Universality of the Kosterlitz-Thouless Transition inHe4Films as a Function of Thickness

Abstract

We report new measurements of thermal transport in 4 He films near the superfluid transition. We have done this to check on the universality of this transition as a function of thickness or T c between 1.37 and 1.88 K. Results from this study show for the first time a thickness or T c dependence of the two characteristic parameters for the thermal conduction, the ratio of diffusion constant to vortex core radius, D/a 2 , and the nonuniversal constant b. We suggest that the increase of b with film thickness is related to the bulk correlation length. PACS numbers: 64.70.-p, 67.40.pm, 67.70. + nThe superfluid transition in 4 He films has been studied extensively as one of the realizations of a twodimensional (2D) x-y system. Various predictions coming from the Kosterlitz-Thouless theory 1 of such a transition have been verified via measurements of the superfluid density, 2,3 thermal transport, 4 " 7 and persistent currents. 8 The transition is in the same universality class as, for instance, 2D melting, the superconducting transition in thin films, and some transitions in liquid crystals. It is thus of considerable theoretical and experimental interest. There are still, however, several aspects of the superfluid transition which merit further attention. Among these is the question of how this transition is modified when one deals with helium films substantially thicker than a few monolayers. One expects that as long as one is in a temperature region where the 3D correlation length would tend to be larger than the film thickness, then the 2D behavior should be manifest. It is clear, however, that aspects of this behavior must be modified in thick films, if for no other reason but the fact that the critical behavior is relegated to a progressively smaller region in temperature as the film's T c approaches the bulk 7\. We report in this Letter a study of thermal transport to look at this behavior. Our work can be viewed from the perspective of finite-size scaling and dimensionality crossover 9 but, perhaps more importantly, it should be viewed as a universality study of the KosterlitzThouless transition. This is analogous to the study of the critical behavior at the 3D superfluid transition along the A line on the pressure or 3 He-concentration plane. 10

The two-dimensional Coulomb gas, vortex unbinding, and superfluid-superconducting films

“…Since the thermal conductance is inversely proportional to the density of free Coulomb gas charges, it should reflect the Kosterlitz-Thouless transition through a rapid decrease with increasing Coulomb gas temperature T CG~T /p. This prediction is in good agreement with measurements (Agnolet et al, 1981;Maps and Hallock, 1981;Finotello and Gasparini, 1985). The n F dependence on an external electric field D (compare Sees.…”

Estimation of the critical dynamics and thickness of superconducting films and interfaces

“…[10][11][12][13] Accordingly the analysis of conductivity or resistivity data in zero magnetic field provide in terms of ϰ z estimates for T c , 0 z , and z / b ͑Refs. 14-17͒ while the dynamical critical exponent z cannot be deter-mined.…”

Suppression of the Berezinskii-Kosterlitz-Thouless and quantum phase transitions in two-dimensional superconductors by finite-size effects

“…These values for the extent of the homogeneous domains are comparable with the dimension of the superconducting patches emerging from scanning tunneling spectroscopy investigations on TiNi 46 and InO x 47 films, as well as with scanning SQUID measurements at the interface LaAlO 3 /SrT iO 3 . 48 To disentangle the T c dependence of L and ξ 0 we used the empirical relationship ξ 0 ∝ T −1/z c with z = 2, 44,45 revealing that the extent of the homogenous domains decreases substantially with reduced T c (Fig.7). Accordingly the enhanced smearing of the BKT transition with reduced T c was traced back to the reduction of the limiting length L and the increase of the vortex core radius ξ 0 with decreasing T c .…”

“…Given the irrelevance of disorder, the reduction of the ratio L/ξ 0 with reduced film thickness or transition temperature (see Fig.4b) is then attributable to: (i) increasing vortex core radius ξ 0 with reduced T c combined with a thickness independent L; (ii) a limiting length L which decreases with film thickness combined with a T c independent ξ 0 ; (iii) a thickness dependence of both, L and ξ 0 , such that the ratio L/ξ 0 decreases with reduced transition temperature. Because the vortex core radius is known to increase with reduced T c as ξ 0 ∝ T −1/z c with z = 2, 44,45 we are left with option (i) and (iii). In order to discriminate between these options we estimate ξ 0 (T c ) from the respective data for the 23.42Å thick Bi film, namely ξ 0 = 6.5Å and T c = 0.41 K, yielding ξ 0 = gT −1/2 c with g = 4.19ÅK 1/2 .…”