Transformer Configuration in Three Dimensional Josephson Lattices at Zero Magnetic Field

Abstract

Recent experiments on Bi2Sr2CaCu20q Y superconductors at zero magnetic field have been performed with a transformer configuration of contacts. We interpret the experimental data on the basis of largescale Langevin dynamical simulations of a three dimensional (3D) Josephson lattice with a current bias through a single plane. We show that the experimentally observed effects can be attributed to linking thermal vortex loop excitations that cause voltages in neighboring superconducting planes to lock in a narrow temperature range near the 3D phase transition. PACS numbers: 74.50.+r, 64.60.Cn, 74.60.Ge, 74.72.Hs Giaever, in a pioneering "dc flux transformer" experiment showed that, with vortices linking two superconducting films, a current drive in the upper film induces locked voltages in both films [1]. A similar contact configuration has been used recently to study nonlocal transport properties of high-T, superconductors [2 -6]. In these experiments a current was fed into one ab face of a single crystal, and both the primary voltage drop (across the same face) and secondary drop (across the opposite face) were measured. Most of the experiments were performed in a magnetic field both in Bi2SrzCaCu20 [2,6] and in YBa2Cu307 [3,4], to probe vortex motion along the crystal c axis through the correlations between the primary and secondary voltages. The experimental results have been interpreted as due to a nonlocal conductivity [7] in the linear regime of the vortex liquid, and due to flux-line cutting phenomena [8] in the nonlinear regime below the irreversibility line. Recently, Wan et al.[5] have conducted transformer experiments at zero magnetic field in Bi2Sr2CaCu20g~, finding a peak in the secondary voltage around the critical temperature T,~Here, we provide a theoretical interpretation of this latter experiment.The high-T, superconductors can be modeled by assuming that, below a mean field transition temperature TM", the relevant physics is given by the thermal fluctuations of the phase 0 in the superconducting order parameter I" =~' Ir~e' . A lattice version of this approach leads to the anisotropic three dimensional (3D) XY model or Josephson lattice [9 -13], the anisotropy arising from the layered nature of the high-T, superconductors. This model has been extensively applied to the study of the thermodynamic phase transitions at both zero [9 -11] and finite magnetic fields [12] in high-T, superconductors.The Hamiltonian of the 3D anisotropic XY model is =g J"cos5~0(r), r, p, where 0(r) is the phase at the 3D lattice site r, 5~0(r) = 0(r + p, ) -0(r), and p, = x, y, z. The anisotropy is gJ = J~/J~~, with J, = J~= J~~a nd J, = Ji.To study a current-driven sample, the flow of current has to be modeled taking into account local dissipation and that a time dependent phase induces a voltage V = (4u/2m. ) (d0/dt), with 4o = h/2e, the quantum of Aux. This is usually studied with current-conserving overdamped Langevin dynamics [13]. The current I~(r) fiowing in each bond of the 3D cubic lattice is taken to be I"(r) =...

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