Defect-Unbinding Transition in Layered Superconductors

Abstract

We establish a new interstitial-vacancy unbinding transition of the Berezinskii-KosterlitzThouless type, transforming the three dimensional pancake vortex lattice of a decoupled layered superconductor into a defected solid. This transition is the natural finite-field extension of the vortex-anti-vortex unbinding transition establishing the zero-field superfluid stiffness. At finite Josephson coupling, the defect unbinding transition turns into a topological decoupling transition.PACS numbers: 74.60.Ec, 74.60.GeThe soft vortex matter in high-temperature layered superconductors exhibits a fascinating rich phase diagram with a variety of phase transitions modifying the various intra-and interplanar correlations. These include a melting transition from a line solid to a line liquid [1][2][3], a sublimation transition taking the solid into a pancake vortex gas [4], and a decoupling transition [4][5][6][7] destroying the superconducting coherence between the planes. In this letter we concentrate on the decoupled limit where the three-dimensional (3D) nature of the vortex system is solely due to the long range electromagnetic interaction between the pancake vortices. We establish that in the crystal phase there is a Berezinskii-Kosterlitz-Thouless (BKT) phase transition which separates the pancakevortex lattice from a defected 3D solid with a finite density of free interstitials and vacancies, see The vortex lattice in layered superconductors is "soft" and melts at low temperatures; for fields B > B λ = Φ 0 /λ 2 (λ = penetration depth) the transition is governed by the shear interaction between pancake vortices in the same layer and thus is close to the two-dimensional dislocation-mediated BKT melting in the individual layers [8]. The 3D nature of the transition becomes explicit only at low fields B < B λ , where the electromagnetic (tilt) interaction between pancake vortices in different layers dominates over the intralayer (shear) interaction due to the planar currents [4]. Here, we study another thermodynamic property of the pancake-vortex latticeits susceptibility to the formation of free defects in the form of pancake-vortex interstitials and vacancies. It has recently been shown [9] for the pancake-vortex lattice in layered decoupled superconductors that the self-energy of (and the logarithmic interaction between) vacancies and interstitials is strongly screened due to the relaxation of the vortex lattice surrounding the defects. We find that the corresponding interstitial-vacancy pair creation can be understood in terms of a simple vortex-anti-vortex pair creation in a superconductor with a vortex-induced suppression of the superfluid density. The usual zero-field BKT transition establishing the superfluid stiffness of the individual superconducting layers [10] therefore has its counterpart at finite fields in the form of interstitialvacancy unbinding in the vortex solid.We start from a rigid vortex lattice in a decoupled layered superconductor and move one pancake by the distance R within the same layer to prod...

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