Topological Properties Of The Three-dimensional Carbon Networks

Carbon element is one of the most abundant elements on the earth,and it is also one of the most familiar elements.Graphite and diamond,as carbon allotropes that humans have come into contact with earlier,are abundant in nature.With the in-depth research on carbon materials,more and more carbon allotropes have been artificially prepared,including:zero-dimensional(0D)Fullerenes,one-dimensional(1D)carbon nanotubes,two-dimensional(2D)graphene and three-dimensional(3D)graphene networks.There are many ways of orbital hybridization of carbon element,such as:sp,sp~2and sp~3hybridization,which makes the physical properties of carbon allotropes with different orbital hybridization are very different.Among the diverse physical properties of carbon allotropes,its topological properties have been the focus of research in recent years.Different from most heavy element topological materials with strong spin-orbit coupling(SOC)effect,carbon element,as a light element,its SOC effect is extremely weak and can even be ignored.Therefore,as one of the candidates for the study of topological materials,there are many novel topological properties in carbon materials waiting for people to explore.At present,various three-dimensional carbon networks based on low-dimensional carbon allotropes have been theoretically proposed.These three-dimensional carbon networks provide a good platform for finding and studying various topological phases.This paper focuses on the topological semi-metallic properties in the three-dimensional carbon networks.The paper is mainly divided into the following five parts:In the Chapter 1,we introduced the research background of carbon materials,the source of topological theory,and the classification and research status of topological semimetals.In the Chapter 2,we introduce the theoretical methods of first-principles calculations and related theoretical calculation methods used in the research work.In the Chapter 3,we propose two types of three-dimensional carbon network structures(WSCN and DHCN)with low symmetry.Both types of carbon network structures are composed of sp~2-hybridized carbon atoms,and both lack inversion symmetry.By analyzing the electronic properties of these two structures,it is found that these two types of carbon networks belong to topological Weyl semimetals.There are four pairs of Weyl points with opposite chirality near the Fermi level of their first Brillouin zone.When strains are applied on the carbon structures,the positions of these Weyl points move,but they will not be destroyed,which is a good proof of the robustness of Weyl points.Subsequently,we analyzed the Fermi surface spectra of the two structures on the[010]projection plane.Our findings provide a feasible method for finding and studying Weyl points in carbon networks.In the Chapter 4,We propose a three-dimensional warped zigzag graphene network(WZGN)based on one-dimensional zigzag graphene nanoribbons.This carbon network is a metastable structure of c-centered orthogonal lattice composed of sp~2-hybridized carbon atoms.The calculated electronic band structure shows that WZGN is a topological Dirac semimetal,and there is a nodal ring protected by inversion symmetry and time-reversal symmetry on the k_y=0 plane of the first Brillouin zone.In addition,we found various‘drumhead’surface states on its[010]projection surface.Our work proposes a three-dimensional carbon network structure with practical significance and value.In the Chapter 5,we summary the result of our study and explicitly described the studies in the future.