Study Of Optical Manipulation Of Higher Order Topological Semimetal And Higher Order Topological Superconductor

Topological matter are a novel type of quantum states that,unlike trivial states of matter,have topologically protected boundary states,singular band structures,and bulk-edge correspondence.Topological phases go beyond traditional phase transition theory and have attracted widespread attention from theoretical and experimental researchers,achieving significant progress in both theory and experiment.Recently,there has been extensive development in the theoretical and experimental study of topological states of matter,with the most notable being topological insulators that possess an insulating bulk state and conducting edge states protected by time-reversal symmetry at the boundary.In recent years,with the deepening of research,the study of topological phases has been further extended to topological semimetals,topological superconductors,topological magnons,and higher-order topological phases.In this thesis,we study the optical drive phase transitions in topological semimetals and higher-order topological phases in superconductors using analytical and numerical methods.First,we discuss the effect of circularly polarized light on higher-order Dirac semimetals.Regardless of the presence of gapless surface Fermi rings,circularly polarized light can drive the higher-order Dirac semimetal to transition to a Weyl semimetal phase with higher-order hinge Fermi arcs.When the propagating direction of circularly polarized light is changed,the ratio of tilt of the Weyl cone changes accordingly.We thus achieve an optical drive phase transition from a type-I to a type-II Weyl semimetal.Using a low-energy continuous model,we further explain the reason for the tilt of the Weyl cone.Second,we also study the Majorana zero modes in higher-order topological superconductors and topological defects.In superconductors,the mixed-time-reversalsymmetry-breaking superconducting pairing can induce a higher-order topological state with localized Majorana zero modes at each corner.For first-order topological superconductors that maintain time-reversal symmetry,topological defects can create two pairs of Majorana zero modes bound at the defect positions,but they can be destroyed by the mixed superconducting pairing and cannot exist in such higher-order topological superconductors.We further analyze the properties of these Majorana zero modes based on edge theory.