Two-dimensional Buckled Hexagonal Tin Layers Investigated By Ab Initio Method

Two-dimensional(2D)Tin atomic layers with hexagonal lattice are attracting extensive attentions for their high specific surface area and topological insulator properties.For the buckling Tin atoms perpendicular to the two-dimensional layer,the standard 2D atomic layer is separated into two planes with a buckling height d,which lead to the transformation beyond 2D lattice with regard to atomistic and electronic structures.This makes the buckling height to be a crucial factor to explore the 2D properties related to atomic arrangements and electronic energy band.Based on the rules from buckling distortion induced by environments in and out of the Tin planes,the atomistic-scale modulations will be possible in the future experimental epitaxiy for 2D Tin layers with a few atomic planes.The LB phase of 2D hexagonal Tin with a buckling height about 1 A is so far the only observation from the experimental research,but in terms of previous first-principle calculations,for the free-standing Tin layer the LB phase is just the metastable structure with higher energy than the HB layer,which was predicted to be 2D stable phase with a buckling height about 2 A.What is the main reason for the missing of HB phase for the free-standing Tin layers in experimental observation.The supporting substrates,the coupling between Tin layers,the oxidization of Tin atoms and other 2D environmental factors,which is the key to control the buckling height of 2D Tin layer?In order to analyze the connection between buckling height and 2D strain,substrate and number of Tin layers,the first-principle calculations have been performed in this paper to demonstrate the possible factors within the atomistic scale.Based on ultrasoft pseudopotential plane-wave method,during our calculations the different 2D hexagonal Tin-layered-models were built to explore the phase stability with regard to buckling height from atomic geometrical parameters to electronic structures.Firstly in order to avoid the geometric stable atomic configuration related to the initial structure,the energy surface E(a,d)as function of 2D lattice constant a and buckling height d,was obtained to determine the HB as the stable phase,the LB as the metastable one,and the planar PL and transition TS lattices as the transition states.The continuing partial density of electronic states near the Fermi level,atomic and bond populations,and differential charge density maps were used to provide the bonding characters between in-plane and out-of-plane Tin atoms.The finite-displace method was also used to give the lattice dynamics properties for the stable and metastable phases.Secondly the possible factors were taken into account to explain the buckling height in the present calculations,the 2D lattice strain,different substrates,coupling between a-few-layers,and the induced alien atoms were all considered in terms of the difference produced by the buckling height.The corresponding atomic geometric parameters and bonding behaviors were introduced to reveal the role of buckling height.The final results indicate that the sp-sp3 hybridization,the p state electrons without involved in s-p hybridizations,distance between atomic layers,and the environments surrounding the Tin atoms,such as the coordinations numbers of alien atoms,are all play important roles to dominate the buckling height of 2D tin layer.It is because the missing of free-standing mono-layer of 2D Tin so that the other environmental factors have to be considered,and this may give rise to the absent of HB phase for 2D hexagonal Tin layers in few-layer-structured samples from experimental lab.