Layer-Hybridized Excitons

• Layer-hybridized excitons are excitonic eigenstates in layered semiconductors resulting from the coherent mixing of intralayer and interlayer (Frenkel and Wannier–Mott) configurations.
• They are realized through tuning mechanisms such as electric fields, pressure, and moiré potentials that control hybridization, oscillator strength, and dipole moments.
• This phenomenon provides a versatile platform for engineering excitonic interactions, transport properties, and many-body effects in diverse material systems.

Searching arXiv for papers on layer-hybridized excitons and related reviews. Search results:

• (Brotons-Gisbert et al., 2024) — "Interlayer and moiré excitons in atomically thin double layers: from individual quantum emitters to degenerate ensembles"
• (Zhao et al., 1 Mar 2025) — "Pressure Tuning of Layer-hybridized Excitons in Trilayer WSe2"
• (Chowdhury et al., 19 Feb 2025) — "Bright hybrid excitons in molecularly tunable bilayer crystals"
• (Erkensten et al., 2023) — "Electrically tunable dipolar interactions between layer-hybridized excitons"
• (Morris et al., 2023)? (closest relevant in provided materials is (Meneghini et al., 2023)) — "Direct visualization of hybrid excitons in van der Waals heterostructures" Layer-hybridized excitons are excitonic eigenstates in layered semiconductors and organic–inorganic interfaces in which intralayer and interlayer excitonic configurations, or Frenkel and Wannier–Mott configurations, are coherently mixed into a single bound state. In the terminology used for atomically thin double layers, they arise when intralayer exciton branches and interlayer exciton branches are tuned into resonance, yielding states of the form $|hX\rangle = C_{IX}|IX\rangle + C_X|X\rangle$ that inherit both a permanent dipole and appreciable optical oscillator strength (Brotons-Gisbert et al., 2024). In organic–inorganic van der Waals heterostructures, an analogous hybridization can occur between a molecular Frenkel exciton and a transition-metal dichalcogenide Wannier–Mott exciton, as demonstrated at the CuPc/MoSe$_2$ interface (Fu et al., 2023). The subject occupies an intermediate regime between ordinary intralayer excitons, which are optically bright but weakly dipolar, and spatially indirect interlayer excitons, which are strongly dipolar but typically weakly emissive.

1. Definition, scope, and distinguishing features

In the current literature, the basic distinction is between three excitonic limits. Conventional intralayer excitons have both electron and hole in the same monolayer, strong oscillator strength, small or zero out-of-plane dipole, and lifetimes in ps. Interlayer excitons bind an electron and hole localized in adjacent layers; reduced wave-function overlap gives large static dipoles $p_\perp \approx e\cdot d$ with $d \simeq 0.6$–$0.8$ nm, lifetimes $\tau \gtrsim 10$–$100$ ns, weak oscillator strength, and strong Stark shifts. Layer-hybridized excitons occur when these two branches are tuned into resonance, for example by a vertical electric field or a moiré potential, so that the resulting eigenstates simultaneously retain dipolar and optical character (Brotons-Gisbert et al., 2024).

A common conflation is to treat layer-hybridized excitons as ordinary interlayer excitons. The defining difference is coherent admixture. In transition-metal dichalcogenide bilayers, this admixture is commonly quantified by mixing coefficients satisfying $|C_X|^2+|C_{IX}|^2=1$, and experimentally it manifests as avoided crossings and oscillator-strength transfer rather than as a purely Stark-shifted dark branch (Brotons-Gisbert et al., 2024). In an earlier bilayer formulation, this same idea was cast as carrier-species-specific layer-hybridization controlled through the interplay of rotational, translational, band offset, and valley-spin degrees of freedom: an electron can remain well confined in one layer while a hole is well extended in both layers, producing excitons with both large optical dipole and large electric dipole (Hsu et al., 2019).

This hybrid character is not restricted to inorganic bilayers. At an organic–inorganic interface, coherent many-body interaction can mix a Frenkel exciton on a molecular layer with a Wannier–Mott exciton in a 2D semiconductor, producing momentum-direct hybrid excitons that differ qualitatively from many momentum-indirect interlayer excitons in pure 2D/2D heterobilayers (Fu et al., 2023).

