🔬 mesoscale physics

Resolving High-Energy States of Interlayer Excitons in MoSe $_2$ /WSe $_2$ Heterostructures

This study utilizes photoluminescence excitation spectroscopy to experimentally resolve a Rydberg-like series of high-energy interlayer exciton states in MoSe $_2$ /WSe $_2$ heterostructures, demonstrating that these states are largely independent of twist angle and align with theoretical predictions based on screened Coulomb interactions.

Original authors: Chirag Chandrakant Palekar, Paulo E. Faria Junior, Tobias Manthei, Maximilian Nagel, Bhabani Sankar Sahoo, Shachi Machchhar, Imad Limame, Martin Podhorský, Jaroslav Fabian, Bárbara Rosa, Stephan Reitz

Published 2026-08-04

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CC BY 4.0

Original authors: Chirag Chandrakant Palekar, Paulo E. Faria Junior, Tobias Manthei, Maximilian Nagel, Bhabani Sankar Sahoo, Shachi Machchhar, Imad Limame, Martin Podhorský, Jaroslav Fabian, Bárbara Rosa, Stephan Reitzenstein

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of atoms as a bustling city where electrons are the citizens. In most materials, these citizens are free to roam, but in a special class of ultra-thin materials called transition metal dichalcogenides (TMDCs), they are a bit more shy. When an electron gets excited by light, it leaves behind a "hole," which acts like a positive charge. Because these materials are so thin, the electron and the hole are glued together tightly by an invisible electric force, forming a tiny, bound pair called an exciton. Think of an exciton as a dancing couple that refuses to let go of each other's hands.

Now, picture stacking two different layers of these materials on top of each other, like making a sandwich. If the electron prefers to stay in the top layer and the hole prefers the bottom, they form a special kind of couple called an interlayer exciton. They are still dancing, but now they are separated by a tiny gap, which makes them last longer and behave in unique ways. Scientists are very interested in these pairs because they could help build faster, more efficient computers and new types of lasers. However, just like a musical instrument, these excitons can vibrate at different energy levels. The lowest level is the "ground state" (the calmest dance), but there are higher, more energetic levels called Rydberg states (the wilder, faster dances). For a long time, scientists could easily see the calm dancers, but the wild, high-energy ones were too faint to spot, leaving a big gap in our understanding of how these materials work.

This paper is about finally catching a glimpse of those elusive, high-energy dancers in a specific sandwich made of Molybdenum Diselenide (MoSe2) and Tungsten Diselenide (WSe2). The researchers used a clever technique called Photoluminescence Excitation (PLE) spectroscopy. Instead of just watching the light the material emits, they shined a tunable laser on it and slowly changed the color (energy) of the light. They looked for specific moments where the material suddenly glowed brighter, which would indicate that the laser had hit a high-energy state and the energy trickled down to the ground state.

The team successfully spotted a whole series of these high-energy states, which they named IX2, IX3, and IX4 (corresponding to 2s, 3s, and 4s-like states). These appeared as distinct "resonances" or peaks in their data, sitting at energies below the main intralayer excitons. The paper suggests that these observations confirm the existence of a Rydberg-like series for interlayer excitons, meaning they follow a predictable pattern of energy steps, much like the rungs on a ladder.

One of the most surprising findings concerns the twist angle—the angle at which the two layers are stacked relative to each other. Scientists often think that twisting these layers changes everything, creating new "superlattices" that alter how the excitons behave. However, the authors found that while the ground state (the calm dancer) shifts its energy significantly when the twist angle changes, the high-energy states (the wild dancers) remain remarkably stubborn. Whether the layers were twisted by 1°, 14°, or 56°, the energy levels of these excited states stayed almost exactly the same. The paper argues that this robustness suggests the twist angle isn't the main boss controlling these high-energy states.

Instead, the researchers propose that dielectric screening—how the surrounding environment (like the air or the glass slide the material sits on) dampens the electric forces between the electron and hole—is the real key. Through computer simulations, they showed that changing the environment (for example, putting the material on a silicon dioxide substrate versus suspending it in air) had a much bigger effect on the energy levels than twisting the layers did. The high-energy states are more sensitive to this "screening" because they are larger and more spread out, making them easier to influence by their surroundings.

In short, the paper doesn't just find these hidden high-energy states; it also reveals that they are surprisingly tough to twist around but very sensitive to their environment. This discovery opens a new door for scientists to study these complex interactions, proving that PLE spectroscopy is a powerful tool for exploring the previously invisible world of excited interlayer excitons.

