Interlayer Exciton Condensates

Updated 14 August 2025

Interlayer exciton condensates are macroscopic phases formed by Bose–Einstein condensation of spatially separated electron–hole pairs with tunable dipolar interactions.
They are investigated using transport, optical, and tunneling spectroscopy to reveal phenomena like vortex formation, enhanced phase stiffness, and topological defects.
Engineering these condensates in van der Waals heterostructures and moiré superlattices underpins novel quantum devices with controllable many-body and topological properties.

Interlayer exciton condensates (ECs) are macroscopic quantum phases formed by the Bose–Einstein condensation (BEC) of excitons—bound electron–hole pairs—in spatially separated electronic layers. The spatial separation leads to reduced recombination rates and/or exotic dipolar interactions, enabling high-temperature condensation scenarios, topologically nontrivial defects, and emergent many-body states. Theoretical studies and an expanding body of experiments in van der Waals heterostructures, quantum Hall bilayers, graphene-based devices, and moiré superlattices have established ECs as a cornerstone of correlated electron systems and synthetic quantum matter.

1. Microscopic Structure and Interactions of Interlayer Excitons

A prototypical interlayer exciton consists of an electron in one two-dimensional (2D) layer bound by Coulomb interaction to a hole in an adjacent layer. The permanent out-of-plane dipole moment—set by the layer spacing d—gives rise to purely repulsive, long-range, and anisotropic dipole–dipole interactions between the excitons (Conti et al., 21 Jul 2025). In several moiré superlattice realizations, additional quantum confinement effects and atomic reconstruction induce in-plane quadrupole moments and complex spatial structures. For example, in H-stacked WS₂/WSe₂ heterobilayers, density functional theory and scanning probe experiments reveal that the excitonic electron in the top layer can delocalize across three neighboring moiré traps, while its hole remains localized, resulting in a three-dimensional excitonic configuration with both vertical dipole and large in-plane quadrupole components (Wang et al., 2022).

The interlayer exciton Hamiltonian thus incorporates nonlocal, repulsive interactions characterized by the dipole moment (proportional to d) and the density, making the system a nearly ideal realization of dipolar Bose gases and opening up regimes unattainable in atomic platforms. In quadrilayers or multilayer stacks, collective phenomena such as biexciton (bound pair) formation and polaronic crossover emerge from a combination of intraplane repulsion and interplane short-range attraction (Xu et al., 2022).

2. Emergence and Control of Many-Body Quantum Phases

The macroscopic condensation of interlayer excitons (EC formation) is controlled by several correlated factors:

Exciton binding energy: Enhanced by smaller d, but at risk of excessive tunneling and recombination if d becomes much less than the excitonic Bohr radius.
Interlayer tunneling: Large momentum mismatches (e.g., through a ~10° twist in double bilayer graphene (Li et al., 20 May 2024)) or spin–valley locking (e.g., in bilayer WSe₂ (Shi et al., 2021)) are required to suppress tunneling, thereby stabilizing ECs even at sub-nanometer spacings.
Carrier density and temperature: The BEC critical temperature $T_c$ is set by the phase stiffness and density, as captured by the Nelson–Kosterlitz relation for 2D systems: $k_B T_{BKT} = (\pi/2) D_s$ , where $D_s$ includes both conventional and geometric contributions (Verma et al., 2023).
External fields and gating: Both exciton density and the nature of their dispersion (parabolic, Mexican hat, etc.) can be tuned by gate voltage, perpendicular electric fields, or magnetic fields, directly controlling phases from uniform superfluid to crystalline or supersolid regimes (Skinner, 2016, Conti et al., 21 Jul 2025).

In moiré-patterned systems, the underlying periodic potential further shapes the single-particle and collective exciton spectrum, allowing for engineering of minibands, localization, and formation of intercell exciton complexes (Wang et al., 2022).

3. Topological and Defect Physics: Vortices and Fractionalization

ECs with macroscopic phase coherence support a spectrum of topological defects:

Vortices: Solutions of the nonlocal Gross–Pitaevskii equation for dipolar interlayer exciton superfluids exhibit vortex core shrinkage as dipolar coupling increases, with the core size (healing length $\xi$ ) dropping and then saturating as $d$ or density is raised (Conti et al., 21 Jul 2025). The density profile develops a characteristic "pileup" at the vortex edge under strong repulsion.
Vortex interactions and lattices: Vortices are everywhere repulsive due to the lack of a short-range attraction, causing robust vortex lattices, and, as their spacing reduces under rapid rotation or increased density, core overlap and clustering signals the approach to an incompressible supersolid transition.
Fractional charge and zero modes: In systems with nontrivial topology and vortex textures of the EC order parameter, such as bilayer 2DEGs adjacent to superconductor films, analytic and numerical BdG studies predict exact zero modes and rational (e.g. $\pm e/2$ ) or irrational (parameter-tunable) fractionalization of layer or axial (layer-difference) charges, depending on the pseudospin potential $\mu$ and symmetry protection (Hao et al., 2010).

The formation of ECs in quantum Hall bilayers, graphene, and TMD heterostructures at half-filled Landau levels also enables skyrmion-like (meron–antimeron) or particle–hole excitations as the lowest-energy charged defects, with the dominant excitation type depending on LL index, carrier side, and screening (Li et al., 20 May 2024, Shi et al., 2021).

