Scaling law for strain dependence of Raman spectra in transition-metal dichalcogenides

Based on ab initio density functional calculation and nonresonant Raman theory, we calculate strain dependent Raman spectra of six kinds of transition-metal dichalcogenides (TMDCs). The biaxial strain dependence of Raman intensity and direct band gap in TMDC monolayers is systematically studied from which we show a scaling law of the Raman intensity and band gap. Out-of-plane A_1g mode has vanishing intensity under a certain strain. Such a strain-induced behavior is found to be universal in the TMDC, and Raman intensity for the six TMDCs can be scaled as a function of Gruneissen parameter γ and Raman wavenumbers in the frame of Morse-type function. The scaling behavior of Raman intensity and direct band gap in TMDCs indicates of some material-independent picture which can be used for new understanding of properties and design of new-type functional devices for electronic and optoelectronic application based on strain engineering.