One-dimensional resistive states in quasi-two-dimensional superconductors: Experiment and theory

Abstract

We investigate competition between one-and two-dimensional topological excitations-phase slips and vortices-in the formation of resistive states in quasi-two-dimensional superconductors in a wide temperature range below the mean-field transition temperature T C0 . The widths w = 100 nm of our ultrathin NbN samples are substantially larger than the Ginzburg-Landau coherence length = 4 nm, and the fluctuation resistivity above T C0 has a two-dimensional character. However, our data show that the resistivity below T C0 is produced by one-dimensional excitations-thermally activated phase slip strips ͑PSSs͒ overlapping the sample cross section. We also determine the scaling phase diagram, which shows that even in wider samples the PSS contribution dominates over vortices in a substantial region of current and/or temperature variations. Measuring the resistivity within 7 orders of magnitude, we find that the quantum phase slips can only be essential below this level.The nature of the resistive state in superconductors attracts much attention from the physics community, since it involves fundamental phenomena and advanced concepts 1,2 such as the mechanisms of high-T c superconductivity, 3 thermal fluctuations, 4,5 macroscopic quantum tunneling, 6-8 coherence, 9 topological excitations, 10 and phase disordering. 11 Resistive states are used in a number of quantum nanodevices, such as logic elements, 12 ultrasensitive detectors of radiation, single-photon counters, and nanocalorimeters. 13,14 Understanding resistive states in nanoscale superconductors is critical for the advancement of fundamental science and the development of novel applications.Phase slips and vortices are elementary topological excitations which create resistive states. 1,2,10 Wires with radius less than the coherence length or stripes with w Ͻ are one-dimensional ͑1D͒ superconductors. In 1D structures, the resistive state is produced by phase slips and is well described by the Langer-Ambegaokar-McCumber-Halperin ͑LAMH͒ theory of thermally activated phase slips ͑TAPSs͒. 1,2,4,5 At low enough temperatures, the quantum phase slips ͑QPSs͒ should be important, 6 but the magnitude of this effect and the characteristic resistance at the transition from TAPSs to QPSs are still under debate. 7,8 In two-dimensional ͑2D͒ superconductors, the resistive state is formed by moving vortices. Above the BerezinskiiKosterlitz-Thouless ͑BKT͒ transition temperature T C , there is a nonzero concentration of free vortices due to thermal unbinding of vortex-antivortex pairs ͑VAPs͒. 15,16 Below T C in an infinite 2D superconductor, VAPs are tightly bound and only a significant bias current can unbind the pairs, resulting in a nonlinear flux flow resistance. In finite size samples, free vortices can exist below T C and produce a linear resistance at low bias currents. 15 It is commonly believed that the transition from 1D phase slip excitations to 2D vortex physics takes place at w / ϳ 1. 1,2,7,12,17 However, despite thorough studies of phase slip and vortex mechanisms, an in...

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

“…The voltage is linearly related to this rate difference.͔ We note that the linear V − I characteristic has been reported for narrow strips in some literatures. [15][16][17] In this paper, we will focus on the narrow strips of width w ϳ 10 and investigate the thermally activated phase slips responsible for current dissipation. The typical width considered here is actually close to the characteristic dimension for the crossover from 2D strip to 1D wire.…”

“…Phase slips of the first kind are numerically obtained when the strip acts as a 1D wire, with the order parameter uniformly distributed along the y direction across the strip. The corresponding saddle point will be called the phase-slip-strip ͑PSS͒ solution 16 and denoted by s…”

“…18 In particular, the mechanism of current dissipation in narrow strips remains an issue. [12][13][14][15][16][17][18] Interpretations of experimental data for these systems involve two distinct mechanisms. While in Refs.…”

“…[1][2][3][4][5][6][7][8][9][10][11] However, the case of quasi-2D narrow superconducting strips has received relatively less attention. [12][13][14][15][16][17][18] The investigation on this intermediate dimension is important as well considering its relevance to some superconducting detecting devices, e.g., superconducting single-photon detectors [12][13][14][15][16][17] and superconducting submillimeter detectors. 18 In particular, the mechanism of current dissipation in narrow strips remains an issue.…”

“…14 and 15, the strips are treated as 2D films in which the current dissipation is attributed to the thermally activated unbinding of VAPs, the competition between 1D phase-slip strips and 2D vortices has been modeled in Refs. 16 and 17 for quasi-2D superconductors. In this paper, we show that, for narrow superconducting strips, typically of a small width w ϳ 10 , [15][16][17] where is the temperature-dependent correlation length, the current dissipation is mostly caused by ͑discrete͒ phase slips, each accomplished by a single thermally activated vortex crossing the strip.…”