Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions

Details Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions

1999-03-15

arxiv.org/abs/cond-mat/9903222v2

Physical Review B60, 7473 (1999)

Physics

Condensed Matter

Statistical Mechanics

18 pages, four Postscript figures, REVTEX style, Physical Review B 1999. We have added one important reference to this version

Scientific paper

10.1103/PhysRevB.60.7473

We have studied a quantum Hamiltonian that models an array of ultrasmall Josephson junctions with short range Josephson couplings, $E_J$, and charging energies, $E_C$, due to the small capacitance of the junctions. We derive a new effective quantum spherical model for the array Hamiltonian. As an application we start by approximating the capacitance matrix by its self-capacitive limit and in the presence of an external uniform background of charges, $q_x$. In this limit we obtain the zero-temperature superconductor-insulator phase diagram, $E_J^{\rm crit}(E_C,q_x)$, that improves upon previous theoretical results that used a mean field theory approximation. Next we obtain a closed-form expression for the conductivity of a square array, and derive a universal scaling relation valid about the zero--temperature quantum critical point. In the latter regime the energy scale is determined by temperature and we establish universal scaling forms for the frequency dependence of the conductivity.

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