Quantum Transport In Quasiperiodic Structures

A one-dimensional(1D)lattice Aubry-Andre-Harper(AAH)model with mosaic quasiperiodic potential is found to exhibit special localization properties,such as clear mobility edges.In this thesis,we extended this mosaic quasiperiodic model to a two-dimensional(2D)model,and its localization characteristics are studied through numerical calculations,including: the phase diagram from the fractal dimension of the wavefunction,the statistical and scaling properties of the conductance.Compared with disordered systems,our model shares many common features but also exhibits some different characteristics in the same dimensionality and the same universality class.For example,the sharp peak at g = 0 of the critical distribution and the large g limit of the universal scaling function β resemble those behaviors of three-dimensional(3D)disordered systems.The full text of the research is as follows:Firstly,Anderson localization theory,quasiperiodic AAH model and mobility edge are briefly introduced.The current numerical methods for calculating the AAH model are described in detail and their respective advantages and disadvantages are compared.At the end of this chapter,the research status of the AAH model is introduced.Next,the calculation methods and definitions of related physical quantities used in the research process of this thesis are introduced,including one-dimensional and two-dimensional tight-binding models,inverse participation rate,fractal dimension,Green’s function and the scaling relationship of metal-insulator transition.Next,some physical properties of the two-dimensional quasiperiodic mosaic AAH model are investigated,and the images of the eigenstate phase diagram,the scaling relationship and the statistical law of conductance are plotted from numerical calculations.The results show that the mobility edge of the extended state-local state transition occurs after the quasiperiodic potential strength reaches a critical point.Also,this chapter summarizes all numerical results for the conductance of the universal scaling function β(g),a result that shows some characteristics different from those of the disordered two-dimensional system.Unexpectedly,these results are similar to some properties found in the three-dimensional disordered system.Finally,all conclusions are summarized and future works are proposed.