The Applications Of Periodic Modulation In Topological Semimetal Model

Recently,periodic modulation has become a popular research tool.It is used in many branches of research fields with plentiful physical diagrams espe-cially in cold atomic systems.Under the fundamental framework of topological insulator,the sophisticated single-particle Floquet theorem and topological clas-sification could be described in these problems with explicit time dependence.According to the continuous research of Dirac and Weyl semimetals in the cold atomic experiments during these years,we choose periodic modulation to study this class of nonequilibrium topological exotic phenomenon.In this context,we study periodic modulation problems in the regime of weakly driving field that the width of static spectrum is of the same magnitude with the driving frequen-cy.We offer a proposal to design a nonequilibrium topological semimetals based on Floquet theorem.In the time-frequency-domain formalism,we calculate the effective Hamiltonian and analyze the high frequency expansion.We classify the driven system as Floquet induced Weyl semimetals and anomalous Floquet Weyl semimetals according to the static mass.Then we study the properties of the edge and the bulk.At last we achieve topological semimetals in a nonequilibrium state which has no correspondence in the static case.The structure of this article is as follows:In the first chapter we introduce the equilibrium topology and nonequilibri-um topology and give a review.In the second chapter,firstly we discuss the Weyl equation and the corre-sponding general definition and characteristics in condensed matter and cold-atom regime including the differences and similarities with topological insulator.Then we show the equilibrium topological semimetal model in the cold atomic system,and we give the specific numerical results of definite topological invariant.In the third chapter,we mainly have a review on Floquet paradigm and for-malism.We give several distinguishable physical interpretations under periodic modulation.In the fourth chapter,we propose the theoretical topological semimetal mod-el in the low frequency driving case based on the picture of two-dimensional Floquet topological insulator.Then we obtain the effective Hamiltonian in the time-frequency-domain Floquet theorem.Furthermore,we do the numerical cal-culation to obtain the quasienergy spectrum.We analyze the differences between the closing and opening of driving field with high frequency expansion.Then we study the bulk and the edge properties,calculate the quasienergy variation a-long the path of high-symmetry points,and the slice Chern number of nearest Floquet bands.In the end a comparison is made between the two Floquet Weyl semimetals.In the last chapter,we conclude and make some proposal.