Symmetry-Dependent Exciton-Phonon Coupling in 2D and Bulk ${\mathrm{MoS}}_2$ Observed by Resonance Raman Scattering

This work describes a resonance Raman study performed on samples with one, two, and three layers ($1L$, $2L$, $3L$), and bulk ${\mathrm{MoS}}_2$, using more than 30 different laser excitation lines covering the visible range, and focusing on the intensity of the two most pronounced features of the Raman scattering spectrum of ${\mathrm{MoS}}_2$ ($E_{2g}^1$ and $A_{1g}$ bands). The Raman excitation profiles of these bands were obtained experimentally, and it is found that the $A_{1g}$ feature is enhanced when the excitation laser is in resonance with $A$ and $B$ excitons of ${\mathrm{MoS}}_2$, while the $E_{2g}^1$ feature is shown to be enhanced when the excitation laser is close to 2.7 eV. We show from the symmetry analysis of the exciton-phonon interaction that the mode responsible for the $E_{2g}^1$ resonance is identified as the high energy $C$ exciton recently predicted [D. Y. Qiu, F. H. da Jornada, and S. G. Louie, Phys. Rev. Lett. 111, 216805 (2013)].

Figure 1

Raman spectra of ${\mathrm{MoS}}_2$ samples with a different number of layers, and recorded with the different laser excitation energies shown in the right side. Panels from left to right correspond, respectively, to 1, 2, and 3 layers, and bulk samples.

Figure 2

Raman excitation profiles of the $E_{2g}^1$ (open squares) and $A_{1g}$ (solid triangles) Raman peaks in (a) monolayer, (b) bilayer, (c) trilayer, and (d) bulk ${\mathrm{MoS}}_2$ samples. The insets show a zoom-in of the data in the range of 1.8–2.2 eV. The red curves represent the fitting of the experimental data by the expression given in Eq. (1).

Figure 3

(a) Energies and (b) damping constants of the $A$, $B$, and $C$ excitons for the samples with a different number of layers. Red stars represent optical absorption values from Ref. [29] for $1L$, $2L$, and $3L$ and from Ref. [30] for bulk.

Figure 4

(a) Ratio of the intensities of the $E_{2g}^1$ and $A_{1g}$ Raman bands, plotted in a logarithmic scale. (b) Atomic displacements of the $A_{1g}$ phonon mode and electronic orbitals of the $A$ and $B$ excitons. (c) Atomic displacements of the $E_{2g}^1$ phonon mode and electronic orbitals of the $C$ exciton.