The Effects Of Quantum Sizes And Gradient Disorder On The Persistent Currents In Finite-width Mesoscopic Rings

Due to the phase coherence of the electronic wave function, we can observe much fancy physical phenomena in mesoscopic system. One very uniquely macroscopical quantum phenomena is the persistent current, induced by the magnetic flux through the centre of a normal mesoscopic ring. This persistent current is a thermodynamic equilibrium, non-dissipative and observable current, flowing around a non-superconducting ring. In this thesis, we will employ the tight-binding model, and theoretically study the effects of quantum sizes and gradient disorder on the persistent current in finite-width mesoscopic rings. The present thesis is organized as follows:In chapter 1, some basic concepts of mesoscopic physics are briefly introduced, and then a brief review of basic theoretical and experimental investigations on the persistent current are presented. We also review the effects of disorder and quantum sizes on the persistent current in mesoscopic rings.In chapter 2, the effect of quantum sizes on the electronic structures and thus the persistent currents of graphene rings are investigated. In zigzag hexagonal graphene rings (HGRs), it is found that the sample ring becomes metallic at odd ring width N but semiconducting at even ring width N, showing up a strange odd-even width effect. In the metallic ring, the persistent current within a flux period is linearly changed with magnetic fluxφ, while it is a sinusoidal periodical function ofφin the semiconducting ring. Especially, this odd-even width effect may be disappeared in the wider rings. In diamond-like graphene rings (DGRs), we calculate the electronic structures and the persistent currents in armchair and zigzag DGRs respectively. It's shown that one third armchair DGRs exhibit to be metallic rings, while all the zigzag ones exhibit to be metallic rings. Especially, in the metallic zigzag DGRs, the persistent currents are declined generally by two orders of magnitude compared with the sizable metallic armchair DGRs. The results show that one can modulate the electronic transport properties of GRs by cutting and patterning their geometries.In chapter 3, we explore the effects of the disorder gradient and the structure sizes on persistent currents in the disorder-order two-dimensional mesoscopic ring. In the absence of disorder gradient, the persistent current firstly decreases and then increases with disorder strength, indicating a localized-ballistic-like transition existing there. In the presence of disorder gradient, the persistent current is decreased. In the case of exponentially decaying disorder, especially, the localized-ballistic-like transition is disappeared, meaning that its observability depends on the distribution of the gradient disorder. In addition, the effects of both the ring width and the penetrative depth of the disorder on persistent currents are explored, showing up a strange quantum sizes effects.Lastly, a conclusion of this thesis is present and some prospects for further investigation are discussed.