2. Microscopic description and model Hamiltonians

The standard minimal description is a two-level excitonic Hamiltonian coupling a bright intralayer exciton $|X\rangle$ to a dipolar interlayer exciton $|IX\rangle$,

$_2$0

where the Stark term shifts the interlayer branch linearly with out-of-plane field $_2$1, the layer spacing is $_2$2 nm in naturally stacked WSe$_2$3 homobilayers, and $_2$4 is the tunneling-induced coupling (Erkensten et al., 2023). The hybridization angle is

$_2$5

and the hybrid-exciton dipole moment follows from the interlayer fraction,

$_2$6

This formulation makes explicit that field control of detuning directly controls dipolarity (Erkensten et al., 2023).

A more microscopic bilayer theory starts from a monolayer-eigenstate exciton Hamiltonian

$_2$7

with valley index $_2$8, layer configuration $_2$9, and tunneling matrix elements $p_\perp \approx e\cdot d$0 that couple intra- and interlayer excitons. Diagonalization by a unitary transform

$p_\perp \approx e\cdot d$1

yields hybrid eigenstates $p_\perp \approx e\cdot d$2 with material- and valley-specific admixture coefficients (Erkensten et al., 2023).

Near a resonance, the hybridized branches exhibit the generic anti-crossing form

$p_\perp \approx e\cdot d$3

with mixing angle determined by

$p_\perp \approx e\cdot d$4

This is the basis of the direct-visualization proposal for MoS$p_\perp \approx e\cdot d$5 homobilayers and the standard interpretation of reflectance anti-crossings in electrically biased bilayers (Meneghini et al., 2023).

At organic–inorganic interfaces, the same structure appears in a Frenkel–Wannier basis,

$p_\perp \approx e\cdot d$6

with $p_\perp \approx e\cdot d$7. In CuPc/MoSe$p_\perp \approx e\cdot d$8, density-functional theory gives an interfacial coupling

$p_\perp \approx e\cdot d$9

linking the lowest unoccupied molecular orbital of CuPc to the MoSe$d \simeq 0.6$0 conduction-band minimum (Fu et al., 2023).

3. Materials platforms and realizations

The foundational experimental realizations were in TMD homo- and heterobilayers. In H-stacked WSe$d \simeq 0.6$1/MoSe$d \simeq 0.6$2, the valence-band offset is small enough and the interlayer valence hopping large enough that holes become strongly hybridized while electrons remain localized; the reported degree of layer-hybridization was $d \simeq 0.6$3, with $d \simeq 0.6$4 and $d \simeq 0.6$5. In H-stacked WS$d \simeq 0.6$6/MoS$d \simeq 0.6$7, the corresponding values were $d \simeq 0.6$8, $d \simeq 0.6$9, and $0.8$0. In MoS$0.8$1 homobilayers, H-stacking yielded $0.8$2 (Hsu et al., 2019). These systems established the central design principle that selective hybridization can occur for one carrier species but not the other.

A complementary route uses strong electric fields to force intralayer and interlayer branches into resonance. In bilayer MoS$0.8$3 and MoSe$0.8$4, an organic/inorganic molecular gating technique based on a top molecular gate of F$0.8$5TCNQ enabled perpendicular fields $0.8$6 V nm$0.8$7, approximately twice higher than previously available. Under these fields, hybridization allowed the discovery of new excitonic species and produced ultra-strong Stark splitting of $0.8$8 meV, with exciton energies tunable over 1.45–2.15 eV (Kovalchuk et al., 2023).

Layer-hybridized excitons also occur at organic–inorganic interfaces. In CuPc/MoSe$0.8$9, the interface has a Type I alignment with an offset $\tau \gtrsim 10$0 eV from the CBM of MoSe$\tau \gtrsim 10$1 to the CuPc LUMO, and low-temperature photoluminescence revealed four interfacial excitonic states, denoted hX$\tau \gtrsim 10$2–hX$\tau \gtrsim 10$3 (Fu et al., 2023). A more synthetic variant is the four-atom-thick hybrid bilayer crystal formed by a single-crystalline perylene diimide molecular crystal atop WS$\tau \gtrsim 10$4. In PDI/WS$\tau \gtrsim 10$5, the interlayer coupling inferred from the band-splitting in GW is $\tau \gtrsim 10$6 eV, and the principal excitons were reported at $\tau \gtrsim 10$7 eV, $\tau \gtrsim 10$8 eV, and $\tau \gtrsim 10$9 eV, with polarization anisotropies $100$0, $100$1, and $100$2 (Chowdhury et al., 19 Feb 2025).

These platforms span distinct microscopic limits—homobilayer intralayer/interlayer mixing, heterobilayer band-offset engineering, and Frenkel–Wannier interfacial coupling—but all realize the same general phenomenon of layer-delocalized excitonic constituents with tunable admixture.

