Strain tuning of optical emission energy and polarization in monolayer and bilayer MoS${}_2$

We use micro-Raman and photoluminescence (PL) spectroscopy at 300 K to investigate the influence of uniaxial tensile strain on the vibrational and optoelectronic properties of monolayer and bilayer MoS${}_2$ on a flexible substrate. The initially degenerate $E^{\prime }$ monolayer Raman mode is split into a doublet as a direct consequence of the strain applied to MoS${}_2$ through Van der Waals coupling at the sample-substrate interface. We observe a strong shift of the direct band gap of 48 meV/(% of strain) for the monolayer and 46 meV/% for the bilayer, whose indirect gap shifts by 86 meV/%. We find a strong decrease of the PL polarization linked to optical valley initialization for both monolayer and bilayer samples, indicating that scattering to the spin-degenerate $\Gamma$ valley plays a key role.

Figure 1

(a) The three-point bending apparatus. Note that the distance between the two top contact points is 6 cm, whereas the extension of a Mo${\text{S}}_2$ flake is in the $\mu \text{m}$ range. (b) The monolayer (black curve) and bilayer (red) ${\text{MoS}}_2$ regions are identified by Raman spectroscopy. (c) The $E^{\prime }$ Raman mode splits into two modes as tensile strain is applied to the monolayer sample. (d) Same as (c) but for a bilayer sample.

Figure 2

Laser excitation at 1.95 eV with ${\sigma }^{+}$ polarization. (a) PL emission detected for ${\sigma }^{+}$ and ${\sigma }^{-}$ polarization for a MoS${}_2$ monolayer at zero strain. (b) Same as (a) but for applied strain of 0.8%. (c) Circular polarization degree of the PL detected at its peak as a function of the applied tensile strain. Dotted lines are a guide to the eye. (d) PL emission detected for ${\sigma }^{+}$ and ${\sigma }^{-}$ polarization for a MoS${}_2$ bilayer at zero strain. (e) Same as (d) but for applied strain of 0.8%. (f) PL Circular polarization degree as a function of the applied tensile strain. Dotted lines are guides to the eye. Inset: The applied strain is kept constant at 0.8% and the PL polarization is measured as a function of the angle of the applied strain with respect to the in-plane mono- and bilayer crystal orientation. (g) Scheme of the band structure for monolayer MoS${}_2$ at zero strain. $K$ and $\Gamma$ valleys and the associated interband transitions are marked; the conduction-band spin splitting in the meV range[7] is not shown.

Figure 3

(a) Measured energy shift for the direct recombination of the MoS${}_2$ monolayer (squares) and bilayer sample (circles), and indirect recombination for the bilayer (triangles) for applied strain between 0% and 0.8%. (b) Calculation (see the main text) of the evolution of the direct and indirect band gap for a MoS${}_2$ monolayer with strain from 0% to 5% applied along the zigzag and armchair directions. (c) Same as (b) but for a MoS${}_2$ bilayer.