| Graphene has broad application prospects in the fields of energy,materials and biomedicine,due to its extraordinary mechanical,optical and electrical properties.The valence and conduction bands of graphene touch at the Fermi level,leading to linear energy-momentum dispersion relations.Its low-energy excitations are massless Dirac fermion,satisfying the relativistic Dirac equation,featured by Dirac cone.The Dirac cone of graphene locate at the six comers of the first Brillouin zone(BZ).Because of the Dirac cone,graphene has excellent properties,such as high carrier mobility,high thermal conductivity,quantum Hall effects(QHE),and so on.These exotic properties of graphene have motivated continuous search for more Dirac maternials by theoretical prediction and experimental exploration.Simultaneously,a series of toy models based on specific lattice patterns have been proposed and demonstrated to possess Dirac cone,such as,Honeycomb lattice,Ruby lattice,Kagome lattice and Lieb lattice and so on.From the structure point of view,reflective symmetry is preserved in these toy models,but the essentiality has never been proved.If a Dirac cone exists in a lattice without reflective symmetry,the family of Dirac materials will be greatly enriched offering a new idea for design Dirac materials.Moreover,the realistic maternials corresponding to the lattice models are quite crucial for achieving the excellent properties to be applied in practice.Therefore,it is more critical to find realistic materials with the above lattice strctures.Most Dirac materials have the valence and conduction bands touching at a point forming a Dirac point.A rare form of Dirac semi-metallic materials,however,have the valence and conduction bands crossing each other,giving nise to a fully closed line at the Fermi level,namely Dirac Node-Line(DNL)semimetal.The realistic materials of two dimensional(2D)DNL semimetals are scarce so far.Most of the reported DNL materials are protected by mirror symmetry and require negligible spin-orbit coupling(SOC)effect.Therefore,searching for the materials that can robust against spin orbit coupling effect and have a stable DNL state is a current concern.In this thesis,we used first-principles theory calculations within the density functional theory(DFT),combined with the Tight-Binding(TB)model to predict the lattices and realistic materials with Dirac cone,which can provide theoretical guidance for the theoretical prediction and experimental realization of Dirac materials.The main research contents and results are summerized as follows:We present an exceptional case:a snub trihexagonal tiling(STT)lattice without reflective symmetry.We demonstrate the existence of Dirac cones in this reflection-symmetry-free lattice by using a single-orbital tight-binding Hamiltonian.The energy gaps due to the SOC effect remind us the topological non-triviality of the STT lattice.The topological non-triviality of the STT lattice is verified by the robust gapless edge states in the nanoribbon of the STT lattice with different edge(zigzag and armchair edge).Using first-principles calculations,we predict a promising candidate 2D material,Be3C4 monolayer to realize this toy model.The dynamic stability of Be3C4 can be proved by phonon spectrum without any imaginary frequency modes.Molecular dynamic simulations confirm the stability of Be3C4 at room temperature.The elastic constants satisfy the criteria of the mechanical stability of 2D sheet,indicating that the Be3C4 monolayer is mechanically stable.The electronic band structure of Be3C4 monolayer is calculated by using first principle theory and tight-binding model.The valence and conduction bands near the Fermi level exhibit a linear dispersion relation,featured by Dirac cones.The Fermi velocities in this unique lattice are even higher than that in graphene.The proposed STT lattice demonstrates the importance of reflective symmetry for 2D Dirac materials.A potential realistic material of STT lattice is proposed.Dirac Node-Line(DNL)semi-metal is a new type of topologically non-trivial materials,but,the realistic materials of 2D DNL semi-metal are scarce at present.Moreover,the DNL state in most of the reported DNL materials can be gapped by SOC effect.Here,we proposed Tight-Binding models of s?pz and px,y?pz orbitals defined on a 2D Lieb lattice.The DNL states in these models are caused by the inversion of the bands with difference symmetries and thus robust against SOC effect.By means of first principles calculations,we demonstrate two candidate materials:Be2C and BeH2 for Lieb lattice of s +pz and px,y,pz models,respectively.Their valence and conduction bands intersect at the Fermi level and form a fully closed line,exhibiting features of DNL semi-metal.More interesting,the DNL states of Be2C and BeH2 are robust against the SOC effect.Their Fermi velocities are much higher than that in graphene,almost four times that of graphene.The non-zero Z2 topological invariant accompanied by the edge states is revealed in these materials.The proposed Lieb lattice open an avenue for the design of 2D DNL semi-metal.Based on first principles calculations,a novel carbon allotrope is proposed,named as super-graphyne,which consist of sp-and sp2-hybridized carbon atoms.The primitive cell contains 16 carbon atoms with the sp:sp2 ratio of 3:1.The dynamical and mechanical stability was verified from phonon spectrum,molecular dynamics simulations and elastic constants.More interestingly,super-graphyne is semi-metallic with highly anisotropic band structure in the reciprocal space featured by node line Dirac semimetals.Along the ?-X direction,there is a Dirac cone centered at X point with the Fermi velocity higher than that in graphene,while the bands are nearly dispersionless along the X-P direction.In addition,the surface states of the bared(001)surface with zigzag edge are spin-polarized,which is related to the unpaired electrons of the sp2-hybridized carbon atoms on the surface,and prefer anti-ferromagnetic(AFM)ordering along zigzag chain.The semi-metallic nature is also preserved in the film. |
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