4. Spectroscopic fingerprints and direct probes

The canonical experimental signature is an avoided crossing in reflectance or photoluminescence as a function of out-of-plane field. In bilayers, this reflects resonant tunneling between bright intralayer and dipolar interlayer branches; in strong-field MoS$100$3 and MoSe$100$4, fitting to a two-level hybridization model yielded interlayer-hole-tunneling matrix elements $100$5–45 meV (Kovalchuk et al., 2023). The borrowed oscillator strength of the interlayer-derived branch is essential: it turns otherwise weakly emissive states into directly observable optical resonances.

At the CuPc/MoSe$100$6 interface, low-temperature photoluminescence showed four new peaks not present in either isolated constituent: hX$100$7 eV, hX$100$8 eV, hX$100$9 eV, and hX$|C_X|^2+|C_{IX}|^2=1$0 eV. Power-dependence measurements obeying $|C_X|^2+|C_{IX}|^2=1$1 with $|C_X|^2+|C_{IX}|^2=1$2 ruled out biexcitons or defect emission. By analogy to the MoSe$|C_X|^2+|C_{IX}|^2=1$3 A-exciton and trion, hX$|C_X|^2+|C_{IX}|^2=1$4 was assigned to a hybrid A-exciton, hX$|C_X|^2+|C_{IX}|^2=1$5 to a hybrid trion, hX$|C_X|^2+|C_{IX}|^2=1$6 to a high-energy mixed Frenkel–Wannier state, and hX$|C_X|^2+|C_{IX}|^2=1$7 to a hybrid B-exciton (Fu et al., 2023).

Temperature dependence further resolves the mixed character. In CuPc/MoSe$|C_X|^2+|C_{IX}|^2=1$8, hX$|C_X|^2+|C_{IX}|^2=1$9, hX$|X\rangle$0, and hX$|X\rangle$1 redshift with increasing temperature according to the standard semiconductor band-gap law and show linewidth broadening by tens of meV above 100 K, indicating strong coupling to MoSe$|X\rangle$2 phonons. By contrast, hX$|X\rangle$3 has anomalously weak temperature dependence and is described by a two-component model in which a blue-shift from lattice expansion nearly cancels a redshift from electron–phonon coupling, a behavior characteristic of Frenkel excitons in organic crystals. Simultaneously, the integrated intensity of hX$|X\rangle$4 tracks the nonradiative-recombination activation energy of the MoSe$|X\rangle$5 A-exciton, approximately 30 meV, showing retained Wannier–Mott character in its lifetime (Fu et al., 2023).

Because many hybrid excitons are momentum-dark or only weakly bright, time- and angle-resolved photoemission spectroscopy has been proposed as a direct imaging tool. For MoS$|X\rangle$6 homobilayers, the predicted tr-ARPES signature is a characteristic double-peak spectrum arising from the hybridized hole in two valence bands at $|X\rangle$7, with peak separation of approximately 0.5–0.6 eV and relative intensities proportional to $|X\rangle$8. The hybrid double-peak appears only after phonon-assisted scattering on 100–400 fs timescales, whereas pure intralayer excitons appear at time zero and relax within $|X\rangle$9 fs (Meneghini et al., 2023). This distinction provides a direct operational criterion between hybrid and non-hybrid excitonic populations.

5. External control, transport, and many-body interactions

In naturally stacked WSe$|IX\rangle$0 homobilayers, electrical tuning produces two interaction regimes. A critical field $|IX\rangle$1 V/nm separates a low-dipole regime, where the hybrid exciton remains intralayer-like with $|IX\rangle$2 nm $|IX\rangle$3 and weak, even attractive, interactions, from a high-dipole regime, where it becomes mostly interlayer-like with $|IX\rangle$4 nm $|IX\rangle$5 and strong dipolar repulsion (Erkensten et al., 2023). In the long-wavelength limit, the interaction is governed by

$|IX\rangle$6

and the density-dependent blueshift obeys the compact scaling $|IX\rangle$7 (Erkensten et al., 2023). For $|IX\rangle$8 cm$|IX\rangle$9 and $_2$00, the predicted spectral blueshifts are $_2$01 meV in the low-dipole regime and $_2$02–30 meV in the high-dipole regime; the same crossover produces anomalous diffusion with exponent $_2$03–1.4 and a diffusion length increasing from $_2$04 $_2$05m to $_2$06 $_2$07m (Erkensten et al., 2023).

