Spin-Orbit Splitting in Single-Layer ${\mathrm{MoS}}_2$ Revealed by Triply Resonant Raman Scattering

Although new spintronic devices based on the giant spin-orbit splitting of single-layer ${\mathrm{MoS}}_2$ have been proposed, such splitting has not been studied effectively in experiments. This Letter reports the valence band spin-orbit splitting in single-layer ${\mathrm{MoS}}_2$ for the first time, probed by the triply resonant Raman scattering process. We found that upon 325 nm laser irradiation, the second order overtone and combination Raman modes of single-layer ${\mathrm{MoS}}_2$ are dramatically enhanced. Such resonant Raman enhancement arises from the electron-two-phonon triple resonance via the deformation potential and Fröhlich interaction. As a sensitive and precise probe for the spin-orbit splitting, the triply resonant Raman scattering will provide a new and independent route to study the spin characteristics of ${\mathrm{MoS}}_2$.

Figure 1

The Raman spectra of ${\mathrm{MoS}}_2$ samples with different thicknesses excited by (a) 325, (b) 457, (c) 488, and (d) 532 nm laser lines, respectively. All the Raman spectra have been normalized by the intensity of the $A_{1g}$ peak. The dashed Raman spectra in Fig. 1a represent the fitting curves. The vertical dashed lines represent the peak positions of the bulk samples.

Figure 2

(a) Schematic of ${\mathrm{MoS}}_2$ monolayer structure (left). The black lines indicate the unit cell in the $ab$ plane. The unit cell (right) for the monolayer clearly shows the spatial inversion symmetry breaking in the monolayer. (b) Schematic diagram for the TRRS process in ${\mathrm{MoS}}_2$, where $v_1$, $v_2$ represent the valence band splitting due to spin-orbit interaction, and $c_i$ represents a conduction band. Detailed discussion on the conduction band splitting and their involvement in the TRRS process is given in the text and in Fig. 3.

Figure 3

The calculated electronic band structures of ${\mathrm{MoS}}_2$ with the SO coupling considered: (a) single layer, (b) bilayer, and (c) bulk. The red ($v_1$ and $c_5$) and blue lines ($v_2$ and $c_6$) represent the spin-up and spin-down states, respectively. The purple arrow in each graph represents the 325 nm laser induced electronic transition from $v_2$ to $c_6$ bands as described in the process (1) in Fig. 2b. Here we only show the positive helicity (${\sigma }_{+}$) case, as an example.

Figure 4

(a)–(d) 3D partial charge density of electronic bands (a) $v_2$, (b) $v_1$, (c) $c_5$, and (d) $c_6$ for single-layer ${\mathrm{MoS}}_2$, respectively. (e)–(h) 2D partial charge density graphs corresponding to the four electronic bands in (a)–(d).