Topology In Periodically Driven System

In the last decades,we witnessed and cheer for the flourishing topological physics in Condensed matter.One of the major topics in this field is to find out and classify the interesting novel topological matters and phenomena,they are characterized by topological numbers such as Chern number,Z2 number.Recent years,more and more work are focusing on enriching the topologically nontrivial candidates through periodically driven the matters.They developed time-independent effective Hamiltonian of time-periodical system to analogize to a static model,which is well studied in last decades.This thesis is going to introduce two relative works about novel topological phenomena in periodically driven systems,also introduce the basic knowledge about topological physics and Floquet theory.In the first work,we use Floquet theory to illustrate that novel Floquet Weyl points can be created in 3D sliding graphene model irradiated by circularly polarised light.Each pair of Weyl points have a two-component semi-Dirac point(SDP)parent,instead of a four-component Dirac point parent.The Weyl semimetal(WSM)phase occurs when the radiation frequency is on the order of magnitude of hopping parameters of lattice,where SDP will emerge successively and evolve to two pairs of Weyl points with the frequency decreasing.The Weyl points emerging due to the overlap of Floquet sub-bands provide a new platform to study Weyl fermions.In the other work,we promote a dimer chain under a w frequency lengthwise AC elctronic field and a 2w frequency perpendicular AC electronic field,and found that the effective 2D lattice is topologically nontrivial under the properly parameters arrangement.Further the effective electric field will cause quantum Hall current,which Fourier transform back to real space is the quantum ratchet current.This phenomenon is so call Quantum Floquet Ratchet effect.This new phenomenon is attractive because it's useful to design novel robust low-energyconsumption electronic applications.