Phonon softening and direct to indirect band gap crossover in strained single-layer MoSe2

Abstract

Motivated by recent experimental observations of Tongay et al. [Nano Lett. 12, 5576 (2012)] we show how the electronic properties and Raman characteristics of single layer MoSe${}_{2}$ are affected by elastic biaxial strain. We found that with increasing strain: (1) the ${E}^{\ensuremath{'}}$ and ${E}^{\ensuremath{'}\ensuremath{'}}$ Raman peaks (${E}_{2g}$ and ${E}_{1g}$ in bulk) exhibit significant redshifts (up to $\ensuremath{\sim}$30 cm${}^{\ensuremath{-}1}$), (2) the position of the ${A}_{1}^{\ensuremath{'}}$ peak remains at $\ensuremath{\sim}$180 cm${}^{\ensuremath{-}1}$ (${A}_{1g}$ in bulk) and does not change considerably with further strain, (3) the dispersion of low energy flexural phonons crosses over from quadratic to linear, and (4) the electronic band structure undergoes a direct to indirect band gap crossover under $\ensuremath{\sim}$3$%$ biaxial tensile strain. Thus the application of strain appears to be a promising approach for a rapid and reversible tuning of the electronic, vibrational, and optical properties of single layer MoSe${}_{2}$ and similar MX${}_{2}$ dichalcogenides.