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Direct versus indirect band gap emission and exciton-exciton annihilation in atomically thin molybdenum ditelluride (MoTe$_2$)

We probe the room temperature photoluminescence of $N$-layer molybdenum ditelluride (MoTe$_2$) in the continuous wave (cw) regime. The photoluminescence quantum yield of monolayer MoTe$_2$ is three times larger than in bilayer MoTe$_2$ and forty times greater than in the bulk limit. Mono- and bilayer MoTe$_2$ display almost symmetric emission lines at $1.10~\rm eV$ and $1.07~\rm eV$, respectively, which predominantly arise from direct radiative recombination of the A exciton. In contrast, $N\geq3-$layer MoTe$_2$ exhibits a much reduced photoluminescence quantum yield and a broader, redshifted and seemingly bimodal photoluminescence spectrum. The low- and high-energy contributions are attributed to emission from the indirect and direct optical band gaps, respectively. Bulk MoTe$_2$ displays a broad emission line with a dominant contribution at 0.94~eV that is assigned to emission from the indirect optical band gap. As compared to related systems (such as MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$), the smaller energy difference between the monolayer direct optical band gap and the bulk indirect optical band gap leads to a smoother increase of the photoluminescence quantum yield as $N$ decreases. In addition, we study the evolution of the photoluminescence intensity in monolayer MoTe$_2$ as a function of the exciton formation rate $W_\mathrm{abs}$ up to $3.6\times 10^{22}~\rm{cm}^{-2} s^{-1}$. The lineshape of the photoluminescence spectrum remains largely independent of $W_\mathrm{abs}$, whereas the photoluminescence intensity grows sub-linearly above $W_\mathrm{abs}\sim 10^{21}~\rm cm^{-2} s^{-1}$. This behavior is assigned to exciton-exciton annihilation and is well-captured by an elementary rate equation model.