Phase-dependent energy spectrum of quasiparticles in a superconducting superlattice

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Abstract
The energy spectrum of the quasiparticle state in a superconducting superlattice is investigated based on the Kronig-Penney superlattice model. Andreev reflection which originates from the multilayered structure is completely taken into account. The energy spectrum of quasiparticles is strongly influenced by the lattice period and the pair-potential phase increment (φ) over one period. From the energy spectrum, the presence of the three states, i.e., the superconducting state, the gapless superconducting state, and the normal state is elucidated and the phase diagram is obtained in the parameter space of the lattice period and the phase difference. If the unit period is short, the reduction of the pair potential is caused by the proximity effect and the difference (φ) of the phase. In such a case, the φ dependence of the supercurrent is very different from the prediction of previous perturbational theories.