Origin of trapped intralayer Wannier and charge-transfer excitons in moiré materials

TL;DR

This work resolves longstanding tensions between continuum moiré models and ab initio approaches for intralayer moiré excitons by solving the Bethe–Salpeter equation in an atomistic Wannier-basis framework that includes hBN dielectric screening. It reveals that exciton character—Wannier-like versus charge-transfer—can be tuned by stacking, twist angle, and environmental screening, with the lowest bright exciton being Wannier-like in WS$_2$/WSe$_2$ heterobilayers but CT-like in twisted WSe$_2$ homobilayers under hBN, and switching otherwise in the absence of screening. An adiabatic-switching analysis links moiré-induced direct/indirect band gaps and electron–hole interactions to trapping and the competition between exciton characters, offering a route to engineer excitonic states through structural and dielectric design. Collectively, the results establish atomistic modeling as a powerful, practical tool for designing and controlling excitonic phenomena in moiré materials, enabling targeted optoelectronic functionalities in 2D heterostructures.

Abstract

Moiré materials offer a versatile platform for engineering excitons with unprecedented control, promising next-generation optoelectronic applications. While continuum models are widely used to study moiré excitons due to their computational efficiency, they often disagree with ab initio many-body approaches, as seen for intralayer excitons in WS$_2$/WSe$_2$ heterobilayers. Here, we resolve these discrepancies using an atomistic, quantum-mechanical framework based on the Bethe-Salpeter equation with localized Wannier functions as the basis for the electronic structure. We show that inclusion of dielectric screening due to hexagonal boron nitride (hBN) encapsulation is essential to reproduce the full set of experimentally observed features of moiré intralayer excitons. Our analysis reveals a competition between Wannier and charge transfer characters, driven by variations between direct and indirect band gaps at high symmetry stacking regions due to atomic relaxations and environmentally tunable electron-hole interactions. Building on this insight, we demonstrate that the lowest-energy bright excitons are Wannier-like in WS2/WSe2 heterobilayers but charge-transfer-like in twisted WSe2 homobilayers, despite having comparable moiré lengths when encapsulated in hBN. In the absence of hBN encapsulation, the lowest-energy bright exciton in twisted WSe$_2$ becomes Wannier-like. These results establish atomistic modeling as a powerful and efficient approach for designing and controlling excitonic phenomena in moiré materials.

Figures (11)

• Figure 1: Comparison of theoretical and experimental Jinobservation2019 results for intralayer excitons of WSe$_{2}$ in WS$_{2}$/WSe$_{2}$. At large twist angles, the exciton spectrum is dominated by the A peak, similar to that of monolayer WSe$_{2}$. At small twist angles, the A peak splits into three peaks, labeled I, II, and III, separated by approximately 90 meV. (a) and (b) show theory and experiments with hexagonal boron nitride (hBN) as the substrate, while (c) shows theory without hBN.
• Figure 2: Spatial distribution of intralayer exciton wavefunctions for a fixed hole in twisted WS$_{2}$/WSe$_{2}$ (with hBN screening) (a) At $\theta = 16^\circ$, peak A exhibits the same behavior regardless of hole position. (b) At $\theta = 0^\circ$, peaks I, II, and III (as shown in Fig. \ref{['theoryvsexpt']}(a)) exhibit distinct behaviors depending on the hole position near high-symmetry stacking regions. Peak I is a trapped Wannier type, peak II is trapped with tiny charge-transfer character, and peak III is delocalized with significant charge-transfer character.
• Figure 3: Spatial distribution of intralayer exciton wavefunctions for a fixed hole in parallely aligned WS$_{2}$/WSe$_{2}$ (without hBN screening) At $\theta = 0^\circ$, peaks I$^\prime$, II$^\prime$, and III$^\prime$ (as shown in Fig. \ref{['theoryvsexpt']}(c)) exhibit distinct behaviors depending on the hole position near high-symmetry stacking regions.
• Figure 4: Adiabatic switching of atomic relaxations and its impact Moiré pattern and in-plane atomic displacements, with atomic relaxation decreasing from top to bottom in the first two columns. The expansion of the AA region with reduced relaxation is highlighted with a circle. The impact of this adiabatic switching on electronic and excitonic structures is shown in the next three columns.
• Figure 5: Origin of moiré trapping of excitons and competition between Wannier and charge-transfer characters.. Schematics of low-energy bright intralayer excitons in WSe$_{2}$ are shown (a) for large twist angles and (b) for parallelly aligned WS$_{2}$/WSe$_{2}$ and (c) based on prior continuum theories Jinobservation2019Wutopological2017Bremtunable2020.