Numerical study of the phase slip in two-dimensional superconducting strips

Abstract

In this paper, we numerically investigate the phase slips in two-dimensional ͑2D͒ superconducting strips using the string method, which has been presented as an efficient tool for the study of thermally activated rare events. In the framework of Ginzburg-Landau ͑GL͒ theory, we calculate the most probable transition pathway for thermally activated phase slips that are responsible for spontaneous current dissipation. Along the most probable pathway, the saddle point of the GL free-energy functional can be located, from which the energy barrier is also determined. We find there exists a critical width w c for narrow strips. Below w c , the strip behaves as a one-dimensional superconducting wire for which the phase slips are described by the LangerAmbegaokar-McCumber-Halperin theory ͓Phys. Rev. 164, 498 ͑1967͒; Phys. Rev. B 1, 1054 ͑1970͔͒. Above w c , however, the 2D character of the strip is recovered, and the phase slips are dominated by vortices crossing the strip. In this 2D regime, our numerical results based on the GL theory are compared to the analytical results of the London theory. While there is good agreement for large strip widths, deviation is noticed for small widths ͑still Ͼw c ͒ because of the closeness of vortex core to the strip edges.

Superconductor to resistive state switching by multiple fluctuation events in NbTiN nanostrips

“…We also assume that the energy barrier shape is smooth around the critical current and that Ω F does not depend on bias current close to the critical current. In this way the role of the bias current is to control ΔF and the approach is compatible with several different phase slip mechanisms 18–22 . Thus we can series develop ΔF in I B to first order around I B = 1 obtaining for a fixed temperature:here , and ΔF′(I B ) = dΔF(I B )/dI B .…”

“…For clarity, in the following a quantized phase change of 2π in the order parameter will be considered a phase slip event. Hence, escape through an energy saddle point which does not involve a vortex core 15–17 , vortex-antivortex pairs splitting 18,19 and single vortices crossing an edge barrier 18,20–22 are possible origins of phase slip events.…”

Energy-level quantization and single-photon control of phase slips in YBa2Cu3O7–x nanowires

“…1c. One-dimensional phase-slip centers described by the Skocpol-Beasley-Tinkham model 23 can appear in superconducting nanowires with width W ≤ 4.4ξ 2,24 , where ξ denotes the coherence length. In wider nanowires, a phase slippage occurs either by the two-dimensional analog of a phase-slip center (i.e., the order parameter is suppressed across the entire nanowire) or a so-called vortex street (i.e., running phase-slip centers, which are also referred to as kinematic vortices) 25,26 .…”

Detection mechanism of superconducting nanowire single-photon detectors

“…Nevertheless, they fit their analytical formula for VPS to the data of [60] and obtain very consistent fit parameters except for the widest meander line with w 170 » nm, see also figure 4(a). As discussed in [62], there may be a cross-over from the VPS dominated fluctuations to VAP as the strip width is increased. The rate of single vortices entering the strip is proportional to the length of the wire, whereas the rate of VAP break-up is proportional to the area of the superconducting film.…”

“…Systematic theoretical and experimental investigations have found strong support for single vortices overcoming the edge barrier as the dominating mechanism leading to dark counts in SNSPD. In [62] numerical methods have been used to compare PSL and VPS. The key finding of this analysis is a critical width w 4.4 0.1 c GL ( ) x »  that coincides with the Likharev-criterion [53].…”