Electron-hole plasma formation dynamics observed through exciton-plasma interactions in transition metal dichalcogenides

How do the many-particle interactions evolve in semiconductors is crucial for understanding light-matter interactions. We observe Coulomb-correlated electron-hole plasma formation via its interaction with excitons in a transition metal dichalcogenide semiconductor. We observe that under intense photoexcitation $\sim {10}^{19}$ per ${\mathrm{cm}}^3$, huge damping destroys the Coulomb correlation and hinders the plasma formation until a majority of the free carriers recombine and the plasma oscillation period becomes sufficiently smaller than the damping time constant. Moreover, only 1%–3% of the injected free carriers form Coulomb-correlated plasma. Our study sheds light on exciton-plasma interactions and quasistatic Coulomb screening, which play pivotal roles in device engineering.

Figure 1

(a) (Upper panel) Linear absorption spectrum (extinction coefficient times sample length $\alpha l$) of multilayered ${\mathrm{MoS}}_2$ obtained by an ultrafast supercontinuum pulse. Corresponding $A$, $B$, $C$, and $D$ excitonic line shapes are disentangled from the continuous background of the band-to-band absorption spectrum and are depicted in the same scale (note the break in the absorption axis). (Lower panel) The optical spectrum of the various pump excitations utilized in this work. The peak amplitudes of the same are in arbitrary units. (b) Transient absorption spectra for 400 nm pump excitation at probe wavelength 375 to 800 nm. Temporal evolution of oscillator strength, resonance energy, and linewidth of $C$ exciton in the presence of (c) 400 nm and (d) 650 nm pump excitation.

Figure 2

Temporal evolution of $\mathrm{\Delta }{A}_C$ and the corresponding $\mathrm{\Delta }{A}_C^{-1}$ for (a) 400 nm (above-resonance) pump and (b) 600 nm (below-resonance) pump excitation. We add dashed lines of exponential and linear types on the $\mathrm{\Delta }{A}_C^{-1}$ as a guide to the eye. (c) The first-order rate constant at different pump wavelengths as estimated from the model in Eq. (2). The spectral shape of the $C$ exciton is indicated by dashed lines in arbitrary units for reference. (d) (Upper panel) Valence band maxima and conduction band minima of multilayered ${\mathrm{MoS}}_2$ adapted from Ref. [37]. (Lower panel) Gradient of the valence band maxima and conduction band minima are displayed. Same values (within 1 eV/$\frac{2\pi }{a}$, where $a$ is the in-plane lattice constant) of the gradients indicate maxima in the joint-density-of-states that correspond to the $C$ exciton states. Filled and unfilled circles indicate photoinduced electrons and holes. Intervalley scattering paths are depicted by arrows.

Figure 3

(a) Pump-induced alteration of $C$ exciton resonance energy (normalized $\mathrm{\Delta }{E}_C$) as a function of pump wavelength and probe delay. (b) Linear variation of $\mathrm{\Delta }{E}_C^{-1}$ with delay for ${\lambda }_p=550$ nm. (c) Time evolution of $\mathrm{\Delta }{E}_C$ and the corresponding contributions from the phonon-induced lattice heating ($\mathrm{\Delta }{E}_{\text{ph}}$) and electron-hole plasma screening ($\mathrm{\Delta }{E}_{\text{EHP}}$) for ${\lambda }_p=400$ nm. (d) Similar variations for ${\lambda }_p=650$ nm which also includes an initial blueshift component due to exciton binding energy reduction ($\mathrm{\Delta }{E}_{\text{BE}}$). (e) Phonon rate constants that indicate hot-carrier cooling timescale. (f) Comparison of the second-order rate constant times initial carrier density as obtained from fitting the bleaching and resonance energy renormalization dynamics with Eq. (2) and Eqs. (4) and (5), respectively. The $C$ exciton absorption spectrum is depicted (arbitrary units in $y$ axis) in dashed lines for convenience.

Figure 4

(a) (axis: left) Variation of photoinduced carrier density, (axis: right) instantaneous scattering time ($\tau$) and instantaneous plasma oscillation period ($\frac{2\pi }{{\omega }_{\text{pl}}}$) with probe delay. Here plasma oscillation period becomes less than the scattering time beyond a crossover probe delay of 1.9 ps. (b) Schematic representation of uncorrelated free-carrier gas and correlated electron-hole plasma. Red (blue) filled circles suggest holes (electrons). (c) Temporal evolution of $\mathrm{\Delta }{E}_C$ upon 415 nm pump excitation with different excitation densities. A yellow triangle is inserted in each curve to indicate the probe delay at which $|\mathrm{\Delta }{E}_C|$ reaches a maximum ($t_D$).