Atom-Based Geometrical Fingerprinting of Conformal Two-Dimensional Materials

The shape of two-dimensional materials plays a significant role on their chemical and physical properties. Two-dimensional materials are basic meshes that are formed by mesh points (vertices) given by atomic positions, and connecting lines (edges) between points given by chemical bonds. Therefore the study of local shape and geometry of two-dimensional materials is a fundamental prerequisite to investigate physical and chemical properties. Hereby the use of discrete geometry to discuss the shape of two-dimensional materials is initiated. The local geometry of a surface embodied in 3D space is determined using four invariant numbers from the metric and curvature tensors which indicates how much the surface is stretched and curved under a deformation as compared to a reference pre-deformed conformation. Many different disciplines advance theories on conformal two-dimensional materials by relying on continuum mechanics and fitting continuum surfaces to the shape of conformal two-dimensional materials. However two-dimensional materials are inherently discrete. The continuum models are only applicable when the size of two-dimensional materials is significantly large and the deformation is less than a few percent. In this research, the knowledge of discrete differential geometry was used to tell the local shape of conformal two-dimensional materials. Three kind of two-dimensional materials are discussed: 1) one atom thickness structures such as graphene and hexagonal boron nitride; 2) high and low buckled 2D meshes like stanene, leadene, aluminum phosphate; and, 3) multi layer 2D materials such as Bi2Se3 and WSe2. The lattice structures of these materials were created by designing a mechanical model - the mechanical model was devised in the form of a Gaussian bump and density-functional theory was used to inform the local height; and, the local geometries are also discussed

Structural phase transition and material properties of few-layer monochalcogenides

GeSe and SnSe monochalcogenide monolayers and bilayers undergo a two-dimensional phase transition from a rectangular unit cell to a square unit cell at a temperature $T_c$ well below the melting point. Its consequences on material properties are studied within the framework of Car-Parrinello molecular dynamics and density-functional theory. No in-gap states develop as the structural transition takes place, so that these phase-change materials remain semiconducting below and above $T_c$. As the in-plane lattice transforms from a rectangle onto a square at $T_c$, the electronic, spin, optical, and piezo-electric properties dramatically depart from earlier predictions. Indeed, the $Y-$ and $X-$points in the Brillouin zone become effectively equivalent at $T_c$, leading to a symmetric electronic structure. The spin polarization at the conduction valley edge vanishes, and the hole conductivity must display an anomalous thermal increase at $T_c$. The linear optical absorption band edge must change its polarization as well, making this structural and electronic evolution verifiable by optical means. Much excitement has been drawn by theoretical predictions of giant piezo-electricity and ferroelectricity in these materials, and we estimate a pyroelectric response of about $3\times 10^{-12}$ $C/K m$ here. These results uncover the fundamental role of temperature as a control knob for the physical properties of few-layer group-IV monochalcogenidesComment: Supplementary information included. Published versio

Phase Transitions in Monochalcogenide Monolayers

Since discovery of graphene in 2004 as a truly one-atom-thick material with extraordinary mechanical and electronic properties, researchers successfully predicted and synthesized many other two-dimensional materials such as transition metal dichalcogenides (TMDCs) and monochalcogenide monolayers (MMs). Graphene has a non-degenerate structural ground state that is key to its stability at room temperature. However, group IV monochalcogenides such as monolayers of SnSe, and GeSe have a fourfold degenerate ground state. This degeneracy in ground state can lead to structural instability, disorder, and phase transition in finite temperature. The energy that is required to overcome from one degenerate ground state to another one is called energy barrier (E¬c). Density Functional Theory (DFT) has been used to calculate energy barriers of many materials in this class such as monolayers of SiSe, GeS, GeSe, GeTe, SnSe SnS, SnTe, PbS, and PbSe along with phosphorene. Degeneracy in the ground state of these materials leads to disorder at finite temperature. This disorder arises in the form of bond reassignment as a result of thermal excitement above a critical temperature (Tc). Tc is proportional to E¬c/KB where KB is Boltzmann’s constant. Any of those materials that have a melting temperature larger than E¬c/KB such as SnSe, SnS, GeSe, and GeS will undergo an order-disorder phase transition before melting point. This order-disorder phase transition will have a significant effect on properties of these 2D materials. The optical and electronic properties of GeSe and SnSe monolayers and bilayers have been investigated using Car-Parrinello molecular dynamics. These materials undergo phase transition from an average rectangular unit cell below Tc to an average square unit cell above Tc where Tc is well below the melting point. These materials will remain semiconductors below and above Tc. However, the electronic, optical, and piezoelectric properties modify from earlier predicted values. In addition, the X and Y points of the Brillouin zone become equivalent as the materials passes Tc leading to a symmetric electronic structure. The spin polarization at the conduction valley vanishes. The linear optical absorption band edge changes its polarization and makes this structural and electronic transition identifiable by optical means

Structural phase transition and material properties of few-layer monochalcogenides

GeSe and SnSe monochalcogenide monolayers and bilayers undergo a two-dimensional phase transition from a rectangular unit cell to a square unit cell at a critical temperature Tc well below the melting point. Its consequences on material properties are studied within the framework of Car-Parrinello molecular dynamics and density-functional theory. No in-gap states develop as the structural transition takes place, so that these phase-change materials remain semiconducting below and above Tc. As the in-plane lattice transforms from a rectangle into a square at Tc, the electronic, spin, optical, and piezoelectric properties dramatically depart from earlier predictions. Indeed, the Y and X points in the Brillouin zone become effectively equivalent at Tc, leading to a symmetric electronic structure. The spin polarization at the conduction valley edge vanishes, and the hole conductivity must display an anomalous thermal increase at Tc. The linear optical absorption band edge must change its polarization as well, making this structural and electronic evolution verifiable by optical means. Much excitement is drawn by theoretical predictions of giant piezoelectricity and ferroelectricity in these materials, and we estimate a pyroelectric response of about 3×10−12 C/Km here. These results uncover the fundamental role of temperature as a control knob for the physical properties of few-layer group-IV monochalcogenides.M. M. and S. B.-L. are funded by an Early Career Grant from the U.S. DOE (Grant No. SC0016139). Y. Y. and L. B. were funded by ONR Grant No. N00014-12-1-1034, and B. M. F. by NSF Grant No. DMR-1206515 and CONACyT (Mexico). J. F. acknowledges funding from the Spanish MICINN, Grant No. FIS2012-34858, and European Commission FP7 ITN MOLESCO (Grant No. 606728). Calculations were performed on Trestles at the Arkansas High Performance Computing Center, which is funded through multiple National Science Foundation grants and the Arkansas Economic Development Commission.Peer Reviewe

Intrinsic Defects, Fluctuations of the Local Shape, and the Photo-Oxidation of Black Phosphorus

Black phosphorus is a monatomic semiconducting layered material that degrades exothermically in the presence of light and ambient contaminants. Its degradation dynamics remain largely unknown. Even before degradation, local-probe studies indicate non-negligible local curvaturethrough a nonconstant height distributiondue to the unavoidable presence of intrinsic defects. We establish that these intrinsic defects are photo-oxidation sites because they lower the chemisorption barrier of ideal black phosphorus (>10 eV and out of visible-range light excitations) right into the visible and ultraviolet range (1.6 to 6.8 eV), thus enabling photoinduced oxidation and dissociation of oxygen dimers. A full characterization of the material’s shape and of its electronic properties at the early stages of the oxidation process is presented as well. This study thus provides fundamental insights into the degradation dynamics of this novel layered material