Ground-state properties of charge and magnetically frustrated two-dimensional quantum Josephson junction arrays

T. K. Kopeć; T. P. Polak

doi:10.1103/PhysRevB.66.094517

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Ground-state properties of charge and magnetically frustrated two-dimensional quantum Josephson junction arrays

T. K. Kopeć, T. P. Polak

DOI 10.1103/PhysRevB.66.094517 · Physical Review B

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Abstract

We study a quantum Hamiltonian that models a two-dimensional array of Josephson junctions with short-range Josephson couplings (given by the Josephson energy EJ) and the charging energy EC—due to the small capacitance of the junctions. We include effects from both the self-C0 and the junction-C1 capacitances in the presence of an external magnetic flux f=Φ/Φ0, as well as uniform background of charges qx. We derive an effective quantum nonlinear σ model for the array Hamiltonian, which enables us a non-mean-field treatment of the zero-temperature phase transition. We calculate the ground-state phase diagram, analytically deriving EJcrit(EC,qx,f) for several rational fluxes f=0, 12, 13, 14, and 16, which improves upon previous theoretical treatments.