Electronic structure of a half vortex

Half vortices spontaneously emerge in corners of d-wave superconductor dot embedded in s-wave superconducting matrix due to the phase interference between superconducting order parameters with different symmetries. Since these half vortices are robust to external perturbations, high potentialities toward novel device applications are expected. In order to clarify quantum features of these half vortices we perform numerical calculations for the electronic structure of d-wave superconductor dot embedded in s-wave superconducting matrix. Consequently, we find that discrete levels appear inside the superconducting gap of the s-wave superconducting matrix due to the coupling between the core states of half vortices and the localized quantized states inside d-dot. These isolated levels may be favorable for the realization of qubits.