Artem V. Polkin | Searcharxiv

arXiv2026

Optical conductivity of a dirty current-carrying superconductor

We develop a full microscopic theory for the optical conductivity, $σ(ω)$, of a dirty current-carrying superconductor. Within the Keldysh sigma model formalism, we obtain the general analytical expression for $σ(ω)$, applicable for arbitrary frequency $ω$, temperature $T$, and dc supercurrent $I$. In addition to altering the usual Mattis-Bardeen conductivity, $σ_1(ω)$, a finite supercurrent introduces two new contributions: $σ_2^\text{qp}(ω)$ from quasiparticle redistribution and $σ_2^\text{SH}(ω)$ from the amplitude (Schmid-Higgs) mode excitation by the ac field. We investigate, both analytically and numerically, the main features of the optical conductivity in the presence of a dc supercurrent. They include a peak in $\text{Re}\,σ(ω)$ above the optical gap and a sign change of $\text{Im}\,σ(ω)$, with both effects becoming more pronounced at higher $I$ and lower $T$. We also elucidate the role of inelastic relaxation, which governs the low-frequency response, leading to a giant microwave absorption and a suppression of the apparent superfluid density at the critical current. The optical conductivity measurement of a superconductor biased by a finite dc supercurrent enables the direct observation of the Schmid-Higgs mode via transport measurements.

cond-mat.supr-con↗

arXiv2026

Thermal phase slips in superconducting films

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, $T_c$, and for arbitrary bias currents below the critical current $I_c$. 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 $I/I_c$, 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 $I\to I_c$ is described by the exactly integrable Boussinesq equation solved by Hirota's method. The instanton size is $L_x\simξ(1-I/I_c)^{-1/4}$ along the current and $L_y\simξ(1-I/I_c)^{-1/2}$ perpendicular to the current, where $ξ$ is the Ginzburg-Landau coherence length. The activation energy for thermal phase slips scales as $ΔF^\text{2D}\propto (1-I/I_c)^{3/4}$. For sufficiently wide strips of width $w\gg L_y$, a half-instanton is formed near the boundary, with the activation energy being 1/2 of $ΔF^\text{2D}$.

cond-mat.supr-con↗