Technical Summary: Resolving High-Energy States of Interlayer Excitons in MoSe2/WSe2 Heterostructures

Problem Statement
Interlayer excitons (IXs) in van der Waals heterostructures (HSs) composed of transition metal dichalcogenide (TMDC) monolayers exhibit unique optical properties, such as electrically tunable emission and long lifetimes, due to the spatial separation of electrons and holes. While the ground states of these excitons are well-characterized, their high-energy excited states (Rydberg-like series) remain largely unexplored. This gap exists primarily because these excited states possess extremely weak oscillator strengths, rendering them nearly invisible to conventional optical characterization techniques like reflection contrast ( $\Delta R/R$ ) spectroscopy. Consequently, direct experimental access to the high-energy IX spectrum has been elusive, limiting the understanding of many-body interactions and dielectric screening effects in these systems.

Methodology
To address this challenge, the authors employed Photoluminescence Excitation (PLE) spectroscopy on MoSe $_2$ /WSe $_2$ heterostructures. Unlike conventional PL, which detects emission under fixed excitation, PLE monitors the emission intensity of a specific state (here, the IX ground state) while scanning the excitation energy. This technique enhances sensitivity to weak optical resonances by tracking the relaxation pathways that feed into the detected emission.

The study utilized heterostructures fabricated via mechanical exfoliation and dry transfer, with specific samples prepared at twist angles of $1^\circ$ , $14^\circ$ , and $56^\circ$ . Measurements were conducted at 4 K. To support experimental findings, the authors performed theoretical calculations using a Wannier-exciton model incorporating screened Coulomb interactions. These calculations modeled various dielectric environments: suspended (air/air), on a SiO $_2$ substrate (air/SiO $_2$ ), and encapsulated in hexagonal boron nitride (hBN/hBN).

Key Contributions and Results

Resolution of a Rydberg-like Series: The PLE measurements successfully resolved multiple resonances below the intralayer exciton energies. The authors assigned these resonances to the $2s$ , $3s$ , and $4s$ -like excited states of the interlayer excitons (denoted as IX $_2$ , IX $_3$ , and IX $_4$ ), establishing a clear Rydberg-like series. The assignment was validated by the excellent agreement between the measured resonance energies and the theoretically calculated energy levels.
Twist Angle Robustness: A significant finding is the robustness of the excited-state spectrum against variations in the twist angle. While the ground state (IX $_1$ ) emission energy exhibits a known dependence on the twist angle, the energy separations of the excited states ( $\Delta E = E_n - E_1$ ) remain remarkably consistent across samples with $1^\circ$ , $14^\circ$ , and $56^\circ$ twist angles. The energy variations for the excited states were minimal (9 meV, 28 meV, and 24 meV for IX $_2$ , IX $_3$ , and IX $_4$ , respectively), indicating that the excited-state ladder is only weakly affected by the moiré potential induced by twist angle.
Dominance of Dielectric Screening: Theoretical analysis revealed that the excited-state spectrum is far more sensitive to the dielectric environment than to the twist angle. Calculations showed that increasing dielectric screening (e.g., moving from suspended to hBN-encapsulated structures) causes a pronounced compression of the excited-state ladder, significantly reducing the energy separation between the ground state and higher-order states. This is attributed to the larger spatial extent (Bohr radius) of the high-energy IX states, which makes them more susceptible to environmental screening.
Validation of PLE Sensitivity: The study demonstrated that PLE spectroscopy provides direct experimental access to high-energy IX states that are inaccessible via reflection contrast. The authors observed that while the integrated intensity modulations for these high-energy states are weak, they are accompanied by distinct, correlated modulations in the emission linewidth and energy of the IX ground state, providing further evidence for the assignment.

Significance
The paper claims that these findings establish the existence of a Rydberg-like series of high-energy interlayer exciton states in van der Waals heterostructures. By demonstrating that PLE spectroscopy can resolve these previously unexplored states, the work opens a direct experimental pathway to investigate fundamental properties of IXs, such as long-range Coulomb interactions and dielectric screening effects. The results highlight that while twist angle is a powerful tool for tuning ground-state properties, the excited-state spectrum is governed primarily by dielectric screening and structural disorder, offering new insights into the engineering of excitonic states in 2D semiconductors.

Technical Summary: Resolving High-Energy States of Interlayer Excitons in MoSe2/WSe2 Heterostructures

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