Interlayer Excitons in vdW Heterostructures

• Interlayer excitons are Coulomb-bound electron-hole pairs across adjacent 2D layers, featuring high binding energies, permanent dipole moments, and tunable optical properties.
• They are engineered in van der Waals heterostructures where moiré potentials and quantum confinement enable the exploration of exotic phases and tailored transport characteristics.
• Advanced electrical and optical gating techniques allow precise control of exciton dispersion, valley polarization, and integration into next-generation optoelectronic devices.

An interlayer exciton consists of a bound electron–hole pair with the electron and hole confined to adjacent but spatially separated atomic layers, most notably in van der Waals (vdW) heterostructures such as transition-metal dichalcogenide (TMD) bilayers. The spatial separation yields a permanent electric dipole moment oriented perpendicular to the layers, distinguishing these excitons from their intralayer counterparts and endowing them with novel properties—including large binding energies, elongated lifetimes, strong dipolar interactions, and highly tunable optical and transport characteristics. Interlayer excitons serve as a flexible platform for exploring many-body phenomena, valley and spin physics, and device concepts for optoelectronics and valleytronics.

1. Definition, Theoretical Models, and Fundamental Properties

Interlayer excitons (IXs) are Coulomb-bound electron–hole pairs with the electron (e–) in one two-dimensional (2D) layer and the hole (h+) in an adjacent layer, separated by a distance $d \sim 0.6–1.0$ nm. The quantum wavefunction factorizes as $$\psi_{\rm IX}(r_e, r_h) \approx \varphi_e(r_e)\varphi_h(r_h)\phi_{\text{rel}}(r_e-r_h)$$, where the envelope $\phi_{\text{rel}}$ describes the in-plane correlation (Brotons-Gisbert et al., 2024).

Key physical properties derive from this geometry:

• Exciton Binding Energy: In a 2D hydrogenic model,

$$E_b = \frac{ \mu e^4 }{ 2 (4\pi \epsilon)^2 \hbar^2 }$$

with reduced mass $\mu$, dielectric constant $\epsilon$. TMD IXs exhibit $E_b\sim 150–300$ meV, one order of magnitude above GaAs quantum wells, and still ∼20% below intralayer exciton binding due to non-negligible interlayer separation and screening (Torun et al., 2018, Horng et al., 2017, Brotons-Gisbert et al., 2024).

• Permanent Dipole Moment: $p = e d \sim 10^{-28}$ C·m ($\sim 30$ Debye), enabling strong electrostatic tunability and pronounced Stark effect (Brotons-Gisbert et al., 2024, Horng et al., 2017).
• Radiative and Nonradiative Lifetimes: The reduced wavefunction overlap suppresses radiative recombination ($\tau_{\rm rad}\sim 10–100$ ns at low T), nonradiative times can be shorter in impure/layer-mismatched systems, yielding total lifetimes exceeding 100 ns in optimal conditions (Brotons-Gisbert et al., 2024, Tan et al., 2019).
• Spin–Valley-Layer Configurations: Optical selection rules depend on stacking, twist, and spin-orbit splitting; effective g-factors span –16 to +7, with valley polarization observable and tunable (Brotons-Gisbert et al., 2024, Tan et al., 2019).
• Stark Effect: Out-of-plane electric fields shift the IX resonance linearly, with energy tunability up to 400 meV demonstrated in strong-field TMD architectures (Kovalchuk et al., 2023, Zhang et al., 2023).

2. Exciton Dispersion, Moiré Engineering, and the Role of Quantum Confinement

The center-of-mass (COM) dispersion of the IX is typically parabolic ($$\psi_{\rm IX}(r_e, r_h) \approx \varphi_e(r_e)\varphi_h(r_h)\phi_{\text{rel}}(r_e-r_h)$$0, $$\psi_{\rm IX}(r_e, r_h) \approx \varphi_e(r_e)\varphi_h(r_h)\phi_{\text{rel}}(r_e-r_h)$$1), but can be nontrivially engineered:

