Inter-Layer Excitons

• Interlayer excitons are Coulomb-bound electron–hole pairs confined in separate layers, featuring permanent dipole moments and enhanced lifetimes.
• Their properties are finely tuned by electric fields, twist angles, stacking order, and dielectric environments, enabling versatile control in quantum devices.
• Distinct spectroscopic signatures, such as long-lived photoluminescence and Stark shifts, provide clear experimental fingerprints for studying these excitons.

Interlayer excitons are Coulomb-bound electron–hole pairs where the constituent carriers reside in spatially separate layers of a van der Waals (vdW) heterostructure or homostructure. These excitons inherit a permanent electric dipole, exhibit elongated lifetimes, possess binding energies on par with or even exceeding those of intralayer excitons, and display emergent spin–valley–layer selection rules. The interplay between quantum confinement, stacking order, internal or externally applied electric fields, and moiré superlattices enables rich tunability of interlayer excitonic properties, spanning from individual localized emitters to collective correlated states and quantum device platforms.

1. Fundamental Properties and Formation Mechanisms

Interlayer excitons (IXs) are realized in atomically thin systems such as TMD bilayers, metal monochalcogenide heterostructures, and graphene-based materials. Their existence fundamentally relies on a spatial separation of the electron and hole, typically enforced by type-II band alignment, vertical electric fields, or symmetry-breaking via alloying.

Key features of IXs include:

• Permanent out-of-plane electric dipole: Due to the spatial separation, IXs exhibit a large dipole moment perpendicular to the layers. This property is central for Stark effect tuning and pronounced dipolar interactions (Brotons-Gisbert et al., 15 Jul 2024).
• Enhanced lifetimes: Reduced electron–hole wavefunction overlap suppresses radiative recombination, resulting in lifetimes from nanoseconds to hundreds of nanoseconds or beyond, far longer than for intralayer excitons (Horng et al., 2017, Rocha et al., 15 Jul 2025).
• Robust binding energies: Despite the spatial separation, screening phenomena and reduced dielectric environment ensure that IXs possess binding energies that are usually only 20–30% lower than those of tightly bound intralayer excitons, often exceeding 100 meV, making them stable at elevated temperatures (Horng et al., 2017, Torun et al., 2018, Ovesen et al., 2018).

Type-II alignment in TMD heterobilayers, internal electric fields from symmetry-breaking alloying (e.g., WS$_{2x}$Se$_{2(1-x)}$ (Masanta et al., 27 Mar 2025)), and moiré trapping in twisted bilayers are all established formation mechanisms (Brotons-Gisbert et al., 15 Jul 2024, Zheng et al., 2022).

2. Tunability: Electric Fields, Twist Angle, and Layer Engineering

The excitonic properties of IXs are significantly tunable by structural and external parameters:

• Electric and Internal Fields: Applying a vertical field ($E$) gives a linear Stark shift ($\Delta E = -p \cdot E$), continuously tuning the IX resonance (Brotons-Gisbert et al., 15 Jul 2024, Kovalchuk et al., 2023). Fields also enable coupling and hybridization between intra- and interlayer excitons, giving rise to new excitonic branches and non-trivial Stark splitting (> 380 meV) (Kovalchuk et al., 2023). In alloyed bilayers, a built-in field due to chalcogen asymmetry acts analogously, producing a type-II alignment and reversed emission helicity (Masanta et al., 27 Mar 2025).
• Layer Number and Stacking: Increasing the number of layers or engineering specific stacking orders in heterostructures shifts the interlayer exciton emission energy (often, but not solely, via a change in band edge alignment) and can enhance exciton lifetimes by further decreasing wavefunction overlap and exchange interactions (Tan et al., 2019, Rocha et al., 15 Jul 2025). In bilayer graphene nanoribbons, stacking order (α vs β) strongly influences the degree of interlayer character and radiative lifetime (Rocha et al., 15 Jul 2025).
• Twist Angle and Moiré Superlattices: A finite twist angle between layers induces a long-wavelength moiré superlattice. The resulting periodic potential yields arrays of "quantum-dot–like" moiré traps for IXs, leading to nearly quantized emission peaks and controllable localization length and inter-dot tunneling amplitude. The moiré wavelength and confinement are directly tunable by $\phi$, the twist angle, and the lattice constant mismatch. This can even drive transitions between quantum dot and miniband physics (Zheng et al., 2022, Brotons-Gisbert et al., 15 Jul 2024).
• Dielectric Environment and Organic Interlayers: Embedding organic molecules or varying environmental dielectric constants modulate both the IX binding energy and transition energy. Increased separation or decreased effective $\varepsilon$ consistently produces a blue shift in emission by reducing screening and overlap (Ji et al., 2020).

