Response of Raman-active modes in monolayer 1T′−WTe2 to charge doping

Monolayer $1{T}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{WTe}}₂$ has been tuned to be superconducting by electrostatic gating in recent experiments, which has been explained by soft-mode-phonon-mediated superconductivity in theory. In addition to the phonon branch softening, the charge doping would also affect the Raman vibration properties of monolayer $1{T}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{WTe}}₂$. In this paper, by using the first-principles calculation, we investigate the response of Raman-active modes in monolayer $1{T}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{WTe}}₂$ to charge doping systematically. It is found that, when doped with electrons, most of the Raman modes are blueshifted, and when doped with holes, most of the Raman modes are redshifted. Anomalously, ${A}_g², {A}_g³$, and ${B}_g³$ modes decrease in frequency with the increasing carrier concentration, while ${A}_g³$ and ${A}_g⁶$ modes have frequency changes with multiple turning points. The frequency of the ${A}_g³$ mode, especially, varies in an ``M'' type with increasing carrier concentration, which is correlated with the out-of-plane vibrational properties of the Te atoms. The other two vibration modes correspond to the Raman spectral peaks, the ${A}_g¹$ and ${A}_g⁴$ modes, whose frequencies vary linearly with the doped charge density. This is important for understanding the Raman spectra of doped ${\mathrm{WTe}}₂$ as well as for monitoring the doping levels in ${\mathrm{WTe}}₂$-based electronic devices with a frequency shift for Raman spectral peaks.