Trion formation dynamics in monolayer transition metal dichalcogenides

We report charged exciton (trion) formation dynamics in doped monolayer transition metal dichalcogenides, specifically molybdenum diselenide $\left(\mathrm{MoS}{\mathrm{e}}_2\right)$, using resonant two-color pump-probe spectroscopy. When resonantly pumping the exciton transition, trions are generated on a picosecond time scale through exciton-electron interaction. As the pump energy is tuned from the high energy to low energy side of the inhomogeneously broadened exciton resonance, the trion formation time increases by $\sim 50\%$. This feature can be explained by the existence of both localized and delocalized excitons in a disordered potential and suggests the existence of an exciton mobility edge in transition metal dichalcogenides.

Figure 1

(a) Calculated relative trion wave function. The positions of a hole and an electron (indicated by + and – signs, respectively) are fixed at 1 nm separation corresponding to the exciton Bohr radius. The asymmetric distribution of the wave function is due to the attractive (repulsive) Coulomb force between the hole (electron) and the second electron. (b) Energy diagram illustrating the two-color pump-probe scheme for measuring the ETF with a finite trion formation time ${\tau }_f$. Pump and probe energies are tuned to the exciton and trion resonances, respectively.

Figure 2

(a) Normalized two-color differential reflectivity (dR/R) measurement at zero pump-probe delay. Exciton (XX) and trion (TT) peaks appear on the diagonal dashed lined. Exciton-trion coupling appears in the spectrum as cross diagonal peaks (XT and TX). The notation XT represents the optical response while resonantly pumping the exciton and probing the trion. Other notations are defined in a similar manner, with the first letter referring to the pump energy and the second letter referring to the probe energy. (b) Delay scans for the four peaks indicated by the circles in (a). XT has a finite rise time to the maximal dR/R signal while other peaks have pulse-width-limited rise times. The excitation pulse (the gray shaded area) is shown for comparison.

Figure 3

(a) Normalized degenerate differential reflectivity measurement at zero delay between the pump and probe pulses. Lorentzian fits to spectral peaks are shown with dotted lines (trion: $\sim 1631$ meV, $\mathrm{FWHM}\hspace{0.17em}\sim \hspace{0.17em}4.5$ meV; exciton: $\sim 1662$ meV, $\mathrm{FWHM}\hspace{0.17em}\sim \hspace{0.17em}6.5$ meV). The pump $\left(\hslash {\omega }_{\mathrm{pump}}\right)$ and probe $\left(\hslash {\omega }_{\mathrm{pr}}\right)$ energies for the nondegenerate ETF experiment are indicated by the arrows. (b) Integrated XT delay scans for the two pump excitation energies (1656 and 1662 meV). When pumping at 1662 meV, the rise to maximum dR/R signal is faster compared to excitation at 1656 meV. The fits to the model (described in the text) are shown as lines.

Figure 4

(a) Dependence of trion formation time on changing pump energy across exciton resonance. The exciton resonance is overlaid for reference. (b) Illustration of different disorder potentials. Excitons below (above) the mobility edge are localized (delocalized) and take longer (shorter) to capture an electron and form a trion.