Theoretical study for the superconducting state in nano-superconductors

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In this research project we studied the Josephson effects in small complex systems composed of unconventional d-wave and conventional s-wave superconductors from viewpoints of both basic physics and quantum devise applications. When a d-wave superconductor with d(x^2-y^2)-symmetry of square shape is embedded in a s-wave superconducting matrix, the system forms a closed 0-π Josephson junction in which vortices with half-flux quanta appear spontaneously. We construct a theory describing the phase dynamics in this complex system. When the size of the system is small enough, the quantum fluctuations dominate the system. We rigorously prove that this system behaves as a quantum two-level system in the quantum regime. The qubit applications were discussed. In this research project we also investigated the intrinsic Josephson effect observed in Bi-2212 high temperature superconductor. The origin of unusual field dependence of the microwave resonance absorption spectrum observed in Bi-2212 under a magnetic field parallel to the layers was clarified. The I-V characteristics and terahertz emission in a stack of intrinsic Josephson junctions were also discussed.