Polaron spectroscopy of a bilayer excitonic insulator

Recent advances in fabrication of two-dimensional materials and their moiré heterostructures have opened up new avenues for realization of ground-state excitonic insulators, where the structure spontaneously develops a finite interlayer electronic polarization. We propose and analyze a scheme where an optically generated intralayer exciton is screened by excitations out of the excitonic insulator to form interlayer polarons. Using quantum Monte Carlo calculations we first determine the binding energy of the biexciton state composed of inter- and intralayer excitons, which plays a central role in understanding polaron formation. We describe the excitations out of the ground-state condensate using BCS theory and use a single interacting-quasiparticle-pair excitation Ansatz to describe dynamical screening of optical excitations. Our predictions carry the hallmarks of the excitonic insulator excitation spectrum and show how changing the interlayer exciton binding energy by increasing the layer separation modifies the optical spectra.

Figure 1

(a) Sketch of the X, IX, T, X-IX complexes in terms of electrons and holes (red and blue circles respectively). For the X-IX, the labeling in Eq. (1) is illustrated. Energies (b) and binding energies (c) for different complexes and as a function of the interlayer distance $d$. These results are the output of QMC calculations with parameters suitable for a $\mathrm{Mo}{\mathrm{S}}_2$/hBN/$\mathrm{W}{\mathrm{Se}}_2$ heterostructure.

Figure 2

Polaron spectra as a function of the density for $d=L_1$ (a) and $d=13L_1$ (b). (c) Slice at $n\simeq 3.5\times {10}^{11}{\mathrm{cm}}^{-2}$ [cyan dotted line in (a) and (b)], to highlight the high visibility of the RP for strong pairing (small $d$) as well as of the X-${\mathrm{IX}}^{*}$ peak at large $d$.

Figure 3

Polaron spectra at the density $n\simeq 2\times {10}^{11}$, as a function of the interlayer separation. The X-${\mathrm{IX}}^{*}$ peak lowers in energy for larger $d$ and gains weight when anti-crossing the repulsive polaron to disappear in the AP-RP gap for large $d$. At large $d$ we are in the Fermi polaron regime and the AP gets closer and closer to the energy of the monolayer trion (dashed cyan line). As for the energy of the AP peak, because of the point-like approximation for X, only the $d\gtrsim 10L_1$ tail of the nonmonotonic behavior of the X-IX binding energy in Fig. 1 is recovered. While for the AP energy one should resort to QMC, the other qualitative features of the spectrum arise from the properties of the EXI and are expected to be independent of the point-like approximation (see also I and J of Supplemental Material [38]).

Figure 4

Density of states of the collective modes of momentum $Q$ for $d=L_1$ and $n\simeq {10}^{12}{\mathrm{cm}}^{-2}$ in the absence of an impurity. In (a) the collective modes are computed from $H_{\text{BCS}}$, i.e., for noninteracting quasiparticles, and only the two-quasiparticle continuum is correctly reproduced. In (b) instead one diagonalizes $\mathcal{A}{\left(Q\right)}_{kp}$, which expresses the action of $H_{\text{el}}$ in the tangent space to $|\text{EXI}\rangle$, and one can see the modes that sometimes are called Higgs and Bardasis-Schrieffer. The more refined calculation of panel (c) is instead based on the linearized equations of motion in the Gaussian manifold and captures the gapless Goldstone branch. The color scale is logarithmic in the three panels.