We present measurements of the superconducting coherence length ξ in thin (d ≤ 100Å) films of MoGe alloy and Nb using a combination of linear and nonlinear mutual inductance techniques. As the alternating current in the drive coil is increased at fixed temperature, we see a crossover from linear to nonlinear coupling to the pickup coil, consistent with the unbinding of vortex-antivortex pairs as the peak pair momentum nearsh/ξ and the unbinding barrier vanishes. We compare measurements of ξ made by this mutual inductance technique to values determined from the films' upper critical fields, thereby confirming the applicability of a recent calculation of the upper limit on a vortex-free state in our experiment.

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

We apply a recently-developed low-field technique to inductively measure the critical pair momentum p c in thin, underdoped films of Y 1−x Ca x Ba 2 Cu 3 O 7−δ and Bi 2 Sr 2 CaCu 2 O 8+δ reflecting a wide range of hole doping. We observe that p c ∝h/ξ scales with T c and therefore superfluid density n s (T → 0) in our two-dimensional cuprate films. This relationship was famously predicted by a universal model of the cuprates with a dopingindependent superconducting gap, but has not been observed by high field measurements of the coherence length ξ due to field-induced phenomena not included in the theory.

Using simple four-terminal resistance measurements and two-coil superfluid stiffness measurements, we observe an extended temperature range wherein both the superfluid density and the resistance are substantially suppressed, in some cases below experimental resolution, in severely underdoped ultrathin films of Ca 0.3 Y 0.7 Ba 2 Cu 3 O 7−δ . This temperature range δ T c , deemed the 'offset', is in some films more than 1/2 of the resistive transition temperature. δ T c scales linearly with the characteristic two-dimensional vortex unbinding temperature T 2D , growing larger with underdoping upon approach to the superconductor-insulator transition. Absent in 3D samples of CaYBCO, we discuss the offset in the context of a previously observed 2D quantum critical point in the vicinity of the superconductor-insulator transition, as well as in the context of intrinsic and extrinsic inhomogeneities in the superconducting state of the film.

No abstract