• Tunable Dispersion: When constituent carriers have a nonmonotonic band dispersion (e.g., "Mexican hat"), the IX dispersion $$\psi_{\rm IX}(r_e, r_h) \approx \varphi_e(r_e)\varphi_h(r_h)\phi_{\text{rel}}(r_e-r_h)$$2 admits regimes—parabolic, quartic/flat, to ring-minimized "moat" shapes—each correlating with a different low-temperature quantum phase. This provides a handle for band and phase engineering via electric/magnetic field or strain (Skinner, 2016).
• Moiré Superlattices: Lattice mismatch or twist between layers generates a moiré potential modulating IX energy landscape: $$\psi_{\rm IX}(r_e, r_h) \approx \varphi_e(r_e)\varphi_h(r_h)\phi_{\text{rel}}(r_e-r_h)$$3, with characteristic periods $$\psi_{\rm IX}(r_e, r_h) \approx \varphi_e(r_e)\varphi_h(r_h)\phi_{\text{rel}}(r_e-r_h)$$4 nm and depths $$\psi_{\rm IX}(r_e, r_h) \approx \varphi_e(r_e)\varphi_h(r_h)\phi_{\text{rel}}(r_e-r_h)$$5 meV. This produces minibands, localized "quantum-dot" trapping, and flattens electronic bands (Brotons-Gisbert et al., 2024, Schmitt et al., 2021). Femtosecond photoemission tomography reveals the corresponding modulated wavefunction and allows extracting potential depth and moiré-induced carrier correlation (Schmitt et al., 2021).
• Quantum Dots and 1D Architectures: In quantum dot or nanoribbon structures (e.g., bilayer graphene nanoribbons), IXs with binding energies $$\psi_{\rm IX}(r_e, r_h) \approx \varphi_e(r_e)\varphi_h(r_h)\phi_{\text{rel}}(r_e-r_h)$$6 eV and radiative lifetimes up to 9.4 μs can be realized. The stacking order, interlayer separation, and lateral confinement precisely control exciton properties (Rocha et al., 15 Jul 2025, Liu et al., 2024).

3. Many-Body Effects: Interactions, Correlated Phases, and Collective Transport

Repulsive dipole–dipole interactions, tunable by the interlayer separation and environment, fundamentally distinguish IX many-body behavior:

• Dipolar Interaction: $$\psi_{\rm IX}(r_e, r_h) \approx \varphi_e(r_e)\varphi_h(r_h)\phi_{\text{rel}}(r_e-r_h)$$7 can reach ∼1 meV at 20 nm separation. This interaction is central to the formation of strongly-correlated bosonic fluids, Wigner crystals, and enables blue-shifting of PL peaks at higher exciton densities (Xu et al., 2022, Miller et al., 2017, Brotons-Gisbert et al., 2024).
• Bose–Einstein Condensation (BEC) and Superfluidity: The criteria $$\psi_{\rm IX}(r_e, r_h) \approx \varphi_e(r_e)\varphi_h(r_h)\phi_{\text{rel}}(r_e-r_h)$$8, where $$\psi_{\rm IX}(r_e, r_h) \approx \varphi_e(r_e)\varphi_h(r_h)\phi_{\text{rel}}(r_e-r_h)$$9, is more accessible than in GaAs systems due to large $\phi_{\text{rel}}$0, high $\phi_{\text{rel}}$1, and long $\phi_{\text{rel}}$2. Quantum degeneracy temperatures $\phi_{\text{rel}}$3 K are reachable in dense, controlled traps (Zhang et al., 2023).
• Correlated and Exotic Phases: By tuning the IX dispersion or the moiré potential, one can access superfluid, Wigner-crystal, supersolid, and other nontrivial phases. For instance, transitions from BEC to Wigner solid occur as the "moat" in excitation spectrum is tuned via external controls (Skinner, 2016).
• Coupled Multilayer Systems: In quadrilayer configurations, interlayer exciton–exciton attraction can induce pairing into biexcitons and the formation of biexciton superfluids at densities $\phi_{\text{rel}}$4 cm$\phi_{\text{rel}}$5 (Xu et al., 2022).

