Phonon Softening and Bandgap Engineering in Strained Monolayer MoS$_2$

By straining monolayer MoS$_2$ with a 4 point bending apparatus, both phonon softening and a shrinking band gap were observed. Raman spectrum demonstrates phonon softening for both bi and single layer MoS$_2$ flakes, with a breaking of the E$^1_{2g}$ degeneracy at large strain. Photoluminescence data shows that the band gap of single layer MoS$_2$ decreases by ~50 meV per \% strain. The direct band gap of bilayer MoS$_2$ decreases by the same rate as for monolayer MoS$_2$ while the indirect band gap of bilayer MoS$_2$ decrease by ~120 meV \% strain. This work clearly demonstrates that MoS$_2$'s band gap and phonons are tunable by strain engineering suggesting a possibility of devices with mechanically tunable optical and electrical properties.