中文摘要：

研究了具有p波超流的一维非公度晶格中迁移率边的性质.发现适当的p波超流可以增加体系中的迁移率边的数目,并且通过多分形分析确定了迁移率边所在的位置.

英文摘要：

The mobility edges which separate the localized energy eigenstates from the extended ones exist normally only in three dimensional systems.For one-dimensional systems with random on-site potentials,one never encounters mobility edges,where all the eigenstates are localized.However,there are two kinds of 1D systems such as correlated disordered models,and the systems of exponentially decaying hopping kinetics,features of mobility edges at some specific values become possible.We study in this paper the properties of the mobility edges in a one-dimensional p-wave superfluid on an incommensurate lattice with exponentially decaying hopping kinetics.Without the p-wave superluid,the system displays a single mobility edge,which separates the extended regime from the localized one at a certain energy.Without the exponentially decaying hopping term,the system displays a phase transition from a topological superconductor to an Anderson localization at a certain disorder strength,where no mobility edge exists.We are interested in the influence of the p-wave superfluid on the mobility edge.By solving the Bogoliubov-de Gennes equation,the eigenvalues and the eigenfunctions are obtained.In order to identify the extending or the localized properties of the eigenvectors,we define an inverse participation ratio IPR.For an extended state,IPR_n~ 1/L which goes to zero at a large L,and for a localized one,IPRnbeing constant.Therefore,the IPR can be taken as a criterion to distinguish the extended state from the localized one,while the mobility edge is defined as the boundary between two different states.We find that,with a p-wave superfluid,the system changes from a single mobility edge to a multiple one,and the number of mobility edges increases with the increased superfluid pairing order parameter.To further obtain the energy or the location of the mobility edge,we investigate the scaling behavior of wave functions by using a multifractal analysis,which is calculated through the scaling index α.The minimum value of the index,with