4. Electrical, Optical, and Valleytronic Control

• Electrical Tunability: IX emission, valley polarization, and lifetime are highly bandwidth-tunable by perpendicular or in-plane fields through the linear and quadratic Stark effect ($\phi_{\text{rel}}$6) and via field-induced hybridization with intralayer states (Kovalchuk et al., 2023, Zhang et al., 2023, Tan et al., 2019).
• Layer and Dielectric Engineering: IX properties can be modulated by the dielectric environment, quantum-well thickness, organic spacers, and alloy composition to optimize binding, emission, and transfer rates (Ji et al., 2020, Masanta et al., 27 Mar 2025, Tan et al., 2019).
• Optical Manipulation: Strong oscillator strength is observed for momentum-direct IXs (up to ∼20% of bright intralayer exciton at room temperature for bilayer MoS$\phi_{\text{rel}}$7), with absorption and emission tailored by band offset and stacking configuration (Gerber et al., 2018, Torun et al., 2018).
• Valley and Spin Polarization: IXs retain and allow control over valley pseudospin, with degrees of polarization $\phi_{\text{rel}}$8 approaching 0.6 at low temperature and persisting at room temperature in engineered structures. Alloying or applying magnetic fields further enhances valley lifetime and enables valleytronic device operation (Masanta et al., 27 Mar 2025, Tan et al., 2019).
• Transport and Circuit Elements: IXs can be driven along potential landscapes defined by patterned gates or moiré structures, realizing excitonic diodes, transistors, and routers with drift velocities up to $\phi_{\text{rel}}$9 cm/s and sub-100 ps switching (Shanks et al., 2022, Zhang et al., 2023).

5. Experimental Realizations, Quantum Emitters, and Device Applications

• Heterostructures and Homobilayers: Both type-II hetero-bilayers (e.g., MoSe$$E_b = \frac{ \mu e^4 }{ 2 (4\pi \epsilon)^2 \hbar^2 }$$0/WSe$$E_b = \frac{ \mu e^4 }{ 2 (4\pi \epsilon)^2 \hbar^2 }$$1, MoS$$E_b = \frac{ \mu e^4 }{ 2 (4\pi \epsilon)^2 \hbar^2 }$$2/WS$$E_b = \frac{ \mu e^4 }{ 2 (4\pi \epsilon)^2 \hbar^2 }$$3) and homobilayer/Janus/alloy systems support strong IX emission at energies determined by band offsets and stacking (Horng et al., 2017, Masanta et al., 27 Mar 2025, Torun et al., 2018).
• Quantum Emitters: Moiré-localized IXs act as zero-dimensional quantum emitters displaying single-photon emission, Stark-tunable energies, and strong antibunching, suitable for quantum optics (Brotons-Gisbert et al., 2024).
• Transport and Optoelectronic Devices: IXs have been implemented in drift-diffusion-based transistor and diode architectures, with long-range transport (diffusion lengths >10 μm), enabling on-chip excitonic circuits. The field-tunable binding, emission, and valley properties are critical for next-generation valley-LEDs and logic devices (Shanks et al., 2022, Zhang et al., 2023).
• Prospects for Room-Temperature Operation: The large $$E_b = \frac{ \mu e^4 }{ 2 (4\pi \epsilon)^2 \hbar^2 }$$4 and valley polarization of engineered IXs hold promise for high-temperature operation in optoelectronic, photonic, and valleytronic devices (Tan et al., 2019).

6. Open Questions and Outlook

Ongoing research addresses the following issues:

• Exciton–Exciton Correlations: The nature of many-body phases—especially in moiré minibands, triangular and honeycomb artificial lattices.
• Dark vs Bright IXs: Identification and manipulation of optically dark exciton states by momentum-resolved spectroscopy and field-induced hybridization.
• Biexciton and Polaron Physics: Formation and control of higher-order correlated states in coupled multilayers and their role in collective transport or condensate physics (Xu et al., 2022, Liu et al., 2024).
• Quantitative Modeling: Precise mapping between theoretical predictions and experimental measurements of IX binding, transport, and decay across varied device architectures (Ovesen et al., 2018, Donck et al., 2018).
• Topological and Quantum Information Applications: The potential use of strongly correlated IX arrays, topological pseudospin textures, and long-lived valley-polarized IXs as quantum circuit elements (Liu et al., 2024).

Interlayer excitons thus provide a uniquely tunable, technologically relevant template for quantum condensed-matter research, combining robust many-body physics with powerful electrical, optical, and structural control in atomically thin materials.