Phonon-induced Markovian and non-Markovian effects on absorption spectra of moiré excitons in twisted transition metal dichalcogenide bilayers

TL;DR

This paper develops a time-convolutionless master-equation framework to analyze how exciton–phonon coupling in twisted TMDC bilayers, and its dependence on the twist angle, shapes the absorption spectra of intralayer moiré excitons. By separating acoustic and optical phonon effects and introducing the generalized phonon spectral density (gPSD), the authors identify a non-Markovian, phonon-sideband–dominated regime at small twist angles and a Markovian, broadened regime at larger angles, with an intermediate magic angle where acoustic scattering is enhanced. In a multi-band setting, intra-band optical-phonon scattering can suppress higher-band peaks when their bandwidth exceeds the optical phonon energy, linking spectral features directly to the moiré band structure and symmetry. The results provide a quantitative framework for interpreting moiré exciton absorption and predict pronounced twist-angle–dependent phonon effects relevant for optoelectronic applications in layered TMDCs.

Abstract

The properties of moiré excitons in twisted bilayers of transition metal dichalcogenides (TMDCs) vary significantly with the twist angle, ranging from quasi localized excitons with flat dispersions for small twist angles to delocalized excitons for larger ones. This twist angle dependence directly impacts the exciton-phonon coupling, which plays a significant role for the optical properties of these materials. In this work we theoretically investigate the twist angle dependent influence of phonons on absorption spectra of intralayer moiré excitons in a twisted TMDC hetero-bilayer. For the lowest-lying intralayer moiré exciton we find that the exciton-phonon coupling interpolates between two physically distinct regimes when tuning the twist angle. At small twist angles non-Markovian polarization dynamics and phonon sidebands dominate the properties of absorption spectra for localized excitons. For larger twist angles Markovian processes become more important leading to additional line broadening. Furthermore, the absorption spectra here show a characteristic asymmetric peak similar to monolayer TMDCs. When taking into account multiple bright moiré exciton bands we find that intraband scattering due to optical phonons has a significant impact on absorption spectra, effectively suppressing absorption peaks of higher lying bands when their bandwidth surpasses the optical phonon energy.

Figures (12)

• Figure 1: Schematic picture of the moiré lattice generation. The two sets of monolayer lattice basis vectors (left) and the moiré superlattice basis vectors (right) are respectively indicated by two vectors sharing the same origin.
• Figure 2: Moiré exciton band structures for different twist angles along high symmetry directions in the first MBZ as indicated in the inset.
• Figure 3: Moiré exciton band structure $\hbar\omega_{n,\bm{k}}$ (left) and corresponding gPSD $\rho_{j=\rm{ac}}^{(1,1)}(\Omega)$ of the lowest lying moiré exciton band due to acoustic pho-non scattering (right) for the three twist angles $\theta=1^{\circ}$ (a), $\theta=3^{\circ}$ (b), $\theta=5^{\circ}$ (c) and three different temperatures $T=4$ K (blue), $T=70$ K (yellow), and $T=200$ K (red). Acoustic pho-non-assisted intra-band transitions from the $\gamma$- to the $m$-point of the lowest lying moiré exciton band (left) are sketched for phonon absorption (red arrows) and emission (green arrows) with black vertical arrows corresponding to the energy mismatch $\hbar\Omega$ that is needed for that transition to occur.
• Figure 4: Dynamics of the absolute value of the moiré exciton polarization $|p_1(t)|$ from Eqs. \ref{['eq:pol_1']} including only acoustic phonon scattering $j=\rm{ac}$ (top) and corresponding time dependent decay rates $\Re[\Gamma_{\rm{ac}}^{(1,1)}(t)]$ calculated via Eq. \ref{['eq:Gamma_t']} (bottom) for the twist angles $\theta=1^{\circ}$ (a), $\theta=3^{\circ}$ (b), and $\theta=5^{\circ}$ (c) at a temperature of $T=4$ K. We compare the full simulations (solid) with the Markov limit (dashed).
• Figure 5: Absorption spectra of the lowest lying moiré exciton band including only acoustic phonon scattering for the twist angles $\theta=1^{\circ}$ (a), $\theta=3^{\circ}$ (b), and $\theta=5^{\circ}$ (c) and the temperatures $T=4$ K (blue), $T=70$ K (yellow), and $T=200$ K (red). Top: Normalized spectra on a linear scale. Bottom: Non-normalized spectra on a logarithmic scale.