Capacitance-matrix and geometrical effects on the ground-state properties of quantum Josephson-junction arrays

T. K. Kopeć; J. V. José

doi:10.1103/PhysRevB.63.064504

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Capacitance-matrix and geometrical effects on the ground-state properties of quantum Josephson-junction arrays

T. K. Kopeć, J. V. José

DOI 10.1103/PhysRevB.63.064504 · Physical Review B

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Abstract

We study the zero-temperature quantum phase transition in a two-dimensional network of Josephson-coupled junctions that include capacitance-matrix effects. Here the charging energy EC of the array is characterized by the interplay of the self-(C0), and mutual-junction (C1) capacitances. We study the competition between EC and the Josephson energy, EJ, by mapping the quantum Hamiltonian of the array onto an effective quantum action that generalizes the classical spherical model and that captures the influence of the spatial and quantum fluctuations. This formulation improves over the mean-field theory method. In this approach the invariance of the phase fluctuation algebra between number and phase operators (given by the Euclidean group E2) is mapped onto the corresponding formulation of the solvable quantum spherical model. We have examined the T=0 superconductor-insulator phase boundary as a function of C0 and C1 for various two-dimensional array geometries, to wit: the square, triangular, and honeycomb lattices.