Directional-dependent thickness and bending rigidity of phosphorene

Verma, Deepti and Hourahine, Benjamin and Frauenheim, Thomas and James, Richard D. and Dumitrică, Traian (2016) Directional-dependent thickness and bending rigidity of phosphorene. Physical Review B (Condensed Matter), 94 (12). 121404(R). ISSN 0163-1829 (

[thumbnail of Verma-etal-PRB-2016-Directional-dependent-thickness-and-bending-rigidity-of-phosphorene]
Text. Filename: Verma_etal_PRB_2016_Directional_dependent_thickness_and_bending_rigidity_of_phosphorene.pdf
Accepted Author Manuscript

Download (981kB)| Preview


The strong mechanical anisotropy of phosphorene combined with the atomic-scale thickness challenges the commonly employed elastic continuum idealizations. Using objective boundary conditions and a density functional-based potential, we directly uncover the flexibility of individual α, β and γ phosphorene allotrope layers along an arbitrary bending direction. A correlation analysis with the in-plane elasticity finds that although a monolayer thickness cannot be defined in the classical continuum sense, an unusual orthotropic plate with a directional-dependent thickness can unambiguously describe the out-of-plane deformation of α and γ allotropes. Such decoupling of the in-plane and out-of-plane nanomechanics might be generic for two-dimensional materials beyond graphene.