Topological Semimetals In Three-dimensional Carbon And Boron Networks

Boron and carbon have abundant allotropes structures due to their rich atomic bonding characteristics.In recent years,the successful preparation of some boron and carbon allotropes has attracted much attention.For example,a variety of two-dimensional(2D)boron structures and some three-dimensional(3D)graphene network structures have been reported experimentally.On the other hand,topological materials are another research hotspot.Topological semimetals of various zero-dimensional points,one-dimensional lines,and two-dimensional surfaces have been proposed and verified experimentally.However,most 3D topological materials proposed to date consist of heavy elements with strong spin-orbit coupling(SOC).The study on topological properties of 3D boron and carbon structures is still rare.In this thesis,we will study topological properties of the 3D boron and carbon materials,including new structures,new topological elements and topological phenomena.This thesis is divided into six chapters.In chapter one,we introduce the research and development of carbon and boron materials.It is particularly noteworthy that 3D carbon crystal structures have been synthesized in the recent two experiments.In addition,we also summarize the research and development of topological semimetals.In chapter two,the density functional method and calculation approaches are introduced.In chapter three,we study the electron and phonon transport properties of the recently discovered carbon honeycombs(CHCs).The results show that these carbon networks are porous triple point topological metals with two independent electron transport channels along the direction of the carbon honeycomb axis.The transport of phonons in these carbon networks is also strongly anisotropic.The calculation results also show that these porous carbon networks possess high storage capacity for gaseous atoms and molecules in agreement with experiment.In chapter four,we provide the classification of topological nodal ring semimetals,and take the carbon networks as an example to show that the complete classification of these topological nodal ring can exist in the carbon structures according to the slopes in their energy dispersion.Type-Ⅰ and-Ⅱ rings are made of two bands of opposite and same-sign slopes(in the direction normal to the ring),respectively,and the type-Ⅲ ring is anisotropic,made of bands having the same-sign slope in one direction but opposite-sign slopes in the other(orthogonal)direction.These topological phases can be transformed into each other through stress interaction in carbon networks.In chapter five,we propose a new 3D boron structure,named as 3D-α’boron,which is proposed to be a nodal chain semimetal.In the momentum space,six nodal lines and rings contact each other and form a novel spindle nodal chain,which are protected by mirror planes,glide plane and PT(parity-time)symmetry.The anisotropic nodal chain results in various drumhead surface states.In addition,3D-α’ boron shows good stability because it is formed by stacking high-stability α’boron sheet.In chapter six,a summary is given to our study and we also explicitly described the studies in the future.