Nonclassical Exciton Diffusion in Monolayer ${\mathrm{WSe}}_2$

We experimentally demonstrate time-resolved exciton propagation in a monolayer semiconductor at cryogenic temperatures. Monitoring phonon-assisted recombination of dark states, we find a highly unusual case of exciton diffusion. While at 5 K the diffusivity is intrinsically limited by acoustic phonon scattering, we observe a pronounced decrease of the diffusion coefficient with increasing temperature, far below the activation threshold of higher-energy phonon modes. This behavior corresponds neither to well-known regimes of semiclassical free-particle transport nor to the thermally activated hopping in systems with strong localization. Its origin is discussed in the framework of both microscopic numerical and semiphenomenological analytical models illustrating the observed characteristics of nonclassical propagation. Challenging the established description of mobile excitons in monolayer semiconductors, these results open up avenues to study quantum transport phenomena for excitonic quasiparticles in atomically thin van der Waals materials and their heterostructures.

Figure 1

(a) Schematic illustration of the relevant phonon-assisted emission of dark excitons in ${\mathrm{WSe}}_2$. (b) Typical luminescence spectrum of hBN-encapsulated ${\mathrm{WSe}}_2$ monolayer at $T=5\mathrm{K}$, after resonant excitation of $X_0$. Colored areas schematically indicate individual components. Corresponding PL transients are presented in the inset. (c) Representative spatially resolved profiles of the dark exciton PSBs at 0 and 400 ps after resonant excitation of $X_0$. (d) Mean squared displacement of the individually measured PL signatures as function of time. Data are vertically offset for clarity.

Figure 2

(a) PL spectra of dark exciton PSBs after resonant, pulsed excitation. (b) PL spectra of the intravalley dark exciton zero-phonon line. (c) Extracted symmetric peak broadening component (full-width-at-half-maximum) representing the temperature-dependent scattering rate. (d) High-energy exponent representing the exciton temperature.

Figure 3

(a) Transient mean squared displacement of the spatial exciton distribution for temperatures between 5 and 50 K. Data are vertically offset for clarity. (b) Measured diffusion coefficients in comparison to the semiclassical expectation from Eq. (1) based on the measured scattering rates, Fig. 2. The shaded area and the lines are guides to the eye. (c) Illustration of the semiclassical exciton propagation and scattering via thermally activated phonon absorption. (d) Temperature-dependent ratio of the mean free path corresponding to measured diffusion coefficients and the de Broglie wavelength of the excitons. Absolute values for the latter are given in the inset. (e) Exciton diffusivity calculated using a microscopic multivalley model in a semiclassical framework and the influence of quantum corrections.