Spatiotemporally resolved transport experiments on fully encapsulated WSe$_2$08 homobilayers directly confirmed that dipole tuning changes the collective expansion of dilute exciton gases. The low-density diffusion coefficient was $_2$09 cm$_2$10 s$_2$11 and independent of hybridization. In the initial anomalous regime, however, the effective diffusivity reached $_2$12 cm$_2$13 s$_2$14 for high-$_2$15 hybrids with $_2$16 nm and $_2$17 cm$_2$18 s$_2$19 for low-$_2$20 hybrids with $_2$21 nm. Time-integrated and time-resolved photoluminescence showed a power-independent quantum yield, with single-exponential decays giving $_2$22–$_2$23 ns and $_2$24 (Tagarelli et al., 2023).

Pressure provides a second tuning axis. In AB-stacked trilayer WSe$_2$25 under 0–6.6 GPa, the hybridization strengths extracted from field-dependent fits obeyed

$_2$26

with average scaling $_2$27 meV/GPa (Zhao et al., 1 Mar 2025). Over the same range, the effective dipole moment decreased from $_2$28 $_2$29nm to $_2$30 $_2$31nm, an 11% reduction, while the intralayer component of the hybrid h-DX1 branch increased from 4.7% at 0 GPa to $_2$32% at 5.5 GPa (Zhao et al., 1 Mar 2025). Pressure therefore redistributes oscillator strength while reducing dipole length, a combination distinct from purely electrical control.

6. Extensions: trions, moiré minibands, quadrupoles, and multilayers

The hybridization concept extends naturally to charged and moiré excitonic complexes. In doped WSe$_2$33 bilayers, the lowest trion states consist of layer-hybridized $_2$34-point electrons and layer-localized K-point holes. At small fields, intralayer-like trions dominate with weak Stark shifts; above a doping-asymmetric critical field, interlayer-like species become lower in energy. The reported switching thresholds were $_2$35 V/nm for the $_2$36-type case and $_2$37 V/nm for the $_2$38-type case, while the emission Stark shift was $_2$39 meV per V/nm and the switchable dipole ranged from small values $_2$40 nm to large values $_2$41 nm (Perea-Causin et al., 2024).

In twisted WSe$_2$42 bilayers, the strongest hybridization occurs not at K but at $_2$43. Ab initio evaluation gave $_2$44 meV and $_2$45 meV, so the lowest K–$_2$46 exciton is pulled down by more than 100 meV; for nearly parallel stacking the lower hybrid branch is pushed down by about 125 meV, and the lowest moiré exciton subband acquires a bandwidth $_2$47 meV (Brem et al., 2020). This establishes a direct link between layer-hybridization and exciton flat-band engineering.

A related but distinct extension is the quadrupolar exciton in WS$_2$48/WSe$_2$49/WS$_2$50 heterotrilayers. There, the electron is coherently hybridized between top and bottom WS$_2$51 layers while the hole localizes in WSe$_2$52, producing a superposition of oppositely oriented dipolar excitons. The tunneling matrix element extracted from experiment was $_2$53 meV and the bare dipole moment $_2$54 $_2$55nm. The lower symmetric branch redshifts for both field polarities and shows no measurable density-dependent blue shift where the corresponding bilayer dipolar exciton blueshifts by $_2$56 meV, consistent with quadrupole–quadrupole rather than dipole–dipole interactions (Li et al., 2022).

Multilayer spin-valley locked superlattices support another variant: every-other-layer dipolar excitons. In trilayer WSe$_2$57, these excitons carry a dipole length $_2$58 nm, giving $_2$59 $_2$60nm, and are hybridized with bright intralayer 1S and 2S excitons by couplings $_2$61 meV and $_2$62 meV. The observed second orbital of the every-other-layer exciton gave a ground-to-excited splitting of 46 meV, corresponding to $_2$63 meV (Zhang et al., 2022). This suggests that layer-hybridization in multilayers is not a minor perturbation but an organizing principle for excitonic fine structure.

Taken together, these developments show that layer-hybridized excitons are not a single material-specific curiosity but a family of coherently mixed bound states whose dipole moment, oscillator strength, lifetime, transport, and many-body interactions can be tuned by stacking registry, twist angle, molecular orientation, pressure, doping, and electric field. A plausible implication is that the most consequential advances will come from platforms that simultaneously allow precise control of admixture and direct optical access to the hybrid branches.