3. Spectroscopic Signatures and Experimental Observations

IXs are distinguished by a rich spectroscopic phenomenology:

• Long-lived PL: IX emission persists for tens to hundreds of nanoseconds due to low recombination rates (Miller et al., 2017, Ovesen et al., 2018). PL spectra often show power-dependent blue shifts, attributed to dipolar repulsion ($\Delta E \propto n$, with $n$ the density) (Miller et al., 2017).
• Doublet and fine structure: Multiple distinct IX transitions are resolved, corresponding to momentum-direct and momentum-indirect recombination channels in the band structure (Miller et al., 2017, Baranowski et al., 2017). Twist-angle induced moiré potentials split IX emission into nearly quantized multiplets (Zheng et al., 2022).
• Opposite-circular polarization: In certain systems (e.g., WS$_{2x}$Se$_{2(1-x)}$ alloys (Masanta et al., 27 Mar 2025) and MoS$_2$/MoSe$_2$/MoS$_2$ stacks (Baranowski et al., 2017)), IX emission under circularly polarized excitation demonstrates a negative or counter-polarized degree of circular polarization. This is attributed to spin–valley–layer coupling and the strong spin polarization of the bilayer valence bands, as captured by bilayer $k\cdot p$ models (Masanta et al., 27 Mar 2025).
• Stark effect spectroscopy: Direct linear shifts of IX emission under out-of-plane electric fields provide a quantitative measure of the permanent dipole, with experimental values (e.g., $d = 3.6\pm0.1$ Å in InSe/GaSe) matching structural interlayer separations (Zheng et al., 2022).
• PL excitation and power dependence: Enhanced IX emission under near-resonant excitation supports the scenario of fast charge transfer and interlayer exciton formation via intralayer excitonic precursor states (Baranowski et al., 2017).

4. Correlated Quantum Phases and Many-Body Physics

The long lifetime and strong dipolar interaction of IXs realize a platform for rich many-body physics:

• Dipolar bosonic liquids and Bose–Hubbard regimes: At higher densities, IXs accumulate and can thermalize, enabling the exploration of degenerate Bose gases, superfluid transport, and possibly Bose–Einstein condensation (Brotons-Gisbert et al., 15 Jul 2024). In moiré superlattices, the Bose–Hubbard model applies:

$$H = -t \sum_{\langle i,j \rangle} (b_i^\dagger b_j + \text{h.c.}) + \frac{U}{2} \sum_i n_i (n_i - 1)$$

with $t$ tunable by moiré period, interlayer coupling, and twist angle, and $U$ representing local dipole–dipole repulsion.

• Collective states and Wigner crystallization: When kinetic energy is flattened (either by moiré confinement or through dispersion engineering, e.g., “Mexican hat” dispersions (Skinner, 2016)), crystalline states or excitonic insulators can be stabilized (Brotons-Gisbert et al., 15 Jul 2024, Xu et al., 2022). The transition between Bose condensate, crystal, or Mott/charge-ordered phases is governed by the IX dispersion, dipolar repulsion, and trap geometry.
• Biexcitons and polaronic states: In quadrilayer systems or dilute/dense bilayer mixtures, interlayer and intralayer exciton interactions support the formation of attractive biexciton states with measurable binding energies, or polaronic quasiparticles with mass renormalization (Xu et al., 2022). Numerical studies yield biexciton binding energies of order $0.3$ meV in coupled fluids.

