The Topological Property And Superconductivity Of Two-dimensional Materials

Graphene is a stable two-dimensional(2D)material with the sp2 hybridized carbon atoms forming a perfect hexagonal honeycomb lattice.With the successful preparation of graphene experimentally,the 2D materials represented by graphene become one of the most popular research topic in the field of material science and condensed matter physics.The electronic band structure of graphene near the Fermi level has a linear energy-momentum relationship named as "Dirac cone",which satisfies the Dirac Equation that is used to describe the relativistic particles.The Dirac cone in graphene provides an ideal model for the study of the foundational physics and application of 2D materials,which in turn promotes the development of spintronics and superconductivity.Based on the graphene honeycomb lattice,the Haldane model and the Kane-Mele model were the earliest theoretical models that describe the quantum anomalous Hall(QAH)and quantum spin Hall(QSH)state,which established an important theoretical foundation for the further study of topological electronic states in 2D materials.The strength of electron-phonon coupling in graphene can be effectively tuned by strain and electron doping,which provides a new way to improve the superconducting transition temperature(Tc)and hence promote the research progresses of superconductivity in 2D materials.Additionally,inspired by the excellent thermal and electron conductivity of graphene,considerable effects have been devoted in searching for new 2D Dirac materials.In the research field of topological property and superconductivity,improving the topologically non-trivial gaps of topological insulators(TIs)or the superconducting gaps of superconductors(SCs)as high as possible is the key point at present.Searching for the experimentally prepared 2D TIs and SCs with larger energy gaps is beneficial to realize the above-mentioned exotic electronic behavior at higher operating temperatures.Meanwhile,exploring and understanding the internal mechanism of 2D TIs and SCs states are of great significance for improving the topological non-trivial gaps and superconducting energy gaps,as well as generating novel quantum phenomena,which will certainly provide theoretical guidance to design and synthesize new 2D material with better performance.In this thesis,using the first-principle calculation and tight-binding(TB)model,the topological properties induced by spin-orbit coupling and the superconducting properties induced by electron-phonon coupling in several new 2D materials are investigated,which is expected to provide the necessary theoretical basis and alterative choices for the applications of 2D materials in the fields of spintronics and superconductivity.The main results are summarized as follows:(1)The strategy of regulating the electronic band structure by hole doping in 2D graphitic carbon nitrides is revealed,and the existence of quantum anomalous Hall state in such kind of metal-free material is demonstrated.In detail,we first discussed the effects of hole doping and tensile strain on electronic spin polarization and local magnetic moment coupling based on the 2D graphitic carbon nitrides(g-C3N4),and found a feasible way to realizing stable ferromagnetic(FM)ground states.Subsequently,by designing crystal structure,we predicted two kinds of 2D graphitic carbon nitrides with the property of spin-gapless semiconductor:g-C1oN9 and g-C14N12.These two materials are all quantum anomalous Hall insulator with stable ferromagnetic ordering,where the strong spin-orbit coupling strength opens topological non-trivial gaps with the Chern number of-1 at the Fermi level.Notably,the non-trivial gaps are larger than that of graphene by about three orders of magnitude,implying the quantum anomalous Hall effect may be realized in these metal-free materials under a higher operating temperature,which opens a new avenue for the applications of graphitic carbon nitrides.(2)2D metal-organic frameworks(MOF),composed of metal atoms and organic ligands,can form various crystal structure along with novel physical properties.In this part,based on the topologically non-trivial HTT-Pt,a MOF with Kagome lattice pattern,we demonstrated that electron-doping(or gate-voltage)can induce multiple transitions from a trivial insulator to a quantum spin Hall insulator,and then to a quantum anomalous Hall insulator.Meanwhile,the heavy metal element,platinum(Pt),makes the HTT-Pt maintain strongest spin-orbit coupling strength among the known organic TIs,and the topologically non-trivial gap can be as large as 42.5 meV,suggesting robustness at room-temperatures.(3)Driven by the rapid advancements in nanotechnology in recent years,the 2D superconductors with truly atomic-scale thicknesses have been established and the studies on ultrathin 2D superconductors have obtained remarkable progresses.Based on an experimentally prepared metal-organic framework:Cu-BHT,we predicted the existence of traditional superconducting properties in such kind of organic materials using first-principle calculations.The Cu-BHT monolayer has a critical temperature(Tc)of 4.43 K,higher than that of bulk Cu-BHT(1.58 K).The enhanced Tc in Cu-BHT monolayer is attributed to the low-frequency vibration mode of Cu and S atoms,which couple with electronic states at the Fermi level strongly.When the Cu-BHT monolayer are stacked into a three-dimensional bulk material,these vibration modes are suppressed,thus weakening the electron-phonon coupling strength.This differs significantly from the mechanism that interface effect improves the T,of some 2D materials,and is of great significance to further enhance the superconducting gap of 2D superconducting materials.(4)Based on the experimentally synthesized C36 solid,we propose a new carbon allotrope(named as ph-graphene)with a penta-hexagonal framework composed by quasi-sp2 and-sp3 hybridized carbon atoms.Similar to graphene,the pz orbital of the quasi-sp2 hybridized carbon atom forms the spin-degenerated Dirac cone at the Fermi level,where the Fermi velocity is about 2.8×105 m/s.Hydrogen atoms adsorption can effectively regulate its electronic properties,including the generation of electronic spin polarization and band gap at the Fermi level.Mainwhile,ph-graphene is a "soft"2D material with the in-plane stiffness of 27.75 GPa·nm,far smaller than that of graphene.So,ph-graphene is expected to be available in the field of flexible electronics.