Vortex-state-mediated Josephson Effect

The Josephson efect is a kind of macroscopic quantum phenomenon that super-current fows through a Josephson junction made of two superconductors connectedby a thin insulating layer by Cooper pair tunneling without any voltage applied.Vortex structures especially the Abrikosov vortex lattices in type II superconductorsattracts a lot of attention. We design a new kind of complex Josephson junctionstructure, which consists of two supercondcting layers each with a hole, and a hol-low normal conducting cylinder. The superconducting layers are connected withthe normal conducting cylinder ideally. Vortex bound states are expected insidethe holes in the superconducting layers. These vortex bound states will involve inthe Josephson tunneling process, which fnally results in a new kind of Josephsonefect—vortex-state-mediated Josephson efect.We investigate the evolution of supercurrent in response to the changing of thesuperconducting phase diference. We fnd that The vortex-state-mediated super-current is enhanced or reduced signifcantly in magnitude depending on the junctionlength, and exhibits several steps with the number of efective propagating channelsin current-phase relaiton at zero temperature. At fnite temperatures, these super-current steps persist in the short junction limit, and develop into sawtooth oscilla-tions if the junction length becomes comparable to the coherence length ξ0=vF/of the superconductor, and in later case a supercurrent reversal can be observed.These fndings may provide a smoking-gun signature of vortex bound states in su-perconductors and promise possible applications in future Josephson devices.This thesis consists of three chapters. Some notions and the research back-ground are introduced in Chapter1. Chapter2is the main body of this thesis,which includes how we model this new kind of Josephson junction structure andprovides details of formulation,calculation, and analysis. We give some concludingremarks in Chapter3.