2026/07/23 by Ivan M. Artemov, Mikhail A. Skvortsov
Physics and Astronomy · #cond-mat.supr-con
10 pages, 3 figures
arxiv created 2026/07/29 · arxiv updated 2026/07/30
We develop a theory of thermal phase slips in disordered superconducting films biased near the critical current Ic(T). Generalizing recent results obtained close to Tc, we show that the optimal fluctuation governing the phase-slip barrier in two dimensions satisfies the exactly integrable Boussinesq equation for arbitrary temperatures T<Tc. Since both the transverse and longitudinal sizes of the optimal nucleus diverge as I→ Ic(T), the Usadel equation for quasiparticles in the presence of a slowly varying order parameter can be solved perturbatively using a gradient expansion. The resulting field theory for a complex order parameter is further reduced to the Boussinesq free energy for a single real field, with the coefficients expressed as Matsubara sums over the solutions of the uniform Usadel equation at Ic(T). The activation barrier near Ic has the asymptotic form ΔF(T,I→ Ic) = E(T) (1-I/Ic)α. We calculate E(T) over the full temperature range for both two-dimensional films (α=3/4) and one-dimensional wires (α=5/4). For films, the theory is valid within a narrow 10% window below Ic(T), where the saddle-point configuration remains vortex-free. For wires, ΔF(T,I→ Ic) provides a good approximation to the activation barrier for all temperatures and currents.