Monoclinic C₂₄:A Novel 3D Topological Nodal-Line Semimetal

The purpose of this thesis is to use first-principles calculations and Wannier tight-binding model analysis to theoretically study the various structurally related properties and body topological properties of a newly discovered carbon allotrope mC₂₄.The main research scheme is to check the mechanical stability,energy stability,dynamic stability and thermodynamic stability of mC₂₄,and to study the newly discovered topological properties of mC₂₄,proving that it is a topological nodal-line semimetal.As we all know,carbon can exist in many ways and has an excellent ability of transition from one phase to another.Based on previous work and research ideas,this dissertation proposes a monoclinic allotrope of carbon with 24 carbon atoms in a unit cell,and studies its topological properties.First,we confirmed the dynamic stability of mC₂₄ based on the phonon spectrum.Then,by studying the energy/volume relationship and comparing it with other allotropes of carbon reported previously,the energy stability of mC₂₄was determined.Then,by calculating its elastic constant,based on the Born stability criterion,the mechanical stability of mC₂₄was also studied.Finally,the thermal stability of mC₂₄was studied based on molecular dynamics simulation.After determining the stability of mC₂₄,special attention to the intrinsic topological response of this newly discovered carbon structure was paid.When the word"topology"comes,we should immediately think that this is a mathematically research object,and the properties of the object are constant under smooth deformation.This dissertation has conducted a comprehensive study on it,including the concept of topological nodal-line semimetal,mC₂₄response to topology,different topological characteristics displayed by mC₂₄,software used to calculate and study these topological responses,and the problems and their countermeasures taken during the course of research.The electronic energy band structure of mC₂₄ shows that there is a single Dirac point near the Fermi level of its energy band structure,and the spin-orbit coupling effect opens a relatively larger band gap.This singular energy band structure indicates that this structure has novel physical properties.Research on its Fermi surface and the nodal-line structure protected by PT symmetry shows that it is a three-dimensional topological nodal-line semi-metal.In order to study the topological properties of the structure,a software called Wannier?Tools was used.The drumhead-like surface states,and the calculation of the Berry phase and Berry curvature bring more novelty to this study,and confirm the characteristics of the topological nodal lines in mC₂₄.The research in this thesis reveals that there is indeed a three-dimensional topological nodal-line structure in mC₂₄,and is expected to realize many applications,especially in photovoltaic electronic equipment.