Physical Mechanics And Electronic Properties Of Two-dimensional Crystals And Metal-organic Frameworks

Materials periodic in in-plane directions but have single or few atomic layers in thickness are called two-dimensional material,an emerging type of materials.Since the discovery of graphene,twodimensional materials including graphene,hexagonal boron nitrogen,few-layered MoS₂ and black phosphorus,have drawn intensive research interests.Due to quantum confinement effect,this new type of material can show special mechanical and physical properties that are different from their bulk counterparts.Another interesting material system is metal-organic framework that is constructed with metal atoms and organic linkers through covalent bonds,hydrogen bonds as well as van der Waals interactions.Because metal-organic frameworks are loosely packed and have relatively lower stiffness compared with common solids,they can show sensitive response to external pressures and temperatures.Through density functional theory simulations,continuum mechanics modeling and development of a new physical model,we investigate the strategies to modulate the electronic structure of two-dimensional materials such as strain-engineering,the novel behavior of the bending of two-dimensional materials,the many-body van der Waals interactions in metal-organic frameworks,and a new possible picture to understand the electronic structures of systems under non-uniform strains.Detailed contents are listed in the following.1)Chirality-dependent bandgap-opening in graphene antidot lattices.We reveal through density functional theory calculations the dependence of bandgap-opening on the lattice vectors in periodic graphene antidot lattices.In triangular antidot lattices,the bandgap-opening complies with a chirality rule,similar to that in carbon tubes.Whether the bandgap opens relies on the lattice vector R=（n（?）+m（?））.The bandgap opens if n-m mod 3 is an integer,and vice versa.This rule stems from the lattice-vector-dependent structural characteristics,and can be understood from Shima and Aoki’s group theory analysis or from the Clar’s sextet analysis.The revealed rule can be widely applied to graphene antidot lattices with different holes or unit cell shapes,allowing for a deep and complete understanding of electronic structures of graphene antidot lattice.2)We propose a mechanism for the fabrication process of one-dimensional structure from monolayer molybdenum disulfide by electron irradiation and unveil the sensitive dependence of bandgap in tri-layer molybdenum disulfide on biaxial strains.To explain the observed phenomenon that irradiating molybdenum disulfide by electrons can fabricate one-dimensional structures Litao Sun et al.’s experiments,we calculate the energy required to knock off the S atom.The S atom at the edges is more readily removed than that at inner positions,which explains for the narrowing of MX₂ ribbon.The ribbon at the critical width spontaneously transform to a new stable one-dimensional structure.We also point out that the mechanism for the top-down fabrication of onedimensional structures is also applicable in other MX₂ materials,which is confirmed by the following experiments of another group.In addition,we investigate the strain tunable electronic structure and Raman properties of tri-layer molybdenum disulfide through density functional theory calculations,in cooperation with Shu Pin Lau et al.’s experiments.The calculations show that both the direct and indirect bandgaps decrease with biaxial compressive strains.Experimentally,the mechanical loading on tri-layer molybdenum disulfide is applied through a pizeo-electric substate and the measured shifts of bandgap and Raman frequeny are in accordence with the calculation.3)Bending induced in-plane strain in two-dimensional crystals.We find through density functional theory calculations that bending in two-dimensional crystals can induce a lateral in-plane strain.In analogy to the Possion effect,we call this phenomenon bending Possion effect.This effect relies on the dimensionality,chemical constituents,bond geometry and is an-isotropic.The bending Possion ratio μ is defined as the ratio of the lateral strain to the curve,and is a function of curvature.The underlying mechanism is the ultra-thin nature of two-dimensional crystals and the coupling between the bending and compressive sides.As the effect exists in a wide range of two-dimensional crystals,we suggest a modified shell model of large deformation,with the lateral deformation considered.4)Many-body van der Waals interactions in metal-organic frameworks.We investigate the role of many-body van der Waals interactions in metal-organic frameworks and compared the performance of many-body dispersion method with that of pair-wise approximations and van der Waals functionals.Two important effects of many-body van der Waals interactions are revealed.First,many-body electron correlation contribution in Ag₃Co（CN）₆,Ag₃Fe（CN）₆ increases the van der Waals cohesive energy,in stark contrast to usual expectations.Second,many-body van der Waals interaction can induce a single-well potential of van der Waals energy for hydrogen atom in H₃Co（CN）₆ and H₃Fe（CN）₆,tending to symmetrize the N-H-N bond.Adding many-body van der Waals energy to PBE energy can qualitatively correctly predict a symmetric N-H-N bond in H₃Co（CN）₆ and an asymmetric one in H₃Fe（CN）₆.5)A possible strategy to treat the electronic structure of systems under non-uniform strains.We propose a possible strategy to treat the electronic structures of materials under non-uniform strains.Through substitution of coordinate,we can construct a fictious Hamiltonian and corresponding fictious wave functions,which have the same eigenvalues as that for the strain-free Hamiltonian and wave functions but have the same boundary conditions as in the strained system.A possible way to solve the electronic structure of the strained system is the perturbation theory.However,challenges of this strategy remain because the fictious Hamiltonian is non-Hermitian.