Nonlinear elastic behavior and anisotropic electronic properties of two-dimensional borophene

Mahdi Faghihnasiri, Homayoun Jafari, Ali Ramazani*, Mostafa Shabani, Sina Malakpour Estalaki, Ronald G. Larson

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

17 Citations (Scopus)


Using first-principles density functional theory calculations, the mechanical and electronic properties of the three main (beta(12), chi(3), and striped) phases of single-layer borophene sheets are calculated under in-plane uniaxial/biaxial strain, including the harmonic strain-energy regions of beta(12), chi(3), and striped phases over the strain ranges of -3.5%-3.5%, -4.5%-4.5%, and -2.5%-2.5%, respectively, along the x direction (the direction of the highest bond orientation). We introduce a method by which the nonlinear behavior of these and any other two-dimensional materials can be investigated even above their ultimate strains, beyond which no-uniform plastic deformation occurs. Defining an appropriate deformation, and utilizing both continuum modeling and special equations based on the density functional theory, a method of computing second-, third-, and fourth-order elastic constants of the three different phases of borophene is presented that utilizes rectangular unit cells, which can substitute for any two-dimensional unit cell. Using this new method, 4 independent second-order, 6 third-order, and 9 fourth-order elastic constants are calculated, which is the complete set of elastic constants for two-dimensional structures. The electronic band structure of borophene shows anisotropic electronic behavior. Despite the metallic character of borophene sheets, applying directional strain based on deformation matrices creates a bandgap in some regions of the Brillouin zones, opening up the possibility of mechanical control of electronic properties. Published under license by AIP Publishing.

Original languageEnglish
Article number145107
Number of pages13
JournalJournal of Applied Physics
Issue number14
Publication statusPublished - 14-Apr-2019
Externally publishedYes



Cite this