| Carbon is one of the most fundamental elements in nature,which has very close relations with human lives.Searching for new three dimensional carbon allotropes has long been an important subject in condensed matter physics and materials science.In recent years,the studies for topological materials,including topological insulators and topological semimetals are developing very fast and has also become one of the hottest topics in condensed matter physics and materials science.In this thesis,we predict a series of new three dimensional carbon allotropes and perform systematical first-principles study on the topological electronic properties of these carbon allotropes.Firstly we predict a new all-sp3 hybridized superhard O16 carbon.It has 16 carbon atoms in its primitive-unit cell in Pbcn symmetry.Like as diamond,the carbon atoms in O16 carbon form all-six-membered rings.The dynamical stabilities of O16 carbon have been confirmed with phonon spectrum calculations and molecular dynamics simulations.The calculated Vickers hardness(Hv)for O16 carbon shows that O16 carbon is potential for being a superhard material.The simulated x-ray diffraction pattern of O16 carbon matches well with the experimental data derived in the diamond rich coatings grown on the stainless steel substrate,providing a reasonable explanation for the experimental data.Previously reported all-sp2 hybridized carbon allotropes tend to have closed nodal rings which is denoted as A-type;and the sp2-sp3 hybridized carbon allotropes tend to have two separate nodal lines which is denoted as B-type.We predict a new sp2-sp3 hybridized oP16 carbon in Pcca symmetry with 16 carbon atoms in its primitive-unit cell.Detailed band structures calculations show that oP16 carbon is a topological nodal line semimetal,in the ky=0 and ky=π mirror planes,the band crossing points form two closed line of nodes with different sizes.When the two nodal rings are projected onto the(010)plane,the topological non-trivial surface states can be found between the two rings.oP16 is the first proposed sp2-sp3 hybridized carbon allotrope but with closed A-type nodal rings.Then we find that the A/B-type nodal line behaviors can be affected by the lattice anisotropy while the bonding types do not matter.Beyond the A/B-type nodal lines,searching for more interesting topological nodal line configurations is also a very important direction.Then we predict a new all-sp2 hybridized carbon allotrope termed as oP-C24 carbon.The detailed band structures calculations show that oP-C24 carbon is a topological nodal line semimetal with a nodal ring protected by spatial inversion(P),time reversal(T),and mirror symmetries(mNL);and nodal lines protected with merely PT symmetries(s-NL).In the first Brillouin zone,the s-NLs and m-NL connect to form a chain network,which is termed as hybrid nodal chain(HNC).The topological nodal line behaviors in this carbon allotrope can be explained based on a two-band k·p model Hamiltonian.Such two-band model generating HNC protected only with PT and mirror symmetries may be realized in a real material for the first time.We also propose three all-sp2 hybridized carbon allotropes in Cccm symmetry.There are 16,32,and 64 carbon atoms in their unit cells,thus they are termed as cco-C16,cco-C32,and cco-C64 carbon,respectively.The band structures calculations show that,the three carbon allotropes are all topological nodal line semimetals,while in cco-C16 and cco-C32 carbon,the nodal lines form the HNCs like as in oP-C24 carbon;in cco-C64 carbon,the nodal line is a single A-type nodal ring,thus there is a topological phase transition from cco-C16,cco-C32,to cco-C64 carbon.The topological nodal line behaviors in the three carbon allotropes can be unified with the same two-band k·p model,by adjusting the model parameters,the topological phase transition from HNC to a A-type nodal ring can be realized.As a result we conclude that either HNC or A-type nodal ring is feasible in systems with PT and mirror symmetries. |
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