We investigated the magnetic flux dependence of the supercurrent in mesoscopic $d$-wave superconducting loops, containing impurities and surface defects, by numerically solving the Bogoliubov–de Gennes equations self-consistently. In the presence of impurities, bound states arise close to the Fermi energy. In the case of a single impurity, the flux-induced current is found to be suppressed. This can be different when more impurities are introduced in the sample due to the quantum interference effect, which depends sensitively on the relative position between the impurities. We further analyze the effect of small surface defects at the inner or outer edge of the loop, and show that indentation and bulge defects have pronounced and different effects on the supercurrent.

• Received 21 April 2011

DOI:https://doi.org/10.1103/PhysRevB.84.132501