In-Plane Propagation of Light in Transition Metal Dichalcogenide Monolayers: Optical Selection Rules

The optical selection rules for interband transitions in ${\mathrm{WSe}}_2$, ${\mathrm{WS}}_2$, and ${\mathrm{MoSe}}_2$ transition metal dichalcogenide monolayers are investigated by polarization-resolved photoluminescence experiments with a signal collection from the sample edge. These measurements reveal a strong polarization dependence of the emission lines. We see clear signatures of the emitted light with the electric field oriented perpendicular to the monolayer plane, corresponding to an interband optical transition forbidden at normal incidence used in standard optical spectroscopy measurements. The experimental results are in agreement with the optical selection rules deduced from group theory analysis, highlighting the key role played by the different symmetries of the conduction and valence bands split by the spin-orbit interaction. These studies yield a direct determination of the bright-dark exciton splitting, for which we measure $40\pm 1\mathrm{meV}$ and $55\pm 2\mathrm{meV}$ in ${\mathrm{WSe}}_2$ and ${\mathrm{WS}}_2$ monolayer, respectively.

Figure 1

Schematics of the excitation or detection geometry of the PL for (a) light propagating perpendicular to the ML plane, detection of the PL from the top of the sample, and (b) light propagating parallel to the ML plane, detection of the PL from the edge of the sample. (c) Detection of the PL from the top of the sample with a $\mathrm{NA}=0.6$ objective. The PL spectrum of $\text{h}\text{−}\mathrm{BN}/{\mathrm{WSe}}_2$ ML/h-BN at $T=13\mathrm{K}$; the polarization of the excitation or detected light is in the ML plane ($x$ direction). The inset shows the PL spectrum measured with a higher NA objective ($\mathrm{NA}=0.82$). (d) Detection of the PL from the edge of the sample. The PL spectrum of $\text{h}\text{−}\mathrm{BN}/{\mathrm{WSe}}_2$ ML/h-BN at $T=13\mathrm{K}$; the polarization of the detected light is in the ML plane ($x$ direction), green line, or perpendicular to it ($z$ direction), red line. (e) Sketch of the band structure of ${\mathrm{WSe}}_2$ ML. The bands are labeled in each valley by the corresponding irreducible spinor representations with arrows in parentheses indicating the dominant electron spin orientation. The green arrows show the transitions optically active for the $x$-polarized light; (f) the green and red arrows show the transitions optically active for $x$-polarized and $z$-polarized light, respectively (light propagating parallel to the ML plane).

Figure 2

Detection of the PL from the edge of the sample. The PL spectrum at $T=13\mathrm{K}$ for (a) $\mathrm{h-BN}/{\mathrm{WS}}_2$ ML/h-BN and (b) $\mathrm{h-BN}/{\mathrm{MoSe}}_2$ ML/h-BN; the polarization of the excitation or detected light is in the ML plane ($x$ direction), green line, or perpendicular to it ($z$ direction), red line.