Collective optical properties of moiré excitons

Abstract

We propose that excitons in moiré transition metal dichalcogenide bilayers offer a promising platform for investigating collective radiative properties. While some of these optical properties resemble those of cold atom arrays, moiré excitons extend to the deep subwavelength limit, beyond the reach of current optical lattice experiments. Remarkably, we show that the collective optical properties can be exploited to probe certain correlated electron states without requiring subwavelength spatial resolution. Specifically, we illustrate that the Wigner crystal states of electrons doped into these bilayers act as an emergent periodic potential for excitons. Moreover, the collective dissipative excitonic bands and their associated Berry curvature can reveal various charge orders that emerge at the corresponding electronic doping. Our study provides a promising pathway for future research on the interplay between collective effects and strong correlations involving moiré excitons.

Figures (4)

• Figure 1: (a) Illustration of tunneling mediated by dipole-dipole interactions (green arrow) of an exciton (indicated by a pair of red and light blue dots) in a moiré potential (yellow) with period $a_M$. The potential can host a Wigner crystal state (WC) of doped electrons (dark blue dots), here a filling of $\nu_e=\frac{1}{3}$ is illustrated. Due to exciton-electron repulsion, the exciton cannot populate the sites occupied by electrons (indicated by the crossed-out dashed path). The remaining available sites form an emergent excitonic lattice. (b) WC at various $\nu_e$ in zero-twist WSe2/WS2xu2020correlatedhuang2021correlated. The remaining empty sites provide a lattice for exciton tunneling shown in panel (a).
• Figure 2: Collective excitonic lineshifts $\Delta_{\bm{Q}}$ (solid lines) and linewidths $\Gamma_{\bm{Q}}$ (dashed) emerging from charge-ordered zero-twist WSe2/WS2 with electron fillings (a) $\nu_e=0$ and (b) $\nu_e=\frac{1}{3}$. The vertical axes are displayed in units of $\gamma N_{\nu_e}$, with $N_{\nu_e}$ defined in Eq. \ref{['eq:N_nu_e_theta']}. The horizontal axes represent the Bloch momentum $\bm{Q}$, which follows a piecewise-linear path through high-symmetry points in the Brillouin zone, as indicated by the hexagon in the inset of (a). Momenta within the light cone are indicated by the green shaded area (size enlarged for clarity). Different colors label distinct single-particle exciton bands. The parameters used are: $a_M=8.25$nm, $\omega_{\mathrm{ex}} =1.55$eV, and $a_W=2$nm Supplementpark2023dipole.
• Figure 3: Dependence of collective lineshifts and linewidths at $\bm{Q}=0$ (a) on $\nu_e$ for all states at zero twist and (b) on twisting angle $\theta$ and $\nu_e$, whose effects manifest in the combined factor $N_{\nu_e}(\theta)$, see Eq. \ref{['eq:N_nu_e_theta']}. Dashed lines in (b) indicate linear fits with slope $1$. Here we set $\delta=0.04$park2023dipole, and $a_W(\theta)= (1+ \theta^2/\delta^2)^{-\frac{1}{4}}a_W(0)$wu2018hubbard; all other parameters are the same as in Fig. \ref{['Fig_2']}.
• Figure 4: Comparison between properties of topological and non-topological collective bands from $\nu_e=0$ and $\nu_e=\frac{1}{2}$, respectively, with Zeeman splitting $\mu_BB=20\gamma$. (a) Dependence of Berry curvature ($\Omega$) on Bloch momentum magnitude $Q$ for the two bands at each $\nu_e$ (labeled by colors and $\Lambda$), with solid and dashed lines indicating results from the full model $\hat{H}'$ and the low-momentum model Eq. \ref{['eq:low_kB_model']}, respectively. The vertical axis is in units of $J/\gamma$, where $J$ is fit from $\Gamma_{\bm{Q}}$ in Fig. \ref{['Fig_2']}(a) using a momentum sample within $Q\leq {\pi}/{25\lambda_{\mathrm{ex}}}$. The gray vertical line indicates the momentum satisfying $JQ^2=\mu_BB$. The inset shows that the dependence of $\Omega$ on the polar angle of $\bm{Q}$ is negligible. (b) The phase of $S_{-+}$ at $k=\frac{2\pi}{\lambda_{\mathrm{ex}}}$ and $\bm{k}_{||}=k_x\bm{e}_x+k_y\bm{e}_y$ for each $\nu_e$. All other parameters are the same as in Fig. \ref{['Fig_2']}.