Kosterlitz-Thouless Transition in Proximity-Coupled Superconducting Arrays

Resnick, Douglas J.; Garland, J. C.; Boyd, J. T.; Shoemaker, Steve; Newrock, R. S.

doi:10.1103/physrevlett.47.1542

Cited by 328 publications

(232 citation statements)

References 14 publications

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“…for 4 He mirrors observations with granular superconductors 4,19 , and superconducting arrays 20 . This was also observed earlier in a less-well-controlled geometry, where proximity and coupling effects could not be identified 21 .…”

Section: Figure 1 | the Confinement Cellmentioning

confidence: 99%

Coupling and proximity effects in the superfluid transition in 4He dots

et al. 2010

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The superfluid transition in 4 He is associated with the onset of an order parameter that is a macroscopic wavefunction. This is similar to the onset of superconductivity in metals and alloys. Yet, some of the hallmark phenomena that are associated with wavefunctions, and are evident in superconductors, have not been identified in 4 He. Here we report proximity effects on the specific heat and superfluid density of a thin 4 He film in equilibrium with an array of larger boxes of 4 He. Comparison with previous data also enables us, by scaling, to deduce an excess specific heat associated with a collective behaviour of weakly coupled boxes. These effects should be relevant to the understanding of experiments where helium has been studied when confined in packed powders, porous materials or other inhomogeneous confinements, where proximity and collective effects must be present but not readily quantifiable 1,2 . Our work also forms a point of comparison and contrast with the case of superconductors 3,4 , and is relevant to studies of Josephson effects in superfluids, coupling effects in arrays of Bose-condensed atoms 5,6 , and magnetic systems where, because of chemical composition, two separate but interacting ordering transitions take place 7,8 .In the case of superconductors, coupling and proximity effects have been well understood for many years. The large correlationlength amplitude ξ 0 makes coupling between two superconductors easy to achieve. Weak links with dimensions of the order of ξ 0 , which can be a metal, an insulator or another superconductor, enable measurements of the familiar Josephson effects (see for instance ref. 9). With 4 He these effects are much more difficult to achieve because ξ 0 is of the order of interatomic dimensions. Furthermore, weak links and coupling between two regions of 4 He cannot be achieved through any material other than 4 He. We can, however, take advantage of the growth of the correlation length with temperature T and critical exponent ν, ξ = ξ 0 |1 − T /T λ | −ν ≡ ξ 0 t −ν near the transition temperature T λ and construct apertures whereby analogous Josephson effects can be realized 10,11 .We are unaware of any theory that describes the effects on thermodynamic properties of a 'grain' or dot of helium due to a coupling to another dot through a weak link, or, for that matter, how this coupling is affected by the geometry or 'strength' of this link. This question arose while attempting to verify finite-size scaling for zero-dimensional crossover 12 . We had measured the heat capacity of helium in arrays of (1 µm) 3 and (2 µm) 3 boxes linked by channels of 1 µm × 1 µm × 0.019 µm and 2 µm × 2 µm × 0.010 µm respectively. These data did not scale anywhere in the critical region 13 . The lack of scaling is unexpected, because for both twoand one-dimensional crossover, at least for T > T λ , other data do scale 14 . More significantly, an analysis of the zero-dimensional data suggested that the smaller boxes had a higher heat capacity than expected 13 . This might result from ...

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Section: Figure 1 | the Confinement Cellmentioning

confidence: 99%

Coupling and proximity effects in the superfluid transition in 4He dots

et al. 2010

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“…In this paper we present the magnetic flux response of the R(T ) of very low superfluid density (high sheet resistance) [11,16] films patterned with a nanoscale array of holes. We use the quality of the flux response at different points along their transitions to determine the presence of well-defined vortices [17] and thus provide insight into where the amplitude fluctuation dominated transport gives over to phase fluctuation dominated transport on an R(T ). In addition, we propose that this method can be used to directly detect the existence of vortices in settings where their presence has been contentious [8].…”

