Trion-trion annihilation in monolayer ${\mathrm{WS}}_2$

Strong Coulomb interaction in monolayer transition metal dichalcogenides can facilitate nontrivial many-body effects among excitonic complexes. Many-body effects such as exciton-exciton annihilation have been widely explored in this material system. However, a similar effect for charged excitons (or trions), that is, trion-trion annihilation (TTA), is expected to be relatively suppressed due to repulsive like-charges, and it has not been hitherto observed in such layered semiconductors. By a gate-dependent tuning of the spectral overlap between the trion and the charged biexciton through an “anticrossing”-like behavior in monolayer ${\mathrm{WS}}_2$, here we present an experimental observation of an anomalous suppression of the trion emission intensity with an increase in gate voltage. The results strongly correlate with time-resolved measurements, and they are inferred as direct evidence of a nontrivial TTA resulting from nonradiative Auger recombination of a bright trion, and the corresponding energy resonantly promoting a dark trion to a charged biexciton state. The extracted Auger coefficient for the process is found to be tunable ten-fold through a gate-dependent tuning of the spectral overlap.

Figure 1

Gate voltage-dependent modulation of excitonic complexes in ${\mathrm{WS}}_2$. (a) Schematic of 1 L ${\mathrm{WS}}_2$/hBN/few-layer graphene device. A gate voltage ($V_g$) is applied between the two contact pads. (b) Color plot of $V_g$-dependent PL intensity (in log scale) and the spectral position variation of the neutral exciton (${\chi }^0$), positive and negative trions (${\chi }^{\pm }$), intervalley trion ( ${\chi }_t^{-}$), and positive and negative charged biexcitons (${\beta }^{\pm }$). $p$-doping and $n$-doping regions are marked. D stands for the broad defect bound exciton emission peak. (c) Fitted peak positions of all the relevant peaks plotted as a function of $V_g$. The error bars obtained from multiple fits are indicated. (d) Zoomed-in portion (marked by a white dashed box) of the color plot (a), plotted in linear scale, depicting (red and yellow lines to guide the eye represent trion and biexciton, respectively) “anticrossing”-like behavior between ${\chi }^{-}$ and ${\beta }^{-}$.

Figure 2

Mechanism for gate-dependent redshift in emission from trion and charged biexciton with nonzero center-of-mass momenta. (a) The vertical transition from the negative trion state ($|{\chi }^{-}\rangle$) to the conduction band ($|\text{CB}\rangle$), emitting one photon, is shown at two different $V_g$ values. At $V_g=0$ V, $|\text{CB}\rangle$ is almost empty, and transition from the bottom of the $|{\chi }^{-}\rangle$ to $|\text{CB}\rangle$ ($Q=0$) is possible (shown by a sky-blue arrow). With increasing $n$-doping ($V_g>0$ V), lower energy $|\text{CB}\rangle$ states are blocked, and the vertical transition occurs at a higher $Q$ value (shown by a yellow arrow). In-plane ($Q_x\text{−}{Q}_y$) slice shows filling of bands up to a radius of $Q$ by the yellow shaded area (bottom panel). The dissimilar curvatures of the two bands result in a redshift in emission at larger filling. (b) The vertical transition from the negatively charged biexciton state ($|{\beta }^{-}\rangle$) to the dark trion ($|{\chi }_D^{-}\rangle$) state, emitting one photon at two different $V_g$ values. $V_g=0$ V transition occurs at $Q^{\prime }=0$ (shown by a dark blue arrow). At finite $V_g$, the $|{\chi }_D^{-}\rangle$ state is blocked up to $Q^{\prime }$, pushing the vertical transition to occur at higher $Q^{\prime }$ (shown by a red arrow). In-plane ($Q_x\text{−}{Q}_y$) slice area, shaded in red, indicates a larger filling compared to (a) (bottom panel). Loss of electrons from the conduction band in order to form ${\chi }_D^{-}$ is represented by a shaded arrow from $|CB\rangle$ to $|{\chi }_D^{-}\rangle$. (c) COM momenta of the emitting ${\chi }^{-}$ and ${\beta }^{-}$ species plotted as a function of $V_g$ indicating a crossover at higher $V_g$.

Figure 3

Evidence of Auger induced trion-trion annihilation. (a) PL peak evolution for a few representative $V_g$ values. The PL spectra and the corresponding fittings of individual peaks are shown by solid lines and shaded areas, respectively. At $V_g=5$ V, almost complete overlap between ${\chi }^{-}$ and ${\beta }^{-}$ is observed, coupled with a strong suppression of ${\chi }^{-}$ peak intensity. (b) PL intensity values of the fitted ${\chi }^{-}$ (blue spheres) and ${\beta }^{-}$ (red spheres) peaks as a function of $V_g$. The shaded region indicates the strong Auger regime. (c) Spectral area overlap of ${\chi }^{-}$ and ${\beta }^{-}$, normalized with respect to ${\chi }^{-}$ area, is plotted with increasing $V_g$. The striking anticorrelation with the ${\chi }^{-}$ peak intensity in (b) is conspicuous in the strong Auger region. (d) TRPL data (open symbols) is fitted with Eq. (5) (solid traces) after deconvolution with the IRF, at representative $V_g$ values. IRF is shown by the light blue shaded area for $V_g=0$ V. (e) Normalized TRPL full width at half-maxima (FWHM) is plotted with respect to $V_g$, indicating a nonmonotonic trend with a reduced value in the strong Auger region. (f) Fitted values of the Auger coefficient ($\gamma$) from (d) are plotted with $V_g$, again showing nonmonotonic variation. The deep shaded region covering (b), (c), (e), and (f) represents the dominant Auger effect, which gradually reduces on both sides.

Figure 4

Schematic diagram depicting the resonant Auger mechanism. (a) Schematic representation of the Auger interaction between two trions (${\chi }^{-}$ and ${\chi }_D^{-}$). When the spectral overlap between the ${\beta }^{-}$ and ${\chi }^{-}$ transition is strong, the nonradiative annihilation of a ${\chi }^{-}$ gives rise to the transition of one ${\chi }_D^{-}$ to ${\beta }^{-}$ state (top panel). When the spectral overlap is reduced, such strong resonance is eliminated, suppressing the Auger efficiency (bottom panel). (b) COM momentum for ${\beta }^{-}$ ($Q^{\prime }$) is plotted with respect to that of ${\chi }^{-}$ ($Q$), obtained from Eq. (3). The energy corresponds to the maximum overlap point, indicated by the red dots in Fig. 3.