Generalization of the Berezinskii-Kosterlitz-Thouless theory to higher vortex densities

Abstract

The Berezinskii-Kosterlitz-Thouless theory for superfluid films is generalized in a straightforward way that (a) corrects for overlapping vortexantivortex pairs at high pair density and (b) utilizes a dielectric approximation for the polarization of the vortex system and a local field correction. Generalized Kosterlitz equations are derived, containing higher order terms, which are compared with earlier predictions. These terms cause the total pair density to remain finite for temperatures above the transition so that it is not necessary to introduce an ad hoc cut-off, as opposed to the original Berezinskii-Kosterlitz-Thouless theory. The lowtemperature bound pair phase is destabilized for small vortex core energy. The behaviour of the stiffness constant and of the correlation length close to the transition is not affected by the higher order terms. A first-order transition as suggested by other authors is not found for any values of the parameters. The pair density is calculated for temperatures below and above the transition. Possible experiments and the applicability of the extended approach are discussed. The approach is found to be applicable even in a significant temperature range above the transition.

Flux noise in high-temperature superconductors

“…From Ref. 6 we see that the exponent ζ vanishes for T ≥ T c and is positive and, to leading order, proportional to √ T c − T below T c . Details may be found in Ref.…”

“…The pair size distribution is intimately related to the pair fugacity y 2 of BKT theory, f (r) = y 2 (r)/r 4 . The modified Kosterlitz recursion relations of the extended BKT theory 6,11 predict that y 2 and the renormalized interaction described by the stiffness constant K approach a finite, temperature-dependend fixed point y 2 (∞), K(∞) for large length scales. Hence, we can solve the recursion relations close to the appropriate fixed point to obtain the leading behavior of the fugacity, and thus of the pair size distribution f (r), at large length scales.…”

NMR and NQR fluctuation effects in layered superconductors

“…This is a good approximation, since the typical pair size is small compared with the average distance between pairs below the transition and even in a significant temperature range above it. 42 In the following we are only interested in the diagonal components of k ␣␤ . They can be written as…”

Critical dynamics of a two-dimensional superfluid near a nonthermal fixed point

“…The 'Dynamical evolution' illustrates trajectories of decaying superfluid turbulence starting from the time where vortices appear, t = tV, approaching the NTFP and finally evolving towards equilibrium. The line marked as 'Thermal states' qualitatively illustrates these quantities for thermal configurations [39][40][41], featuring a steady decrease of inverse coherence with inverse mean vortex-antivortex distance and including a Berezinskii-Kosterlitz-Thouless (BKT) phase transition. An unbinding of vortices of opposite circulation characterises the approach to the NTFP before finally all vortices decay, lD → 0, to establish equilibrium phase coherence, here at a temperature below the BKT transition.…”

“…(7), which is a measure for the width of the normalized first-order coherence function and is less sensitive to noise in the tails of g (1) (r). In this way, the dynamical evolution towards and away from a non-thermal fixed point can be compared to the properties of near-equilibrium states of a two-dimensional degenerate Bose gas [39][40][41][44][45][46]. Arrows mark the direction of the flow and indicate that critical slowing down occurs near the NTFP.…”