Abstract
Josephson junctions hybridized with an array of superconducting islands are studied. Assuming large on-site Coulomb interactions, a particle number and a Josephson critical current are calculated as functions of voltages of two leads based on a hard-core boson model, which is equivalent to a spin system with boundary fields. After the Wigner-Jordan transformation, an additional factor depending on the parity of the particle number appears at the boundary. This factor neglected in the previous issues crucially determines properties of the junction. The boundary effects due to this factor are discussed by studying resonant tunneling peaks in critical currents and phase dependence of Josephson currents.
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