Thermal phase slips in superconducting films

Abstract

A dissipationless supercurrent state in superconductors can be destroyed by thermal fluctuations. Thermally activated phase slips provide a finite resistance of the sample and are responsible for dark counts in superconducting single-photon detectors. The activation barrier for a phase slip is determined by a space-dependent saddle-point (instanton) configuration of the order parameter. In the one-dimensional wire geometry, such a saddle point has been analytically obtained by Langer and Ambegaokar in the vicinity of the critical temperature Tc and for arbitrary bias currents below the critical current Ic. In the two-dimensional geometry of a superconducting strip, which is relevant for photon detection, the situation is much more complicated. Depending on the ratio I/Ic, several types of saddle-point configurations have been proposed, with their energies being obtained numerically. We demonstrate that the saddle-point configuration for an infinite superconducting film at I→Ic is described by the exactly integrable Boussinesq equation solved by Hirota's method. The instanton size is Lx∼ξ(1−I/Ic)−1/4 along the current and Ly∼ξ(1−I/Ic)−1/2 perpendicular to the current, where ξ is the Ginzburg-Landau coherence length. The activation energy for thermal phase slips scales as ΔF2D∝(1−I/Ic)3/4. For sufficiently wide strips of width w≫Ly, a half instanton is formed near the boundary, with the activation energy being 1/2 of ΔF2D.

Source-reported materials — not catalogue approval

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