Dark exciton-exciton annihilation in monolayer ${\mathrm{WSe}}_2$

The exceptionally strong Coulomb interaction in semiconducting transition-metal dichalcogenides (TMDs) gives rise to a rich exciton landscape consisting of bright and dark exciton states. At elevated densities, excitons can interact through exciton-exciton annihilation (EEA), an Auger-like recombination process limiting the efficiency of optoelectronic applications. Although EEA is a well-known and particularly important process in atomically thin semiconductors determining exciton lifetimes and affecting transport at elevated densities, its microscopic origin has remained elusive. In this joint theory-experiment study combining microscopic and material-specific theory with time- and temperature-resolved photoluminescence measurements, we demonstrate the key role of dark intervalley states that are found to dominate the EEA rate in monolayer ${\mathrm{WSe}}_2$. We reveal an intriguing, characteristic temperature dependence of Auger scattering in this class of materials with an excellent agreement between theory and experiment. Our study provides microscopic insights into the efficiency of technologically relevant Auger scattering channels within the remarkable exciton landscape of atomically thin semiconductors.

Figure 1

Schematic illustration of exciton-exciton annihilation (EEA) channels in ${\mathrm{WSe}}_2$. (a) The annihilation of $A$ excitons (purple) gives rise to a higher-lying HX exciton state (green). (b) Regular intravalley (I blue) and additional intervalley Auger recombination processes (II orange and III red) involving momentum-dark ${\mathrm{KK}}^{\prime }$, $\mathrm{K}\mathrm{\Lambda }$, and $\mathrm{K}\mathrm{\Gamma }$ excitons, respectively. The spin-split conduction bands are distinguished by black and grey lines, respectively.

Figure 2

Auger matrix elements $W$ and valley-specific exciton densities in hBN-encapsulated ${\mathrm{WSe}}_2$. (a) Intravalley and intervalley exciton Auger matrix elements ${\left|W\right|}^2$ evaluated at $\mathbf{Q}={\mathbf{Q}}^{\prime }=0$ and their dependence on the final (HX) state quantum index $n$. The matrix elements decrease rapidly with $n$ due to the small overlap between initial $1s$ states and $n>1s$ HX states. (b) Temperature-dependent valley-specific exciton densities in thermal equilibrium illustrating the crucial impact of intervalley $\mathrm{K}\mathrm{\Lambda }$ (orange) and ${\mathrm{KK}}^{\prime }$ (red) excitons and weak impact of intravalley (blue) excitons.

Figure 3

Temperature dependence of the Auger coefficient $R_A$ for hBN-encapsulated ${\mathrm{WSe}}_2$. (a) Theoretically calculated $R_A$ illustrating the separate contributions of intravalley and intervalley Auger processes ($\mathrm{KK}$, ${\mathrm{KK}}^{\prime }$, and $\mathrm{K}\mathrm{\Lambda }$, respectively), cf. Fig. 1. We reveal that the recombination of two $\mathrm{K}\mathrm{\Lambda }$ excitons is the dominant process for temperatures above 30 K. (b) Experimentally extracted Auger coefficients from time-resolved PL measurements. Error bars represent lower and upper limits for the extracted values. The inset illustrates the density-induced recombination rate $r_A^{\exp }$, from which the Auger coefficient can be extracted from the slope.

Figure 4

Substrate and temperature dependence of the Auger coefficient $R_A$ in monolayer ${\mathrm{WSe}}_2$ from microscopic theory. (a) $R_A$ as a function of screening and temperature, revealing a nonmonotonic temperature behavior. (b) Screening dependence of $R_A$ for different temperatures $T=50,100$, and 300 K. (c) Temperature-dependent Auger coefficients in the case of hBN-encapsulation (${\epsilon }_s=4.5$) and for the ${\mathrm{SiO}}_2$ substrate (${\epsilon }_s=2.45$). As illustrated in the inset for the $\mathrm{K}\mathrm{\Lambda }$ Auger process, the increase in screening from ${\epsilon }_s=2.45$ to ${\epsilon }_s=4.5$ makes the Auger scattering more off-resonant leading to a less efficient $R_A$ in hBN-encapsulated TMDs.