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Physical review. B, Condensed matter

Critical behavior of vortices in layered superconductors

Stephen W. Pierson

Published Mar 1, 1995• 36 citations
Publisher

Abstract

The critical behavior of vortices in layered systems is studied. The vortex interactions that we use approximate those of vortices in a layered superconductor. We do a mathematically rigorous, real-space renormalization-group study on our model to derive the recursion relations. Terms not found by other studies on layered systems have been derived. It is found that one of the new terms contributes to layer decoupling just above the transition temperature, behavior which is consistent with Monte Carlo studies of this system. By analylzing the correlation length, we are able to study the dependence of the transition temperature and of the size of the three-dimensional (3D) critical region on the strength of the interlayer coupling. The size of the 3D critical region above the transition is found to depend on the interlayer coupling in a way which is different than that predicted by others. We study our results in the context of the high-temperature superconductors and find that they are in good accord with experiments on these materials.

DOI
10.1103/physrevb.51.6663

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We have performed a Wilson-Kogut renormalization-group study of Kosterlitz-Thouless-Berezinskii (KTB) layers coupled to one another by a Lawrence-Doniach-type term, in zero field. The recursion relations that we derive are valid when the interlayer coupling \ensuremath{\lambda} is weak and correctly reduce to the recursion relations for the KTB transition when \ensuremath{\lambda}=0. We find that there is crossover away from the two-dimensional KTB behavior and that the size of the upward shift in the transition temperature and the critical region are weakly dependent on \ensuremath{\lambda}. We apply our findings to layered high-temperature superconductors and conclude that their critical behavior at zero field is explained by our model.
Motivated by the interplay between 2D and 3D scaling signatures observed in unconventional layered superconductors, we present a systematic Monte Carlo study of the three-dimensional classical XY model with anisotropic in-plane J∥J_\parallelJ∥​ and inter-plane J⊥J_\perpJ⊥​ couplings. Our study includes very small values of the system anisotropy Δ=J⊥/J∥Δ=J_\perp /J_\parallelΔ=J⊥​/J∥​ not studied before, and focuses on characterizing the crossover from quasi-2D topological scaling to genuine 3D critical behavior. The numerical results for the critical temperature unambiguously reveal a logarithmic scaling with ΔΔΔ, directly related to the topological scaling in the 2D limit. Despite the 3D nature of the layered XY criticality, topological scaling signatures survive up to system sizes comparable to the crossover length ℓJ\ell_JℓJ​, which diverges at small ΔΔΔ with a scaling behavior reminiscent of the Berezinskii-Kosterlitz-Thouless (BKT) transition. This shows that genuine 3D symmetry-breaking behavior emerges only at exceedingly large system sizes when the anisotropy is very strong. Our results indicate that new experimental evidence is required to clarify the extent to which the critical signatures observed in layered strongly correlated materials are shaped by their pronounced anisotropy.
New qualitative picture of vortex length-scale dependence has been found in recent electrical transport measurements performed on strongly anisotropic BSCCO single crystals in zero magnetic field. This indicates the need for a better description of the 3D/2D crossover in vortex dimensionality. The vortex-dominated properties of high transition temperature superconductors with extremely high anisotropy (layered systems) are reasonably well described in the framework of the layered XY model which can be mapped onto the layered sine-Gordon model. For the latter we derive an exact renormalization group (RG) equation using Wegner's and Houghton's approach in the local potential approximation. The agreement of the UV scaling laws find by us by linearizing the RG equations with those obtained previously in the literature in the dilute gas approximation makes the improvement appearant which can be achieved by solving our RG equations numerically.
We investigate the critical behavior of the gauge-glass model for the vortex-glass transition in three-dimensional superconductors, including screening of the interaction between vortices. A Monte Carlo study of the linear resistivity and a scaling analysis of current-voltage characteristics indicates that screening destroys the finite-temperature transition found earlier when screening was neglected. The correlation-length exponent at the resulting zero-temperature transition is found to be $\ensuremath{\nu}=1.05\ifmmode\pm\else\textpm\fi{}0.01$.
Fundamental properties of the Kosterlitz-Thouless-Berezinskii (KTB) transition which occurs in systems in the universality class of the two-dimensional X-Y model are reviewed here with an emphasis on the real-space renormalization-group analysis used to derive the recursion relations. A derivation of the unique temperature dependence of the correlation length of this system will be presented and the signatures of the KTB transition in electronic transport measurements will be explained. Extensions of this model and technique to layered superconductors will also be presented. The size of the three-dimensional (3D) critical region, the nature of the 3D cross-over, and the effect of a finite electric current will be discussed.
We consider the fluctuation conductivity in the critical region of a disorder induced quantum phase transition in layered d-wave superconductors. We specifically address the fluctuation contribution to the system’s conductivity in the limit of large (quasi-two-dimensional system) and small (quasi-three-dimensional system) separation between adjacent layers of the system. Both in-plane and c-axis conductivities were discussed near the point of insulator-superconductor phase transition. The value of the dynamical critical exponent, z = 2, permits a perturbative treatment of this quantum phase transition under the renormalization group approach. We discuss our results for the system conductivities in the critical region as function of temperature and disorder.