Fluctuations of vortices in layered high-Tcsuperconductors

Abstract

The temperature T s of spontaneous creation of vortex lines in Josephson coupled layered superconductors is obtained by taking into account the entropy contribution to the free energy due to thermal distortions. For Bi-and Tl-based high-T c superconductors and superlattices, the superconducting critical temperature T s lies noticeably below the mean-field transition temperature T c o (T c o -T s « 4 K or more). The contribution of thermal distortions to the free energy causes significant changes in the temperature and field dependences of magnetization below T s seen in Bi compounds.PACS numbers: 74.60.GeThe importance of topological excitations in the thermodynamics of two-dimensional (2D) magnets and superconductors was first discussed by Berezinskii and Kosterlitz and Thouless [1]; for a review see [2]. Above the Kosterlitz-Thouless (KT) transition temperature TKT> which lies below the mean-field transition temperature T c o, thermally induced free vortices are present in 2D superconductors giving rise to dissipation and persistentcurrent decay. The spontaneous creation of free vortices above TKT occurs due to the entropy contribution to the free energy F = e-Ta, where e = (<^d/167r 2 A 2 ) ln(iJ/£) and a = ln(i2 2 /£ 2 ) are the vortex energy and its entropy (cj)o is the flux quantum, A is the London penetration depth, £ is the coherence length, TTR 2 and d are the system area and thickness). Above TKT? which is given implicitly by <t>ld 32TT 2 A 2 (T)'(1) the free energy is negative, and spontaneous creation of vortices is favorable.Generalizations of the KT approach to layered (but still three-dimensional) high-T c superconductors [3][4][5] were stimulated by experiments that show the KT scaling behavior of resistivity; Bi-2:2:1:2 and superlattices YBaCuO/PrBaCuO are perhaps the best example (see review [6] and references therein). The idea behind the generalizations was brought about by the observation that in the absence of interlayer superconducting coupling, 2D vortices of different layers interact only via the magnetic field, which provides the same logarithmic dependence of the vortex energy e on the sample size as in 2D superconductors [5,7]. This made feasible the KT transition [3-5], i.e., spontaneous creation of 2D vortices and antivortices within the same layer above the temperature obtained by solving Eq. (1) with d replaced by the interlayer distance s. However, even in the case of weak Josephson coupling [8], e increases linearly with R [9], while the entropy a of a 2D vortex still changes only logarithmically. In these circumstances, thermally induced spontaneous creation of free 2D vortices (in the low concentration limit) is virtually impossible.In the following, taking into account the entropy contribution to the free energy due to thermal distortions of vortices, we show that thermally induced spontaneous creation of vortex lines should occur in Josephson coupled layered materials above some temperature T s < T c $. We estimate the difference T c o-T s to be as high as 5-10 K for Bi-and T...

Entropy, vortex interactions, and the phase diagram of heavy-ion-irradiatedBi2Sr2CaCuBeek1, Kończykowski2, Drost3 et al. 2000Phys. Rev. B403290View full textAdd to dashboardCite

“…Am −1 K −1 , we see that the (constant) contribution of the entropy term 43 can amount to 20 % of the temperature derivative of ∂M rev /∂ ln B, at most. The nonmonotonic field dependence of the reversible magnetization has a straightforward explanation in terms of the lowering of the vortex free energy by pinning onto the columnar defects.…”

“…Such a contribution may arise from vortex positional 40,43,44 and order parameter amplitude fluctuations. 40,47,48 The entropy contribution to the free energy is believed to be important in layered superconductors because of the "crossing point" behavior observed in the reversible magnetization at T * 1 and T * 2 .…”

“…13,15,49,50 Supposing that a description in terms of the London model is appropriate, and hence, that vortex positional fluctuations give the dominant contribution to S, it was derived in Ref. 43 that the crossing point arises in the unirradiated material when the field dependence of the two terms contributing to M rev ,…”

Evidence for Kosterlitz-Thouless and three-dimensionalXYcritical behavior inBi2Sr2CaCuSchneider1, Giannini2 2009Phys. Rev. B17170View full textAdd to dashboardCite

“…Although approximate treatments have been invoked to describe the thermodynamic properties of such materials, the essential ingredient, the Kosterlitz-Thouless behavior of the associated zero field transition, 8 has mostly not been taken into account. 9,10,11 Only recently, this behavior was incorporated by combining Kosterlitz-Thouless (KT) renormalization-group flows and explicit computations for plasmas. 12 On this basis the field and temperature dependence of the magnetization density, m (H c , T ), for temperatures T near to and below the KosterlitzThouless (KT) transition temperature T KT was determined for magnetic fields H c applied perpendicular to the superconducting sheet.…”

Landau and Ott scaling for the kinetic energy density in the low-Tcconventional superconductorsLi2Pd3BDoria1, Salem‐Sugui2, Badica3 et al. 2006Phys. Rev. B121112View full textAdd to dashboardCite

“…High-T c materials display an upward curvature in the irreversibility line, attributed, among others, to high-field diamagnetic fluctuations [16,17,18]. The Landau and Ott definition of the upper critical field H c2 (T ) brings a new switch to this controversial issue as it displays no upward curvature.…”