Exciton dynamics in atomically thin MoS${}_2$: Interexcitonic interaction and broadening kinetics

We report ultrafast pump-probe spectroscopy examining exciton dynamics in atomically thin MoS${}_2$. Spectrally and temporally resolved measurements are performed to investigate the interaction dynamics of two important direct-gap excitons ($A$ and $B$) and their associated broadening kinetics. The two excitons show strongly correlated interexcitonic dynamic, in which the transient blue-shifted excitonic absorption originates from the internal A-B excitonic interaction. The observed complex spectral response is determined by the exciton collision-induced linewidth broadening; the broadening of the $B$-exciton linewidth in turn lowers the peak spectral amplitude of the $A$ exciton. Resonant excitation at the $B$-exciton energy reveals that interexcitonic scattering plays a more important role in determining the broadening kinetics than free-carrier scattering.

Figure 1

(a) Simplified band structure of bulk MoS${}_2$. The black line is the lowest conduction band, and the two orange lines are the highest valence bands split by the interlayer interactions. The two arrows are the direct-gap exciton transitions, namely the $A$ (red arrow) and $B$ (blue arrow) excitons. (b) Raman spectrum with 532-nm excitation laser pulse of thin MoS${}_2$ film sample. (c) AFM image for thin MoS${}_2$ film sample. Inset: the height profile of AFM image in main panel.

Figure 2

Spectrally and temporally resolved ultrafast response after resonant excitation at the $B$ exciton with 10 $\mu {\mathrm{J}/\mathrm{cm}}^2$of pump fluence. (a) DT spectra in the photon-energy range between 1.7 and 2.15 eV. (b) Corresponding temporal dynamics with five different probe-photon energies are shown. Inset: a schematic band structure of MoS${}_2$ near the $K$ point of the Brillouin zone.

Figure 3

Ultrafast interexcitonic transients. (a) Absorption spectrum (thick gray line) and the corresponding fit (dashed black) using the sum of two $A$ (red) and $B$ (blue) absorption Gaussians are shown. (b) Spectrally resolved DT spectra (black open circles) with excitation at the $B$-exciton resonance are shown as a function of $\Delta t$. The red and blue dashed lines indicate the equilibrium peak position of the $A$ and $B$ excitons, respectively. The small arrows indicate the red shifts in the DT spectra. (c) Spectrally integrated DT areas of the absorption Gaussians. (d) Initial build-up dynamics of the $A$ and $B$ excitons (red and blue lines, respectively) and the transient blue shifts of the $A$ and $B$ exciton energies (open squares and triangles, respectively). Inset: a schematic illustrating the transient blue shift of the absorption Gaussians (${\alpha }_0$, without the pump; ${\alpha }_{\mathrm{shifted}}$, with the pump) leads to the red shift of the DT spectra of Δ$T$ (black solid line). (e) Recovery dynamics of the transient blue shift and the corresponding single-exponential fit are shown for the $A$ and $B$ exciton energies (red and blue lines, respectively).

Figure 4

Exciton linewidth broadening. (a) Schematic illustration for the exciton Γ broadening. The gray line shows the equilibrium absorption without the pump. The photo-induced collision leads to the broadening of the $A$ and $B$ excitons (red and blue lines, respectively). (b) Corresponding DT spectra for $A$ (Δ$T_A$, dashed red line) and (Δ$T_B$, dashed blue line) excitons are schematically shown. The overall DT spectra (Δ$T$ = Δ$T_A$ + Δ$T_B$, black solid line) show that the DT amplitude at the $A$ exciton is smaller than that of the Δ$T_A$, as indicated by the black downward-facing arrow. (c) Temporal dynamics of the Γ broadening for the $A$ and $B$ excitons (red open squares and blue open triangles, respectively) and the corresponding bi-exponential fits (red solid for the $A$ exciton and blue solid for the $B$ exciton) after resonant excitation at the $B$ exciton energy. (d) DT spectra with resonant excitation at the $B$-exciton energy (red open circles) and those at the $C$ exciton (green filled circles) are shown. The solid lines (green for the resonant excitation at the $C$ exciton and black for that at the $B$ exciton) represent the corresponding fits to the measured DT spectra at $\Delta t$ = 0.1 ps. The red and blue dashed lines indicate the equilibrium peak positions of the $A$ and $B$ exciton energies, respectively.

Figure 5

Pump-fluence-dependent spectral responses with resonant excitation at the $B$ exciton. (a) DT spectra with different pump fluences of 30 $\mu {\mathrm{J}/\mathrm{cm}}^2$, 20 $\mu {\mathrm{J}/\mathrm{cm}}^2$, and 10 $\mu {\mathrm{J}/\mathrm{cm}}^2$ at a fixed pump-probe time delay of 0.1 ps. (b) Pump-fluence-dependence of blue shift of the $A$ and $B$ exciton center. (c) Linewidth broadening of the $A$ and $B$ excitons as a function of pump fluence. (b), (c) Red open squares and blue open triangles correspond to the $A$ and $B$ excitons, respectively. Gray solid line is an eye-guide for a linear response.