Take two sheets of atomically thin crystal, stack them, and twist one by a degree or two. The atomic lattices no longer line up. Instead, a larger pattern emerges — a moiré pattern, the same kind of interference you see when two fine grids are overlaid. That pattern is not just visual. It is a real, periodic modulation of the energy landscape that excitons feel. In that landscape, excitons can be trapped, ordered, and made to interact in ways that no single layer allows.
Moiré excitons are excitons in a moiré superlattice. They are the reason twist angle has become a design variable in two-dimensional materials, and the reason a field that began with “twistronics” in graphene has expanded to “moiré photonics” and “moiré excitonics” in semiconductors.
What a moiré pattern is
When two periodic lattices with slightly different periods or orientations are overlaid, the combined pattern has a longer period than either lattice alone. That longer period is the moiré period. For two identical lattices twisted by a small angle, the moiré period grows as the angle shrinks: a twist of a degree or two produces a superlattice with a period of ten nanometers or more, spanning many atomic unit cells. For lattices with a small lattice mismatch, a moiré pattern appears even at zero twist, because the mismatch itself produces a beating between the two periods.
In a bilayer of transition metal dichalcogenides, the moiré pattern means that the local stacking — which atoms sit over which — varies smoothly across the sample, repeating with the moiré period. At some positions, a metal atom in the top layer sits directly over a metal atom in the bottom layer. At others, it sits over a chalcogen atom, or over a hollow site. Each local stacking has a slightly different interlayer coupling, a slightly different band gap, and a slightly different exciton energy.
The result is a periodic potential for excitons, with minima at particular stacking sites and maxima at others. The depth of that potential — the energy difference between minima and maxima — can be on the order of tens to well over a hundred milli-electron-volts in some heterobilayers, depending on material, twist, and whether the exciton is intralayer or interlayer. That is large compared to thermal energy at low temperature and comparable to or larger than the exciton linewidth in clean samples. It is deep enough to trap excitons.
Moiré potentials and trapped excitons
An exciton in a moiré superlattice does not move freely. It sees a landscape of wells. If the wells are deep and the temperature is low, the exciton localizes in a well, like a particle in a trap. Its motion is quantized into discrete levels within the well, and its emission narrows and shifts to reflect the local environment.
In photoluminescence, moiré-trapped excitons appear as multiple peaks or as a series of sharp lines, rather than the single broad peak of a free exciton. The number of peaks, their spacing, and their polarization reflect the structure of the moiré potential and the symmetry of the trapping sites. In some samples, the trapped exciton emission shows a striking pattern of circular polarization that alternates between neighboring sites, a signature of the local symmetry and of the valley physics that is coupled to the moiré lattice.
At higher temperature or in shallower potentials, excitons are not fully trapped. They hop between wells, or move in minibands — narrow bands formed by the periodic potential, analogous to the bands formed by the atomic lattice itself but on a much larger length scale and a much smaller energy scale. The crossover from localized to delocalized behavior, and the formation of moiré minibands, is a central theme in moiré exciton physics, and it can be tuned by twist angle, which sets the period, and by electric field, which can shift the relative energies of different sites.
The moiré potential is different for different exciton species. Intralayer excitons, whose electron and hole are in the same layer, feel a modulation that comes mainly from the local band gap and interlayer coupling. Interlayer excitons, whose electron and hole are in different layers, feel a stronger modulation, because their energy depends directly on the alignment of the two layers. Interlayer moiré excitons are therefore more deeply trapped, with longer lifetimes and sharper localization. That is why many of the most striking moiré exciton experiments use heterobilayers with type-II alignment.
Twist angle as a knob
Twist angle is the primary control parameter. It sets the moiré period: smaller angle, larger period, fewer wells per area, deeper and more isolated traps. Larger angle, smaller period, more wells, shallower and more overlapping. At very small angles — a fraction of a degree — the lattice can reconstruct, meaning the atoms shift to form large domains of preferred stacking separated by narrow domain walls, rather than a smooth sinusoidal modulation. Reconstruction changes the potential from a smooth landscape to a network of domains, with consequences for exciton trapping and transport.
Twist also sets the momentum mismatch between the two layers, which governs whether interlayer excitons are bright or dark, as discussed in the interlayer exciton article. At zero or near-zero twist, the valleys align and interlayer excitons can be bright. At larger twist, they become momentum-dark. Moiré physics and momentum physics are therefore coupled: the same angle that sets the superlattice period also sets the optical selection rules.
Fabricating a sample with a precise twist angle is a delicate operation. The standard method is tear-and-stack: a monolayer is torn, one half is rotated by the desired angle, and the two halves are stacked. The actual angle achieved can differ from the target by a fraction of a degree, and the angle can vary across the sample. Characterizing the angle — by optical signatures, by scanning probes, or by electron microscopy — is part of the experiment. Reproducibility across samples remains a challenge, and papers that report moiré exciton properties typically specify the twist angle and the method used to determine it.
