Upper limit of metastability of the vortex-free state of a two-dimensional superconductor in a nonuniform magnetic field

Abstract

We calculate the magnetic field above which vortices necessarily appear in a two-dimensional superconducting film in a non-uniform magnetic field applied near its center, as in two-coil measurements of superfluid density. Experiments suggest that free vortices appear when the Meissner screening current density is large enough that the free-energy barrier for separating tightly-bound vortex-antivortex (V-aV) pairs into free vortices is comparable to k B T , not at the much lower thermodynamic critical field. Specifically, we calculate the applied magnetic field above which there exists no metastable state without vortices. There is a simple analogy with the appearance of phase-slip-centers in a one-dimensional superconducting wire. 74.25.Op, 75.40.Mg

Measuring the superconducting coherence length in thin films using a two-coil experiment

“…We have empirically identified the applied driving magnetic field associated with vortex-antivortex pairs unbinding en masse in the films, informed by a microscopic model which includes flux pinning. Our data on eight films fit well to Lemberger and Ahmed's recent calculation of the upper bound of the vortex-free state as a function of superfluid density 7 , and we are able to extract values of the superconducting coherence length from these data in quantitative agreement with values measured from the films' upper critical fields.…”

Local imaging of diamagnetism in proximity-coupled niobium nanoisland arrays on gold thin films

“…The actual applied field (or field coil current) at which nonlinearity due to vortex dynamics begins to occur is necessarily smaller than this maximum vortex-free field, which is consistent with the SQUID measurements (Figure 2 (f)). In a homogeneous 2D superconductor, vortices are expected to first appear at the position with the highest superfluid momentum, i.e., the position where the vector potential |A(r)| is largest [47,49], and we expect the same to be true for the ordered array. Any vortices that are present will experience a force due to the local AC applied field from the field coil.…”

“…One candidate is motion of vortices induced in the 2D superconducting system above a lower critical field B crit 0 , as has been studied theoretically for uniform applied fields [44,45] and for nonuniform applied fields in the context of two-coil mutual inductance susceptibility measurements [46][47][48]. Lemberger and Ahmed [47] found that for a 2D superconductor in the weak screening (large Λ) limit with Ginzburg-Landau coherence length ξ subject to a nonuniform field from a point dipole or small current loop, there can be no vortex-free state above a lower critical field B crit 0 ≈ Φ 0 /(2ρ 0 ξ), where ρ 0 Λ is the radial distance from the magnetic source at which the applied field changes sign. This relationship between the coherence length ξ and the onset of vortex-related nonlinear magnetic response has been used to measure ξ in superconducting thin films [48].…”

Doping-dependent critical Cooper-pair momentum in thin underdoped cuprate films

“…The critical pair momentum p c is computed from the lowtemperature values of B NL by a calculation of Lemberger and Ahmed [12] using an idealized version of our experimental configuration. We report values of p c for our cuprate films using this result, assuming that the measured B NL coincides with the applied field at which the Meissner state is becomes unstable, and vortex-antivortex pairs unbind en masse [13].…”