Figure 1

(a) Lattice structure and linear chain models of 2 and 3L-MoS${}_2$. Inversion symmetry applies to 2, not 3L-MoS${}_2$. (b) C modes and (c) LBMs in 2 and 3L-MoS${}_2$. (d) High-frequency optical vibration modes for 1 and 2L-MoS${}_2$. The symbol under each mode is its irreducible representation. R or IR indicate if the mode is Raman, or infrared active, or both. The theoretical results based on the diatomic chain model are also indicated.Reuse & Permissions

Figure 2

(a) Raman spectra of 5, 6L, and bulk MoS${}_2$. (b) Raman spectra of 5 and 6L-MoS${}_2$ measured for $\mathit{XX}$ (red) and $\mathit{YX}$ (blue) polarizations. The irreducible representation of each mode is indicated.Reuse & Permissions

Figure 3

(a) Stokes and anti-Stokes Raman spectra of ONL-MoS${}_2$ in the low-frequency range. (b) Stokes and anti-Stokes Raman spectra of ENL-MoS${}_2$. The spectrum of bulk MoS${}_2$ is also included in (a), (b). Dashed and dotted lines in (a), (b) are guides to the eye. (c) Position of typical C and LB modes as a function of $N$. (d) FWHM of C and LBM as a function of $N$. Solid lines in (c), (d) are guides to the eye.Reuse & Permissions

Figure 4

Position of C modes as a function of $N$ for (a) ENL-MoS${}_2$ and (b) ONL-MoS${}_2$. Position of LBMs as a function of $N$ for (c) ENL-MoS${}_2$ and (d) ONL-MoS${}_2$. The blue open circles are the experiment data. The red crosses are the diatomic chain model calculations. The irreducible representation of each mode is also indicated. Solid lines are guides to the eye.Reuse & Permissions

Figure 5

Position of (a) C modes and (b) LBMs as a function of $N$. The blue open circles are the experimental data. The diameter of the circles represents the Raman intensity of each mode. The red crosses are calculations based on the diatomic chain model (DCM). The black solid lines in (a) and (b) are, respectively, fitted by ${\omega }_C\left(N\right)={\omega }_C\left(2\right)\sqrt{1+cos(N_0\pi /N)}$ ($N\ge 2N_0$) and ${\omega }_{\mathrm{LBM}}\left(N\right)={\omega }_{\mathrm{LBM}}\left(2\right)\sqrt{1-cos(N_0\pi /N)}$ $N\ge 2N_0$ for the phonon branches originating from 2L-$N_0=1$, 6L-($N_0=3$) and 10L($N_0=5$)-MoS${}_2$ based on the monatomic chain model (MCM). The gray dashed lines are another set of the C and LB modes based on the MCM.Reuse & Permissions