The Construction Of Two Dimensional Quasicrystal Model And Its Physical Properties

Quasicrystals have become one of the current research hotspots because of their good corrosion resistance,thermoelectricity,and optical properties.In order to explore the physical properties of quasicrystals,this paper selects a two-dimensional quasi-crystal model constructed using Fibonacci sequences as the research object.One-dimensional quasi-periodic order is constructed using the Fibonacci sequence,a two-dimensional quasicrystal model was constructed by cutting and projecting,by changing the transition items and lattice ordering,the relationship between the chern number and Fermi surface of models is analyzed.This article is mainly divided into three parts:First,a one-dimensional quasi-periodic sequence is solved using the Fibonacci sequence.A plan named conumbering was introduced.Using the Fibonacci sequence,the parallelogram was selected in a two-dimensional space,and the integral grid points contained in it were projected and analyzed.It was found that the spacing of the grid points after projection was arranged in a quasi-periodic manner.Second,it mainly introduces how to build a two-dimensional quasi-crystal model.A two-dimensional quasi-crystal model was constructed using the Fibonacci sequence.The nearest neighbor transition terms were randomly generated in the model.The quasi-crystal model obtained at this time is formed by the rhombuses with equal sides and equal areas.Third,this part mainly introduced the annular model and two dimensional quasi crystal transition items in the model,the relationship between the chern number and Fermi surface of models is analyzed.details as follows:1.The nearest-neighbor transitions are randomly generated.In the nested hexagonal lattice,the next nearest neighbor transition item is added.The variation of the chern number with the Fermi surface is observed.The analysis shows that the chern number of this model is not an integer,that is,this model cannot open the gap and cannot achieve the topological nature.2.Based on the first method to further explore the model.Nearest neighbortransition a randomly generated,adding next nearest neighbor transitions in a non-nested hexagonal lattice.Again,analysis the relationship between the chern number change with the Fermi surface,it is concluded that the chern number of models is still not an integer,that is,this model cannot open gaps.3.Based on the above two methods,transform the model parameters,delete parts of grid point,more close to the Haldane model brings out the standard of the model.Model are divided into two groups: one group is nearest neighbor transition randomly generated,the next nearest neighbor transition is the same as the Haldane model;The other group is the same as the Haldane model in the nearest neighbor transition and the next nearest neighbor transition.The topological properties of the model can be analyzed by comparing the transitions between the two groups of models.