Correlated states and many-body physics
When moiré wells are deep and excitons are dense enough to fill a significant fraction of them, interactions matter. Excitons in neighboring wells repel each other if they are dipolar, or attract and bind if conditions favor it. The system becomes a lattice of interacting bosons, analogous to cold atoms in an optical lattice but in a solid-state platform with optical readout.
Several correlated phenomena have been explored. At integer fillings — one exciton per moiré site, for example — the system can form an ordered state, a kind of exciton crystal or Mott-like state, where repulsion prevents double occupation and the excitons lock into place. At fractional fillings, more exotic orders have been proposed. When the moiré lattice is combined with charge carriers, the interplay of excitons and electrons can produce correlated insulating states, Wigner crystals, and other phases that are the subject of active research.
Moiré superlattices also host correlated electronic states without excitons — Mott insulators, generalized Wigner crystals, and Chern insulators in twisted bilayer graphene and in twisted transition metal dichalcogenides. Excitons are both a probe of those states and a participant. An exciton’s energy and spectrum shift when the underlying electronic state changes, so exciton spectroscopy can be used to detect correlated phases. Conversely, excitons can dress and interact with those phases, producing new quasiparticles and new optical signatures.
The language here is deliberately careful. Many moiré correlated states are established, especially on the electronic side. Some excitonic correlated states are supported by strong evidence; others remain proposed or contested. The field moves quickly, and the distinction between a well-established phase and a promising interpretation matters. Good reporting distinguishes them.
Valley, topology, and optical selection
Moiré superlattices add a layer of valley and topological physics. In transition metal dichalcogenides, the two valleys — often labeled K and K’ — are related by time reversal and have opposite optical selection rules for circular polarization. The moiré potential can have different depths and different symmetries for the two valleys at a given site, and the local optical selection rules can vary across the superlattice. The result is a spatially patterned valley physics, where the polarization of emission encodes which moiré site the exciton occupies.
In some moiré systems, the minibands carry nontrivial topology, meaning they have a Berry curvature that gives rise to Hall-like responses. Excitons in topological minibands are a frontier topic, connecting moiré excitonics to topological photonics and to proposals for dissipationless exciton transport. The experimental signatures are subtle, and the field is still establishing which effects are robust.
What moiré excitons enable
Moiré excitons enable a new kind of quantum simulation. A moiré superlattice is a periodic array of traps, with a period that can be tuned from a few nanometers to tens of nanometers, a depth that can be tuned by material and field, and a filling that can be tuned by excitation or gating. That is a controllable lattice for bosons, with optical initialization and readout. Cold atoms in optical lattices offer a similar platform, but moiré excitons operate in a solid, at higher temperatures, and with direct coupling to light.
They also enable single-photon sources. A single moiré-trapped exciton, isolated in a well, can act as a quantum emitter, producing one photon at a time. Unlike a quantum dot, whose position is fixed by growth, a moiré emitter’s position is set by the superlattice, and an array of emitters can be created deterministically across the sample. The uniformity and indistinguishability of those emitters — whether photons from different sites are identical enough for quantum interference — is an active question.
And they enable tunable optics. Because the moiré potential and the exciton energy can be tuned by twist, gate, strain, and temperature, moiré devices offer a route to spectrally tunable emitters, modulators, and sensors. The tuning is not just a shift of a peak; it is a change in the landscape itself.
Challenges
Moiré exciton experiments demand exceptional sample quality. The superlattice is sensitive to twist disorder, strain, bubbles, and contamination, all of which distort the periodic potential and broaden the spectra. Encapsulation in hexagonal boron nitride helps, but it does not eliminate disorder. Comparing results across groups requires careful attention to fabrication, twist characterization, and measurement conditions.
Theoretical modeling is also demanding. A moiré superlattice with a period of ten nanometers contains hundreds of atoms per unit cell, making first-principles calculations expensive. Continuum models and tight-binding models are widely used, but they depend on parameters that must be fitted or computed, and different models can give different predictions for well depths and miniband structures. The interplay of theory and experiment — using spectra to constrain models, and models to interpret spectra — is a central part of the field.
Sources and further reading
For moiré superlattices, twistronics, and moiré excitons, see review articles in Nature Reviews Materials, Nature Photonics, Nature Physics, and Reviews of Modern Physics on moiré materials, moiré excitons, and twistronics in two-dimensional semiconductors. For moiré-trapped interlayer excitons and their polarization signatures, see primary and review literature on transition metal dichalcogenide heterobilayers at small twist angles. For correlated states in moiré superlattices, see reviews on correlated physics in twisted bilayer graphene and twisted transition metal dichalcogenides. For moiré quantum simulation and single-photon emission from moiré traps, see recent reviews on moiré photonics and moiré quantum emitters. Where this article gives potential depths or period scales as ranges, that reflects the variation across materials, twist angles, and models reported in that literature.