Effect of surface defects on order modulations in mesoscopic p-wave superconducting loops

The effect of surface defects on the modulations of order parameters in mesoscopic p-wave superconducting noncircular loops with threaded magnetic flux is investigated by numerically solving the Bogoliubov-de Gennes equations self-consistently. For the case of a square loop, the sharp-jump evolution of the total energy and the sawtooth pattern of the current in flux take place when a square indentation defect is introduced at the center of the outer or inner boundary, accompanied by phase transitions between the states with diagonal-symmetric and asymmetric spatial profiles of chiral orders. Particularly, peculiar spatial patterns of the orders can occur with moving the indentation defect farther from the edge center or positioning the bulge defect at the inner or outer edge of the sample. Furthermore, the cases of two rectangular loops with different outer sizes were investigated where we consider the effect of a square indentation defect in the middle of the short or the long side of the sample. More complicated phenomena on the order modes can be found due to the aspect-ratio effect as well as the defect effect. Graphical abstract