Josephson half-quantized vortices in long square π junctions around d-dot

We investigate patterns composed of four Josephson half-quantized vortices around a square dot of d-wave high-T c superconductor (d-dot) embedded in the conventional superconductor matrix by solving the time-dependent Ginzburg-Landau equation considering the Josephson coupling between s and d-wave superconductors at the interface. With increasing the d-dot size, we find that possible patterns of Josephson half-quantized vortices around the d-dot change from 2 diagonal patterns to 6 patterns including non-diagonal ones. In array configurations of d-dots, these 2 and 6 patterns enable to create novel frustrated systems which are useful for computing devices