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Magnetic-flux periodic response of nanoperforated ultrathin superconducting films

et al. 2006

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We have patterned a hexagonal array of nano-scale holes into a series of ultrathin, superconducting Bi/Sb films with transition temperatures 2.65 K < Tco <5 K. These regular perforations give the films a phase-sensitive periodic response to an applied magnetic field. By measuring this response in their resistive transitions, R(T ), we are able to distinguish regimes in which fluctuations of the amplitude, both the amplitude and phase, and the phase of the superconducting order parameter dominate the transport. The portion of R(T ) dominated by amplitude fluctuations is larger in lower Tco films and thus, grows with proximity to the superconductor to insulator transition.The superconductors originally considered by BCS exhibited spectacularly sharp transitions from a finite resistance to zero resistance as a function of temperature [1]. Fluctuation effects were negligible. Presently, a great deal of attention focuses on low superfluid density superconductors for which fluctuations strongly influence and substantially broaden their phase transitions. These include the high temperature superconductors [2], and in particular, their underdoped versions [3,4,5], and ultrathin superconducting films near the superconductor to insulator transition (SIT) [6,7,8,9,10]. For the latter, resistive transitions, R(T ), can develop widths comparable to or greater than the apparent mean field transition temperature, T c0 [11].To discuss the effects of fluctuations on the R(T ) it is helpful to consider the two component superconductor order parameter ψ = |ψ 0 |e iφ . In bulk elemental superconductors, the sharp R(T ) reflect the near simultaneous appearance of a finite amplitude, |ψ 0 |, and long range coherence of the phase, φ. In low superfluid density superconductors, however, the amplitude first forms at high temperatures and phase coherence develops at lower temperatures [2,12,13,14]. High on a transition quasiparticles transiently form Cooper pairs, which enhances the quasiparticle or fermionic contribution to the conductivity, σ f . These pair or amplitude fluctuations give rise to the initial drop in R(T ) [15]. At very low values of R, a substantial Cooper pair density exists and the conductivity of these bosons, σ b , controls R(T ). σ b is limited by the motion of vortices which causes fluctuations in the phase of the cooper pair condensate. In between, a two fluid model may best describe the transport [7].Physical interpretations of the R(T ) in high sheet resistance films especially those near the SIT relies heavily on distinguishing the amplitude and phase fluctuation dominated regimes [3,4,5,6]. Most often, explicit models for σ f (T ) and σ b (T ) do not exist as a guide and qualitative arguments must prevail. In this paper we present the magnetic flux response of the R(T ) of very low superfluid density (high sheet resistance) [11,16] films patterned with a nanoscale array of holes. We use the quality of the flux response at different points along their transitions to determine the presence of well-defined vortic...

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“…The XY -type of transition is related by duality to roughening transitions in solid-on-solid and related models [5]. Apart from the XY model, BKT transitions are found, among others, in vertex models [6], models of crystal surfaces [7], the antiferromagnetic triangular Ising model [8], string theory [9], network systems [10], superfluid systems [11], and superconducting systems [12]. These models may involve long-or short-range interactions.…”

Section: Introductionmentioning

confidence: 99%

Berezinskii-Kosterlitz-Thouless-like percolation transitions in the two-dimensionalXYmodel

Deng

Blöte

2011

Phys. Rev. E

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We study a percolation problem on a substrate formed by two-dimensional XY spin configurations using Monte Carlo methods. For a given spin configuration, we construct percolation clusters by randomly choosing a direction x in the spin vector space, and then placing a percolation bond between nearest-neighbor sites i and j with probability p ij = max(0,1 − e −2Ks x i s x j ), where K > 0 governs the percolation process. A line of percolation thresholds K c (J ) is found in the low-temperature range J J c , where J > 0 is the XY coupling strength. Analysis of the correlation function g p (r), defined as the probability that two sites separated by a distance r belong to the same percolation cluster, yields algebraic decay for K K c (J ), and the associated critical exponent depends on J and K. Along the threshold line K c (J ), the scaling dimension for g p is, within numerical uncertainties, equal to 1/8. On this basis, we conjecture that the percolation transition along the K c (J ) line is of the Berezinskii-Kosterlitz-Thouless type.

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Kosterlitz-Thouless Transition in Proximity-Coupled Superconducting Arrays

Cited by 328 publications

References 14 publications

Coupling and proximity effects in the superfluid transition in 4He dots

Coupling and proximity effects in the superfluid transition in 4He dots

Magnetic-flux periodic response of nanoperforated ultrathin superconducting films

Berezinskii-Kosterlitz-Thouless-like percolation transitions in the two-dimensionalXYmodel

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