Density functional LCAO calculations of vibrational modes and phonon density of states in the strained single-layer phosphorene

Abstract

The paper presents an investigation of phosphorene under axial strain on the phonon density of states and vibrational modes. The studies were performed by means of density functional theory (DFT) within the linear combination of atomic orbitals (LCAO). The strained models were constructed using optimised supercell techniques. The vibrational mode spectra were estimated for strains applied for both the zigzag and armchair directions of phosphorene. This approach is an attractive candidate for the calculation the dynamical matrix of the system because its numerical complexity gradually increases together with the size of the analysed cell. The shift of peaks in the PDOS of black phosphorene is monotonic, and inversely proportional to the applied strain over the zigzag direction. This relation is valid for small strains (below 10%) of peaks corresponding to modes B2g and Ag2. For a strain applied over the armchair PDOS, the shifts are proportional to the strain. The peak shifts tend to become higher as the strain increases. This dependence is not monotonic, and is clearly more rapid for compressing strains. Moreover, the peaks shift slower for an armchair strain than for a zigzag strain, revealing its strong anisotropy.