Superconducting phase transition in quantum three-dimensional Josephson junction arrays: c-axis anisotropy and charge frustration effects

Abstract

We study the quantum phase transition in three-dimensional network of Josephson-coupled junctions including anisotropy and capacitance-matrix effects. The quantum effects are due to the charging energy EC which is related to interplay of self-(C0) and mutual (or junction C1) capacitances. The anisotropy is defined as the ratio of the in-plane Josephson energy EJ‖ to the interlayer one EJ⊥. The external charge frustration effects are also considered at both zero and finite temperatures. To capture the effects of quantum and spatial fluctuations we go beyond the mean-field level description. Noting that the invariant of phase fluctuation algebra between number and phase operators (given by the Euclidean group E2) is related to the closure relation of the corresponding solvable quantum spherical model we map the quantum Hamiltonian of the array onto an effective action of a generalized spherical model in the path integral formalism. Subsequently, we examine the T=0 and finite-temperature superconductor-paracoherent phase boundary as a function of various control parameters.

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