Study Of Topological Bloch Oscillation And Some Specific Topological States

In recent years,topological insulators have aroused a wide interest among physics researchers.Unidirectional transmission of electrons is stable at the interface of topological insulators with topological phase transition,which have an attractive prospect in realizing new electronic devices.Therefore,topological insulators have became a hotspot in condensed matter physics in recent years,and the concept has been quickly penetrated into other disciplines of physics such as optics,electromagnetism,Bose-Einstein condensates and so on.In this dissertation,we study the effects of topological systems on traditional Bloch oscillations,and find some special linear and nonlinear topological eigenstates.The main research work and achievements are as follows:(1)We studylight propagation in the array of helical waveguides with transverse refractive index gradient,both in 1D and 2D geometries.While wave packets in such modulated systems still experience BOs,their amplitude and direction strongly depend on waveguide rotation radius.Our finding suggests potential applications of the helical waveguides in the control of path and direction of light beam propagation.For critical helix radius,the band collapses becoming flat;thus the propagation of any light beam in the structure in this regime is free of diffraction.(2)We study the Bloch oscillations of topological edge states.We find that a complete Bloch oscillation undergoes a transition from a edge state on one side to an bulk state,then coupling to a edge state on the other side,finally coupling back to the edge state on the original side.Since the wave packet have to pass through the Brillouin region twice to complete a Bloch oscillation,the Bloch oscillation period of topological state is twice as long as that of ordinary system.(3)We investigate the behavior of optical transmission in the longitudinally modulated nanowire arrays and propose the concept of surface plasma topological insulator(PTIs).In order to obtain the non-trivial SPPs topological edge states,we break the time inversion symmetry of the system by longitudinal modulation of the nanowires.SPPs topological state has the both advantages of SPP mode and topological insulator: it not only breaks through the diffraction limit of light,but also can avoid backscattering due to the defects of the immune structure in the transmission process.(4)In the semiconductor microcavity array,we study the topological states under the spin-orbit coupling in detail.The energy level splitting of TE and TM polarization modes of the photons in the microcavity forms an artificial spin orbit coupling system,which breaks the time inversion symmetry of the system.In the one-dimensional SSH array,we study the topological zero-energy modes which localized in the center of energy spectrum,and analyze the regulation effect of time inversion symmetry breaking on energy level of zero-energy mode.In the two-dimensional SSH array,we study the topological zero-energy mode which can move along the lattice edge,and propose the concept of one dimensional zero energy mode.Owing to the breaking of the symmetry of time inversion,a pair of counterpropagating edge modes,of which one has a momentum k and the other has-k,is no longer of energy degeneracy.Thus,strong ability to bypass obstacles appears in the process of transmission.In addition,we study the topological unidirectivity of ring edge states in a hexagon graphene lattice with finite size.Furthermore,with the combined action of nonlinearity,pump light and loss,we find topological bistable phenomenon in the topological gap.(5)In a Bose-Einstein condensed matter system,we systematically studied Bragg scattering of topological states in the Zeeman lattice.Two chiral topological edge states(rashba-soc and dresselhau-soc)were obtained by using the Zeeman effect and SOC,which broke the time inversion symmetry of the system.We coupled two topological states to form a new topological state which localized on the lattice interface.When periodic perturbation modulation is introduced on the lattice interface,we realize Bragg scattering of topological states.If the system satisfies both the law of conservation of energy and the matching condition of momentum,the topological modes can be transformed into each other efficiently.Finally,after introducing nonlinear response into the system,we consider the cross-phase modulation and self-phase modulation between two topological modes to obtain the stable Bragg topology solitons.