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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2506.18130 |
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| _version_ | 1866911487303352320 |
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| author | Skvortsov, Mikhail A. Polkin, Artem V. |
| author_facet | Skvortsov, Mikhail A. Polkin, Artem V. |
| contents | 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 $ΔF^\text{2D}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18130 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermal phase slips in superconducting films Skvortsov, Mikhail A. Polkin, Artem V. Superconductivity Exactly Solvable and Integrable Systems 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 $ΔF^\text{2D}$. |
| title | Thermal phase slips in superconducting films |
| topic | Superconductivity Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2506.18130 |