Theory of the lower critical magnetic field for a two-dimensional superconducting film in a nonuniform field

Abstract

We consider the first appearance of vortices in a two-dimensional (2-D) superconducting film exposed to a non-uniform magnetic field, B a , produced by a nearby coil. The film has "infinite" radius, R f , and thickness t about equal to the coherence length, ξ. The coil is approximated as a point dipole. We find that the first vortex-bearing state to appear has both a vortex and an antivortex. The Gibbs free energy of this state is lower than the vortex-free state when the maximum applied perpendicular field, i.e., the applied field, 0

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

“…In a 2-D superconducting film in a non-uniform field applied near its center, there is stable vortex-free thermodynamic state only for applied fields below a very small thermodynamic critical field 1,2 . Thus, as a practical matter, the vortexfree state is always metastable just like a 1-D wire.…”

“…Recent measurements on thin Nb and amorphous MoGe films agree. 10 Since the thermodynamic lower critical field is orders of magnitude smaller than the measured external critical field 1,2 , there must be a high free-energy barrier for creation of vortices. The applied field at which this barrier vanishes has been calculated, e.g., Ref.…”

“…This field is orders of magnitude larger than the thermodynamic applied field where vortices would appear if not for the high freeenergy barrier for breaking nascent vortex-antivortex (V-aV) pairs. 1,2 The calculation is useful for determination of the inplane Ginzburg-Landau coherence length, ξ, from the onset of strong non-linear effects in two-coil experiments [3][4][5][6][7][8][9] for measuring the magnetic penetration depth, λ.…”

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

“…This suggests that there is another mechanism contributing to the onset of nonlinearity and dissipation in these arrays. 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.…”

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]. For T < 8 K, B NL is essentially flat (Figure 4), consistent with calculations of p c (T ) in s-wave [14] and d-wave superconductors [15].…”