Flat Bands In Novel Two-dimensional Carbon Materials

Two-dimensional materials have a broad platform in basic science and nanometer fields due to their unique structures and exotic electronic properties,which have become the focus of continuous attention.Among them,carbon has become the first choice to study two-dimensional materials due to a variety of hybridization methods.The abundant physical properties of two-dimensional carbon materials have attracted extensive attention to the allotrope of two-dimensional carbon.In recent years,most studies on two-dimensional carbon allotropes have been based on their band gaps to explore their electrical conductivity and optical applications.For example,graphene has been extensively studied due to its unique Dirac cone and high valence electron mobility.However,the formation of flat bands by two-dimensional carbon materials has not been much discussed.The interesting physics carried by the flat band is something that anyone cannot ignore.Flat bands in momentum space have attracted much attention because of amazing physical phenomena behind them,such as superconducting,Wigner crystallization,super-solids,fractal geometries,magnets with dipolar interactions,Floquet-physics effect.In this paper,we propose two ways to construct the flat band:one is to construct the flat band by lattice,and an example of lattice realization is found in real carbon materials;the other is through a simple allotrope of carbon.We also studied their electronic properties.This thesis has a total of five chapters.In the first chapter we briefly introduce the current state of research on two-dimensional thin film materials,and introduce some methods for constituting flat bands and the unique electronic properties of flat bands.In chapter two,we introduce the first-principles theory and the tight-binding model.In chapter three,we construct an interlocking-circles lattice and obtain isolated flat bands by calculating the tight-binding model of establishing a lattice point at the intersection of the ring and the ring.And find an example of how this interlocking-circles lattice can be achieved:a new atomic structure of hydrogenated graphene is obtained by chemical modification of graphene.It is noteworthy that the isolated flat bands appear near the Fermi energy(EF)and can host interesting physical phenomena such as ferromagnetism,the anomalous quantum Hall effect.Through orbital analysis and tight-binding calculations,it is demonstrated that our atomic model is a good example for the realization of interlocking-circles lattices.In the case of hole doping and electron doping,the spin simplicity of the flat band is spontaneously enhanced to form flat band ferromagnetic with spin splitting.We believe that interlocking-circles lattices provide a useful platform for the realization of isolated flat bands.At the same time,the emergence of interlocking-circles lattices opens the door to the creation of new two-dimensional materials,and the implementation of this lattices with different atomic materials will also attract people’s research interest.In chapter four,we present a two-dimensional allotrope structure of carbon and calculate the electronic properties of the structure based on first principles.It is made up of the desired triangle(isosceles triangle)and octagonal of carbon,and can carry flat bands and associated physical phenomena.It is worth noting that in this structure,a flat band appears near EF,and only the p_z state exists near EF.Due to the hole doping and electron doping of the flat bands,strong magnetism is generated in the structure,which leads to the spin splitting of the band.We also use a simple tight-binding model to describe the flat band structure.This planar carbon allotrope has an energy 0.01 e V/atom higher than Kagome-graphyne and is energetically more favorable than many previously proposed carbon allotropes,indicating that it is likely to be synthesized in experiments.In chapter five,we summarize the previous studies and show the prospect about the studies in the future.