5. Applications: Tunable Devices and Quantum Platforms

IXs present unique features for device implementation:

• Field-effect tuning: External fields modulate the IX energy and lifetime, underpinning devices such as excitonic transistors and diodes. Engineered potential landscapes (via lithographically defined gates or moiré arrays) enable unidirectional IX transport and excitonic circuitry, with measured flow velocities up to $2\times10^7$ cm/s and on/off switching timescales approaching 14 GHz (Shanks et al., 2022).
• Quantum emitters and information: Moiré-trapped IXs with minimized inhomogeneous broadening and engineered selection rules offer promising platforms for single-photon sources and quantum information applications (Brotons-Gisbert et al., 15 Jul 2024).
• Room-temperature stability and valleytronics: Exciton binding energies above thermal thresholds ensure robust operation at high temperatures. Coupled with robust and switchable valley polarization, IXs are attractive for valleytronic and spintronic devices (Baranowski et al., 2017, Masanta et al., 27 Mar 2025, Tan et al., 2019).
• Tunable radiative and non-radiative lifetimes: Radiative lifetimes are strongly parameter-sensitive; AGNR heterobilayers, for instance, exhibit IX lifetimes from 1 ns to nearly 10 μs depending on stacking and band alignment (Rocha et al., 15 Jul 2025).

6. Theoretical Modeling and Experimental Methodologies

Predictive understanding and quantitative tuning of IX properties are grounded in advanced ab initio and model Hamiltonians:

• First-principles methods: Band structures are calculated using DFT with spin–orbit and vdW corrections. Quasiparticle gaps are obtained via $GW$ approximation, and excitonic effects via the Bethe–Salpeter Equation (BSE), capturing inter- and intralayer character, binding energies, and oscillator strengths (Torun et al., 2018, Rocha et al., 15 Jul 2025).
• Effective mass and Dirac models: Dirac-type Hamiltonians encapsulate the spin–valley–layer coupling, spin–orbit splitting, and the influence of structural asymmetry or external fields (Donck et al., 2018, Masanta et al., 27 Mar 2025).
• Many-body theories and numerical techniques: Hypernetted chain and exact diagonalization methods are used to compute ground state energies, pair correlation functions, excitation spectra, and phase transitions in coupled exciton fluids (Xu et al., 2022, Liu et al., 14 Aug 2024).
• Optical spectroscopy: Time-resolved photoluminescence, helicity- and power-resolved PL, reflection contrast spectroscopy, and far-infrared magneto-optical absorption are central tools for experimental IX characterization (Miller et al., 2017, Horng et al., 2017, Zheng et al., 2022, Liu et al., 14 Aug 2024).

7. Perspectives and Challenges

The IX research field is rapidly expanding. Key open areas and challenges include:

• Stability and coherence: Understanding and engineering the interplay of dark–bright exciton states, intervalley scattering, and non-radiative channels for optimized quantum coherence and emission characteristics (Masanta et al., 27 Mar 2025).
• Correlated electronic phases: Elucidating the emergence of magnetism, superconductivity, and other correlated phases in flat-band or moiré-engineered heterostructures, especially under carrier doping (Zheng et al., 2022).
• Scalable synthesis and device integration: Developing alloyed or directly grown bilayer systems with robust type-II alignment and minimal defect densities for high-performance and scalable device applications (Masanta et al., 27 Mar 2025).
• Quantum dot and nanoribbon architectures: Extending IX engineering into 1D and 0D nanostructures, where size, confinement, and topological textures (via pseudospin–orbit coupling) offer further degrees of freedom for control (Liu et al., 14 Aug 2024, Rocha et al., 15 Jul 2025).

In summary, interlayer excitons constitute a multifaceted platform for the investigation and engineering of quantum many-body physics, optoelectronic devices, and novel phases of matter, leveraging the rich control available in van der Waals heterostructures and related materials systems.