Biot-Savart correlations in layered superconductors

Abstract

We discuss the superconductor to normal phase transition in an infinite-layered type-II superconductor in the limit where the Josephson coupling between layers is negligible. We model each layer as a neutral gas of thermally excited pancake vortices. We assume the dominant interaction between vortices in the same and in different layers is the electromagnetic interaction between the screening currents induced by these vortices. Our main result, obtained by exactly solving the leading order renormalization group flow, is that the phase transition in this model is a Kosterlitz--Thouless transition despite being a three--dimensional system. While the transition itself is driven by the unbinding of two-dimensional pancake vortices, an RG analysis of the low temperature phase and a mean-field theory of the high temperature phase reveal that both phases possess three-dimensional correlations. An experimental consequence of this is that the jump in the measured in-plane superfluid stiffness, which is a universal quantity in 2d Kosterlitz-Thouless theory, will receive a small non--universal correction (of order 1% in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$). This overall picture places some claims expressed in the literature on a more secure analytical footing and also resolves some conflicting views.

16 pages, 2 figures; minor typos corrected, references added

References in corpus (13)

• Vanishing of phase coherence in underdoped Bi_2Sr_2CaCu_2O_8+d
• Two-Dimensional Superconducting Fluctuations in Stripe-Ordered La(1.875)Ba(0.125)CuO(4)
• Dynamical layer decoupling in a stripe-ordered, high T_c superconductor
• Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin cuprate films
• Superfluid Density in a Highly Underdoped YBCO Superconductor
• Kosterlitz-Thouless behavior in layered superconductors: the role of the vortex-core energy
• Thin superconductors and SQUIDs in perpendicular magnetic field
• Strongly nonlinear magnetization above $T_c$ in $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{CaC}{\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$
• On the magnetization of two-dimensional superconductors
• Pancake vortices
• Flux-Cutting in YBa${}_2$Cu${}_3$O${}_{7-\delta }$ single crystals: Experiment and Phenomenological model
• Vortices in magnetically coupled superconducting layered systems
• Renormalization group approach to layered superconductors

Cited by in corpus (8)

• Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders
• Effective 2D thickness for the Berezinskii-Kosterlitz-Thouless-like transition in a highly underdoped La${}_{2-x}$Sr${}_x$CuO${}_4$
• Uniaxial linear resistivity of superconducting La(1.905)Ba(0.095)CuO(4) induced by an external magnetic field
• Tuning from failed superconductor to failed insulator with magnetic field
• Berezinskii-Kosterlitz-Thouless Transition in Heavy Fermion Superlattices
• Evolution of superconducting correlations within magnetic-field-decoupled CuO(2) layers of La(1.905)Ba(0.095)CuO(4)
• Evidence for Correlated Dynamics near the Berezinskii-Kosterlitz-Thouless-like Transition in Highly Underdoped La${}_{2-x}$Sr${}_x$CuO${}_4$
• Transport Properties of Stripe-Ordered High Tc Cuprates