Exciton-Exciton Interaction beyond the Hydrogenic Picture in a ${\mathrm{MoSe}}_2$ Monolayer in the Strong Light-Matter Coupling Regime

In transition metal dichalcogenides’ layers of atomic-scale thickness, the electron-hole Coulomb interaction potential is strongly influenced by the sharp discontinuity of the dielectric function across the layer plane. This feature results in peculiar nonhydrogenic excitonic states in which exciton-mediated optical nonlinearities are predicted to be enhanced compared to their hydrogenic counterparts. To demonstrate this enhancement, we perform optical transmission spectroscopy of a ${\mathrm{MoSe}}_2$ monolayer placed in the strong coupling regime with the mode of an optical microcavity and analyze the results quantitatively with a nonlinear input-output theory. We find an enhancement of both the exciton-exciton interaction and of the excitonic fermionic saturation with respect to realistic values expected in the hydrogenic picture. Such results demonstrate that unconventional excitons in ${\mathrm{MoSe}}_2$ are highly favorable for the implementation of large exciton-mediated optical nonlinearities, potentially working up to room temperature.

Figure 1

${\mathrm{MoSe}}_2$ monolayer microcavity. (a) Outline of the microcavity structure: a ${\mathrm{MoSe}}_2$ monolayer (red) and bilayer (green) embedded in polymethyl methacrylate (PMMA) (pale blue) are sandwiched between two Bragg mirrors (DBR). (b) White light image of the microcavity; the ${\mathrm{MoSe}}_2$ layers have been color shaded and outlined. The experiments performed at 105 K (127 K) were realized in the area labeled (1) [(2)]. The bare cavity measurements have been done in the area labeled (3). (c) ${\tilde{g}}_x(0)$ dependence on $\mu$, and (d) ${\tilde{g}}_s(0)$ dependence on $a_B$. The dashed line and gray area show hydrogenic exciton (HE) theory corrected by a factor ${\alpha }_0=3.3\pm 0.8$ following [24] (see text). The black squares highlight HE theory for CdTe, ZnSe, ZnO, CuBr, and CuCl [25]. The hollow square shows the 30% enhanced HE theory for ${\mathrm{MoSe}}_2$ [54]. The blue diamond is a measurement in a GaAs microcavity taken from [24]. Our best measurements are shown as red circles. The upper axis in (c) indicates the bulk exciton binding energy for each material [25]. Room-temperature-stable excitons are on the right side of the vertical dashed line [25].

Figure 2

Nonlinear transmission spectroscopy. Measured normalized transmission spectra $T(\omega )/\mathrm{Max}(T)$ at $T=127\mathrm{K}$ (a) and $T=105\mathrm{K}$ (b). The spectra are stacked from the lowest used pulse energy $W$ (bottom) to the highest (top). The pulse energy $W$ used for each spectrum is indicated on the right axis. The laser pulse spectrum is shown in (a),(b) as a red dotted line. The dashed vertical black lines in (a),(b) highlight the polaritonic resonances in the linear regime. The theoretical fits are shown as solid gray lines. (c) Spatially resolved lower polariton transmission peak energy measured at $T=127\mathrm{K}$, across the excitation spot diameter, for increasing $W$ [same color code as in (a)]. The spatial laser intensity profile is shown as a red dotted line. The spectra in (a) have been measured at $y=0$ (dashed vertical line). (d) Color-scaled normalized transmission spectra at $W=451\mathrm{pJ}$ versus the polarization state $|\theta ⟩$ (vertical axis). The circle symbols show the lower polariton peak energy; the solid black line is a theoretical fit $B_0+B_{\theta }{\sin }^{2}2\theta$ following Eqs. (3) and (4), where $B_0=7.9\mathrm{meV}$ and $B_{\theta }=-2.7\mathrm{meV}$.