One-dimensional Josephson arrays as superlattices for single Cooper pairs

Abstract

We investigate uniform one-dimensional arrays of small Josephson junctions ($E_J\ll E_C$, $E_C=(2e{)}^2/2C$) with a realistic Coulomb interaction $U(x)=E_C\lambda \exp (-|x|/\lambda )$ (here $\lambda \gg 1$ is the screening length in units of the lattice constant of the array). At low energies this system can be described in terms of interacting Bose particles (extra single Cooper pairs) on the lattice. With increasing concentration $\nu$ of extra Cooper pairs, a crossover from the Bose gas phase to the Wigner crystal phase and then to the superlattice regime occurs. The phase diagram in the superlattice regime consists of commensurable insulating phases with $\nu =1/l$ ($l$ is integer) separated by superconducting regions where the current is carried by excitations with {\em fractional} electric charge $q=\pm 2e/l$. The Josephson current through a ring-shaped array pierced by magnetic flux is calculated for all of the phases.

4 pages (LATEX), 2 figures

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• Quantum-Phase Transitions of Interacting Bosons and the Supersolid Phase
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Cited by in corpus (9)

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• Quantum Phase Transitions in Superconducting Arrays with General Capacitance Matrices
• Signatures of quantum phase transitions in the dynamic response of fluxonium qubit chains
• Renormalization-group study of gate charge effects in Josephson-junction chains
• Josephson junction chains with long-range interactions: Phase slip proliferation versus Kosterlitz-Thouless transition