relaxation times are expected to be significantly different in these materials [26], which may have a significant effect for measurements on the ps timescale [39]. Here we exploit these recent advances in generating high intensity THz fields to study the intrinsic nonlinear response of metamaterials made out of YBCO.…”

Resistive state triggered by vortex entry in YBa 2 Cu 3 O 7−δ nanostructures

“…For the temperature dependence of the London penetration depth in the full temperature range we have used the two fluid model k L ðTÞ ¼ 20]. An approximate expression for the temperature dependence of the coherence length can be obtained from the formula of the Ginzburg Landau depairing current density [21] J…”