4. Quantum Geometry and Phase Stiffness

The collective phase stiffness—a central quantity controlling BKT criticality and superfluidity—receives not only the expected "conventional" kinetic contribution (governed by exciton effective masses and densities) but also a "geometric" contribution arising from the nontrivial momentum dependence of Bloch wavefunctions in the constituent bands (Verma et al., 2023). This geometric stiffness, encoded by the quantum geometric tensor (or quantum metric), amplifies the total stiffness and can enhance $T_{BKT}$ by factors of up to three in TMD bilayer models with realistic parameters. As a result, ECs in flat-band or topologically nontrivial systems become more robust and accessible at experimentally achievable temperatures.

This geometric enhancement is especially relevant for systems engineered to maximize the Berry curvature and quantum metric, for example via alignment, strain, or heterostructure design.

5. Experimental Probes and Observable Signatures

A range of experimental signatures establish the existence and properties of interlayer ECs:

Transport: In quantum Hall bilayers and twisted bilayer graphene, incompressible EC states appear as vanishing longitudinal conductivity and anomalous plateaus in resistance maps at half-filling of Landau levels, with transitions between different excitation gaps and incompressible states as a function of displacement field, density, and LL index (Eisenstein, 2013, Li et al., 20 May 2024).
Optics (PL and EL): Optical signatures—sharp photoluminescence (PL) peaks, sudden intensity jumps at critical density, threshold-like electroluminescence (EL) in bias-controlled devices, and linewidth narrowing—point to condensation, long coherence times, and criticality (Sigl et al., 2020, Wang et al., 2021). PL energy jumps and replica features further reveal the formation of intercell exciton complexes in moiré superlattices (Wang et al., 2022).
Noise and photon statistics: Super-Poissonian photon statistics (photon bunching) near EL thresholds, and transition to Poissonian (coherent) statistics above threshold, confirm critical fluctuations and condensation (Wang et al., 2021).
Capacitance and tunneling spectroscopy: Penetrating capacitance and nonlinear suppression of the Coulomb pseudogap serve as probes of both ground-state incompressibility and the buildup of interlayer electron–hole correlations preceding condensation (Eisenstein et al., 2019).

6. Extensions: Pairing, Polaritonics, and Non-Equilibrium Dynamics

Interlayer ECs support a variety of extensions and emergent phases:

Pair superfluidity: With vertically stacked dipolar bilayers, collective pairing into molecular interlayer bound states (IX molecules) gives rise to a superfluid of pairs, which can be distinguished from independent dipole superfluids by a discontinuity in the chemical potential at balanced densities. At finite temperature and imbalance, a cascade of BKT transitions—first for the pair superfluid, then for unpaired excess excitons—has been confirmed by QMC methods and connected to photoluminescence energy jumps (Zimmerman et al., 2022).
Polariton condensation: Embedding bilayer TMDs (MoS₂, WSe₂) in high-quality cavities enables hybridization of bright intralayer and dark interlayer excitons; appropriately tuned, polariton branches can have >90% interlayer character while remaining optically accessible due to hybridization, allowing for nonlinear effects and facilitating BEC of interlayer exciton polaritons (König et al., 2022).
Dynamical and nonequilibrium ECs: Under finite chemical potential bias (e.g. by voltage or optical pumping), ECs exhibit dynamical Josephson effects: bias-induced precession of the order parameter phase, oscillating Josephson currents, and a bias-controlled crossover from dark (only tunneling, no light emission) to bright (coherent photon emission) condensate regimes. Placement in an optical cavity can favor superradiant emission at controlled frequencies and enhance the bright phase (Zeng et al., 2023, Sun et al., 2023).

7. Engineering, Applications, and Future Directions

The diverse set of experimental platforms—semiconductor bilayers, van der Waals heterostructures, atomic and lattice-engineered TMDs, twisted multilayer graphene—offer highly tunable systems for the realization and control of ECs. This tunability allows exploration of exotic quantum phases (supersolid, crystalline, fermionized states (Skinner, 2016, Conti et al., 21 Jul 2025)), engineering of emergent multipole moments (quadrupoles in moiré heterostructures (Wang et al., 2022)), scaling of BKT temperatures via quantum geometry (Verma et al., 2023), and direct electrical and optical manipulation of condensation regimes.

Applications are envisioned in topological quantum devices (leveraging the anyonic and fractionalized excitations in vortex-bound states (Hao et al., 2010)), ultrafast optoelectronics (due to the high oscillator strengths and long lifetimes (Jauregui et al., 2018)), and robust dissipationless transport. The knowledge of how stacking order, filling fraction, interlayer registry, and quantum confinement tune exciton interactions provides an emergent "materials-by-design" framework for correlated quantum matter. Ongoing directions include the pursuit of device architectures for high-temperature superfluidity, single- or multi-mode superradiance, and quantum manipulation exploiting the valley, spin, and moiré degrees of freedom.

In summary, the field of interlayer exciton condensates encompasses a range of correlated bosonic phases where spatially separated electrons and holes form long-lived, mobile dipoles with tunable interactions. The resulting macroscopic quantum order, defect structure, and response to tuning parameters have been mapped both theoretically and experimentally across multiple platforms and regimes, positioning ECs as foundational elements for both the paper and the engineering of quantum condensed matter.