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Physical review. B, Condensed matter

Critical behavior of a layered-superconductor model

Stephen W. Pierson, Oriol T. Valls, H. Bahlouli

Published Jun 1, 1992• 22 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.45.13035

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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.
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.
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.
The standard treatment of the Kosterlitz-Thouless-Berezinskii (KTB) transition is supplemented here by the inclusion of free-vortex screening effects. We obtain the high-density corrections to the KTB critical behavior. The size of the KTB critical region is extracted, and is found in most cases to be quite small. The tricritical point, separating second-order (KTB) phase transitions from first-order transitions, is also determined. We make predictions concerning similar KTB-like transitions, such as in the layered cuprate superconductors.
We explore the implications of Berezinskii-Kosterlitz-Thouless (BKT) critical behavior on the two-dimensional (2D) quantum superconductor-insulator (QSI) transition driven by the tuning parameter x. Concentrating on the sheet resistance R(x,T) BKT behavior implies: an explicit quantum scaling function for R(x,T) along the superconducting branch ending at the nonuniversal critical value Rc = R(xc); a BKT-transition line T(c)(x) [proportionality] (x - x(c))(zν[overline]), where z is the dynamic exponent and ν[overline] the exponent of the zero-temperature correlation length; independent estimates of zν[overline], z and ν[overline] from the x dependence of the nonuniversal parameters entering the BKT expression for the sheet resistance. To illustrate the potential and the implications of this scenario we analyze the data of Bollinger et al (2011 Nature 472 458) taken on gate voltage tuned epitaxial films of La2-xSrxCuO4 that are one unit cell in thickness. The resulting estimates, z ~/= 3.1 and ν[overline] ~/= 0.52, indicate a clean 2D-QSI critical point where hyperscaling, the proportionality between d/λ(2)(0) and Tc, and the correspondence between the quantum phase transitions in D dimensions and the classical ones in (D + z) dimensions are violated.
We study the quasi-two-dimensional quantum O(2) model, a quantum generalization of the Lawrence-Doniach model, within the nonperturbative renormalization-group approach and propose a generic phase diagram for layered three-dimensional systems with an O(2)-symmetric order parameter. Below the transition temperature we identify a wide region of the phase diagram where the renormalization-group flow is quasi-two-dimensional for length scales smaller than a Josephson length lJ{l}_{J}lJ​, leading to signatures of Kosterlitz-Thouless physics in the temperature dependence of physical observables. In particular the order parameter varies as a power law of the interplane coupling with an exponent which depends on the anomalous dimension (itself related to the stiffness) of the strictly two-dimensional low-temperature Kosterlitz-Thouless phase.