Nonlinear and Negative Effective Diffusivity of Interlayer Excitons in Moiré-Free Heterobilayers

Interlayer exciton diffusion is studied in atomically reconstructed ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterobilayers with suppressed disorder. Local atomic registry is confirmed by characteristic optical absorption, circularly polarized photoluminescence, and $g$-factor measurements. Using transient microscopy we observe propagation properties of interlayer excitons that are independent from trapping at moiré- or disorder-induced local potentials. Confirmed by characteristic temperature dependence for free particles, linear diffusion coefficients of interlayer excitons at liquid helium temperature and low excitation densities are almost 1000 times higher than in previous observations. We further show that exciton-exciton repulsion and annihilation contribute nearly equally to nonlinear propagation by disentangling the two processes in the experiment and simulations. Finally, we demonstrate effective shrinking of the light emission area over time across several hundreds of picoseconds at the transition from exciton- to the plasma-dominated regimes. Supported by microscopic calculations for band gap renormalization to identify the Mott threshold, this indicates transient crossing between rapidly expanding, short-lived electron-hole plasma and slower, long-lived exciton populations.

Figure 1

(a) Schematic illustration of an interlayer exciton in a $H_h^h$ reconstructed ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterobilayer. (b) PL peak energy map at $T=5\mathrm{K}$. (c) Representative PL spectrum under low-density pumping. (d) Reflectance contrast derivative with fit from transfer matrix analysis. (e) Circularly polarized PL after ${\sigma }_{+}$ polarized, pulsed excitation with $g$ factors from magneto-optical measurements. (f) Reflectance contrast derivative $R_C$ and (g) degree of circular polarization $P_{\mathrm{circ}}=(I_{+}-I_{-})/(I_{+}+I_{-})$. (h) Optical selection rules for $H_h^h$-stacked ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterobilayer (adapted from Ref. [39]).

Figure 2

(a) Schematic illustration of transient microscopy. (b) Temperature-dependent, linear diffusion coefficient $D_0$ at injection density of $1.2\times {10}^{11}{\mathrm{cm}}^{-2}$ electron-hole pairs per pulse ($0.5\mathrm{\mu }\mathrm{J}{\mathrm{cm}}^{-2}$). (c) Effective diffusion coefficients extracted during the first 100 ps. (d) Calculated free particle band gap, renormalized due to the presence of free charge carriers, and measured exciton peak energy. (e) Line shape broadening at the Mott transition.

Figure 3

(a) Mean-squared displacement of IX for selected densities in units of $n_0=1.2\times {10}^{11}{\mathrm{cm}}^{-2}$. Lines represent simulation results using Eq. (1) due to annihilation only (dotted), repulsion only (dashed), and their combination (solid). (b) Simulated relative increase of $\mathrm{\Delta }$${\text{I}}_{\text{PL}}=[{\text{I}}_{\text{PL}}(t)-{\text{I}}_{\text{PL}}(0)]/{\text{I}}_{\text{PL},\max }$; scale bar is $1\mathrm{\mu }\mathrm{m}$. (c) Spatially dependent time ${\tau }_{\max }$ for the PL to reach its maximum, extracted from measurements and simulation using best fit $U_0=1.7\times {10}^{-15}\mathrm{eV}{\mathrm{cm}}^2$. (d) Measured density dependence of the PL decay time and relative yield, corresponding to the exciton-exciton annihilation coefficient $R_A=5\times {10}^{-3}{\mathrm{cm}}^2/\mathrm{s}$.

Figure 4

(a) Streak camera image of the spatially and time-resolved PL at $T=5\mathrm{K}$ in the high-density regime of about $6\times {10}^{12}{\mathrm{cm}}^{-2}$ ($50n_0$, pump energy density: $25\mathrm{\mu }\mathrm{J}{\mathrm{cm}}^{-2}$) above the Mott transition; the PL intensity is normalized at each time step. (b) Upper: time-resolved mean-squared displacement in experiment comparing high ($50n_0$) and intermediate ($15n_0$) densities. (b) Lower: simulation results showing the implications of a generic two-component model: rapidly expanding, short-lived plasma and longer-lived, slower excitons. (c) Corresponding time-dependent effective diffusion coefficients extracted from $D_{\mathrm{eff}}\propto \partial {\sigma }^2/\partial t$. (d) Schematic illustration of the two-component model.