Theoretical Study On Topological Effects Of Phonons

Phonon,which is one of the most important elementary excitations in condensed matter physics,plays an important role in both fundamental physics and pratical appli-cations.On the other hand the discovery of topological states of quantum matter,such as the quantum（anomalous/spin）Hall effects and topological insulators,has changed our understanding about the classification of matter phases and revolutionized the re-search of both fundamental physics and material science.In this thesis we brought the concept of topology to the study of phonon:From the fundamental theory of lat-tice vibrations we derived a theoretical method to deal with topological properties of phonon.Based on this method we investigated a series of two dimensional（2D）or three dimensional（3D）topological phonon states and their novel topological quantum effects.First,we derived a Schr（?）dinger-like equation for phonon,based on which the phonon Berry connection,Berry curvature,and Chern number can be properly defined,and the non-equilibrium Green’s function method of phonon can be generalized for the transport study of topological phonons.We applied the method to 2D honeycomb lattice model with broken time-reversal symmetry.This lattice realizes a phononic Haldane model which describes the quantum（anomalous）Hall-[Q（A）H-]like effects of phonons.The Q（A）H-like effects support one-way edge states,which are useful for dissipationless phonon waveguide and high-efficiency phonon diode.Next,we studied topological effects of phonons in 2D Kekulé lattice（i.e.2D honeycomb lattice under Kekulé distortion）.In this system we found Kekulé phonons can be characterized by pseudospin degree of freedom.Pseudospin polarized phonons have quantized pseudosangular momentum and quantized Berry phase.Pseudospin-momentum locked topological boundary states can be realized at the interface of Kekulé lattices.Moreover,the pseudospin supports a series of novel quantum physical phenomena:the pseudospin Zeeman effect,the pseudospin Hall effect and the pseu-dospin contrasting（Raman/Infrared）optical selection rule.As realistic material can-didates,we propose that the graphene-Sb₂Te₃heterostructure and the biaxial strained graphene can host Kekulé phonons.Finally,we found that 3D lattices with C_nv（n=3,4,6）group symmetry e.g.tri-angular,hexagonal,and tetragonal lattices can realize nontrivial Z₂topological phonon states.For different parameters,two different types of pseudospin-momentum locked surface states can be realized:the type-I surface states have linear dispersion relation,quantized Berry phase±π,and pseudospin winding number±1;the type-II surface states have quadratic dispersion relation,quantized Berry phase 2π,and pseudospin winding number 2.When travelling across a phononic barrier potential,the two dif-ferent kinds of topological surface states exhibit different chiral transport behaviors,which can be used for phononic transistor.