Modulations Of Chiral Order Parameters In Mesoscopic P-wave Superconducting Systems

With the development of nanofabrication techniques,novel quantum effects in mesoscopic superconducting systems as well as their practical applications become a very promising research domain.The size of a mesoscopic superconducting sample is comparable to the magnetic-field penetration depth ? or the coherence length ?.Its superconducting property is strongly affected by the sample size,boundary conditions as well as the impurities and defects.Particularly,stable topological states in mesoscopic p-wave superconductors with broken time-reversal symmetry have attracted considerable interest due to the existence of quantum confinement effects.Based on our previous works,the project aims at a theoretical investigation of the modulations of chiral order parameters in mesoscopic p-wave superconducting systems in the framework of the Bogoliubov-de Gennes theory.Through considering proper physical models,the effects of impurities and surface defects will be studied systematically.Main results are summarized as follows:(1)We first study the influence of magnetic or non-magnetic impurities on the modulations of chiral order parameters.When a single non-magnetic impurity is involved into the loop system,the gap parameter is strongly modified with tuning flux for finite impurity strength.Particularly,an impurity-induced intermediate state with asymmetric feature of the order-parameter distributions shows up stably.Due to the appearance of energy jumps at the points of phase transitions,pronounced sawtooth-like patterns of the currents are induced,which are highly sensitive to the located impurity site.(2)We have investigated the effect of surface defects on the modulations of order parameters in mesoscopic p-wave superconducting noncircular loops.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.