Universal Jump in the Superfluid Density of Two-Dimensional Superfluids

Nelson, David R.; Kosterlitz, J

doi:10.1103/physrevlett.39.1201

Cited by 1,310 publications

(968 citation statements)

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“…The superfluid onset for the uniform 48.3 nm film is consistent with the t c in other uniform films 14 . The smallest value in ρ s /ρ at the transition is also consistent with, but somewhat larger (∼20%) than, the expected Kosterlitz-Thouless (KT) jump 27,28 (indicated by the dashed-dotted horizontal line). For a uniform 31.7 nm film the expected position of t c and expected KT jump are indicated with the crossed solid vertical and dashed horizontal lines respectively.…”

Section: Figure 1 | the Confinement Cellsupporting

confidence: 63%

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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 Cellsupporting

confidence: 63%

“…3 is the region where the film orders. The calculated subtraction for the contribution of a uniform film 28 . The solid vertical line is at the expected t c for a uniform 31.7 nm film.…”

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 fact, by a suitable rescaling of the coordinates in the spatial and time directions, the stiffness of the renormalized isotropic Gaussian model can be written as ¯= ͑ ͒ 1/2 . If the transition is in the KT universality class, then a universal jump 21 is expected for ¯as a function of g at the transition given by ¯=2/ g. Figure 6 shows that the finite-size behavior of ¯appears consistent with the expected universal jump for the phase stiffness. For each system size, the intersection of the data with the dotted line representing the universal jump prediction provides an upper bound estimate of the critical coupling.…”

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confidence: 52%

Field-induced superconductor-to-insulator transition in Josephson-junction ladders

Granato

2005

Phys. Rev. B

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The superconductor-to-insulator transition is studied in a self-charging model for a ladder of Josephson junctions in the presence of an external magnetic field. Path integral Monte Carlo simulations of the equivalent ͑1+1͒-dimensional classical model are used to study the phase diagram and critical behavior. In addition to a superconducting ͑vortex-free͒ phase, a vortex phase can also occur for an increasing magnetic field and small charging energy. It is found that an intervening insulating phase separates the superconducting from the vortex phases. Surprisingly, a finite-size scaling analysis shows that the field-induced superconducting-to-insulator transition is in the KT universality class, even though the external field breaks time-reversal symmetry. DOI: 10.1103/PhysRevB.72.104521 PACS number͑s͒: 74.40.ϩk, 74.81.Fa, 73.43.Nq, 74.25.Qt Superconductor-to-insulator transitions in Josephson junction arrays have attracted considerable interest. 1-5 Such arrays can currently be fabricated in any desired geometry both in one and two dimensions 4,5 with well-controlled parameters. When charging effects due to the small capacitance of the grains or junctions dominate, strong quantum fluctuations of the phase of the superconducting order parameter may drive the system into an insulating phase at zero temperature, leading to a superconductor-to-insulator transition as a function of charging energy or an external magnetic field. In two dimensions, the universality class of these transitions have already been investigated in detail numerically, 6 both in relation to experiments 3,4 and theoretical predictions. 7-9 Nevertheless, there are also remarkable quantum phase transition scenarios 10 that can take place in a Josephson-junction ladder in a magnetic field as in Fig. 1 which have not been investigated experimentally or numerically. Interestingly, a Josephson-junction ladder provides the simplest onedimensional version of the array allowing the study of commensurability effects due to the flux lattice 10-13 or charge frustration, 14 in the presence of quantum fluctuations.An important aspect of the Josephson-junction ladder in Fig. 1 is the approximate relation to the quantum sineGordon model, 15 as first shown by Kardar. 10 For an increasing magnetic field, there is a transition from a ͑vortex-free͒ superconducting phase to a vortex phase, where flux penetrates the ladder, in the absence of quantum fluctuations. This transition is the analog of the commensurateincommensurate transition 16 described by the sine-Gordon model. For small fields, the phases in different branches of the ladder are locked to each other while in the vortex state exponentially interacting kinks ͑vortices͒ appear that unlock the phases leading to a one-dimensional vortex lattice. The inclusion of quantum fluctuations due to charging effects leads to the interesting prediction that an insulating phase should occur in the vicinity of this transition and therefore a direct transition from the ͑vortex-free͒ superconducting phase to the vort...

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“…Since the Kosterlitz-Thouless RG equations for the XY model [1,13,14] lead to the prediction that the helicity modulus ϒ jumps from the value 2/(πβ ) to zero at the critical temperature, one can check if the same occurs for vector Potts models. In Fig.…”

Section: Pos(lattice 2011)304mentioning

confidence: 99%