Fig. 2: Lattice deformations of the A1′(Γ), LA(K), and LA(M) modes in TMDCs and their optical modulations (e.g., differential transmittance ΔT/T0) associated coherent phonon (CP) spectra.
a Asymmetric lattice deformations of the A1′(Γ) and LA(K) modes. Q(t) represents the atomic displacements oscillating over time. The + and − signs of Q(t) denote the directions of vibrations. Lattice deformations of the A1′(Γ) and LA(K) modes are asymmetric because the atomic structures with +Q and −Q displacements are not identical. b Symmetric lattice deformations of the LA(M) mode. In contrast with the asymmetric A1′(Γ) and LA(K) modes, the lattice deformations of +Q and −Q displacements of the LA(M) mode superimposed after the lattice translation are identical. c Lattice oscillations of the asymmetric A1′(Γ) and LA(K) modes, with derived optical responses and CP spectra. As +Q and −Q displacements yield asymmetric atomic structures, nonlinear optical modulations with respect to the phonon frequency ω can be recorded as higher-order CP signals. d Lattice oscillation of the symmetric LA(M) mode, the derived optical response and CP spectrum exhibiting only even orders of the phonon frequency, due to the even function behavior of the optical response.
