Diffusivity Reveals Three Distinct Phases of Interlayer Excitons in MoSe_{2}/WSe_{2} Heterobilayers

Spatial Filtering of Interlayer Exciton Ground State in WSe2/MoS2 Heterobilayer

Long-life interlayer excitons (IXs) in transition metal dichalcogenide (TMD) heterostructure are promising for realizing excitonic condensates at high temperatures. Critical to this objective is to separate the IX ground state (the lowest energy of IX state) emission from other states' emissions. Filtering the IX ground state is also essential in uncovering the dynamics of correlated excitonic states, such as the excitonic Mott insulator. Here, we show that the IX ground state in the WSe2/MoS2 heterobilayer can be separated from other states by its spatial profile. The emissions from different moiré IX modes are identified by their different energies and spatial distributions, which fits well with the rate-diffusion model for cascading emission. Our results show spatial filtering of the ground state mode and enrich the toolbox to realize correlated states at elevated temperatures.

Two-Dimensional Moiré Polaronic Electron Crystals

Two-dimensional moiré materials have emerged as the most versatile platform for realizing quantum phases of electrons. Here, we explore the stability origins of correlated states in WSe_{2}/WS_{2} moiré superlattices. We find that ultrafast electronic excitation leads to partial melting of the Mott states on timescales 5 times longer than predictions from the charge hopping integrals and that the melting rates are thermally activated, with activation energies of 18±3 and 13±2  meV for the one- and two-hole Mott states, respectively, suggesting significant electron-phonon coupling. A density functional theory calculation of the one-hole Mott state confirms polaron formation and yields a hole-polaron binding energy of 16 meV. These findings reveal a close interplay of electron-electron and electron-phonon interactions in stabilizing the polaronic Mott insulators at transition metal dichalcogenide moiré interfaces.

Ultralow Auger-Assisted Interlayer Exciton Annihilation in WS2/WSe2 Moiré Heterobilayers

Transition metal dichalcogenide (TMD) heterobilayers have emerged as a promising platform for exploring solid-state quantum simulators and many-body quantum phenomena. Their type II band alignment, combined with the moiré superlattice, inevitably leads to nontrivial exciton interactions and dynamics. Here, we unveil the distinct Auger annihilation processes for delocalized interlayer excitons in WS2/WSe2 moiré heterobilayers. By fitting the characteristic efficiency droop and bimolecular recombination rate, we quantitatively determine an ultralow Auger coefficient of 1.3 × 10-5 cm2 s-1, which is >100-fold smaller than that of excitons in TMD monolayers. In addition, we reveal selective exciton upconversion into the WSe2 layer, which highlights the significance of intralayer electron Coulomb interactions in dictating the microscopic scattering pathways. The distinct Auger processes arising from spatial electron-hole separation have important implications for TMD heterobilayers while endowing interlayer excitons and their strongly correlated states with unique layer degrees of freedom.

Twisted van der Waals Quantum Materials: Fundamentals, Tunability, and Applications

Twisted van der Waals (vdW) quantum materials have emerged as a rapidly developing field of two-dimensional (2D) semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single photon emission, nonlinear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moiré patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This paper offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moiré superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes, lasers, and photodetectors. It highlights the unique ability of moiré superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moiré superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.

Nonlinear and Negative Effective Diffusivity of Interlayer Excitons in Moiré-Free Heterobilayers

Interlayer exciton diffusion is studied in atomically reconstructed MoSe_{2}/WSe_{2} heterobilayers with suppressed disorder. Local atomic registry is confirmed by characteristic optical absorption, circularly polarized photoluminescence, and g-factor measurements. Using transient microscopy we observe propagation properties of interlayer excitons that are independent from trapping at moiré- or disorder-induced local potentials. Confirmed by characteristic temperature dependence for free particles, linear diffusion coefficients of interlayer excitons at liquid helium temperature and low excitation densities are almost 1000 times higher than in previous observations. We further show that exciton-exciton repulsion and annihilation contribute nearly equally to nonlinear propagation by disentangling the two processes in the experiment and simulations. Finally, we demonstrate effective shrinking of the light emission area over time across several hundreds of picoseconds at the transition from exciton- to the plasma-dominated regimes. Supported by microscopic calculations for band gap renormalization to identify the Mott threshold, this indicates transient crossing between rapidly expanding, short-lived electron-hole plasma and slower, long-lived exciton populations.

Strongly Localized Moiré Exciton in Twisted Homobilayers

Artificially molding exciton flux is the cornerstone for developing promising excitonic devices. In the emerging hetero/homobilayers, the spatial separated charges prolong exciton lifetimes and create out-plane dipoles, facilitating electrically control exciton flux on a large scale, and the nanoscale periodic moiré potentials arising from twist-angle or/and lattice mismatch can substantially alter exciton dynamics, which are mainly proved in the heterostructures. However, the spatially indirect excitons dynamics in homobilayers without lattice mismatch remain elusive. Here the nonequilibrium dynamics of indirect exciton in homobilayers are systematically investigated. The homobilayers with slightly twist-angle can induce a deep moiré potential (>50 meV) in the energy landscape of indirect excitons, resulting in a strongly localized moiré excitons insulating the transport dynamics from phonons and disorder. These findings provide insights into the exciton dynamics and many-body physics in moiré superlattices modulated energy landscape, with implications for designing excitonic devices operating at room temperature.

Evidence for Exciton Crystals in a 2D Semiconductor Heterotrilayer

Two-dimensional (2D) transition metal dichalcogenides (TMDC) and their moiré interfaces have been demonstrated for correlated electron states, including Mott insulators and electron/hole crystals commensurate with moiré superlattices. Here we present spectroscopic evidence for ordered bosons─interlayer exciton crystals in a WSe2/MoSe2/WSe2 trilayer, where the enhanced Coulomb interactions over those in heterobilayers have been predicted to result in exciton ordering. Ordered interlayer excitons in the trilayer are characterized by negligible mobility and by sharper PL peaks persisting to an exciton density of nex ∼ 1012 cm-2, which is an order of magnitude higher than the corresponding limit in the heterobilayer. We present evidence for the predicted quadrupolar exciton crystal and its transitions to dipolar excitons either with increasing nex or by an applied electric field. These ordered interlayer excitons may serve as models for the exploration of quantum phase transitions and quantum coherent phenomena.

Recent progress of exciton transport in two-dimensional semiconductors

Spatial manipulation of excitonic quasiparticles, such as neutral excitons, charged excitons, and interlayer excitons, in two-dimensional semiconductors offers unique capabilities for a broad range of optoelectronic applications, encompassing photovoltaics, exciton-integrated circuits, and quantum light-emitting systems. Nonetheless, their practical implementation is significantly restricted by the absence of electrical controllability for neutral excitons, short lifetime of charged excitons, and low exciton funneling efficiency at room temperature, which remain a challenge in exciton transport. In this comprehensive review, we present the latest advancements in controlling exciton currents by harnessing the advanced techniques and the unique properties of various excitonic quasiparticles. We primarily focus on four distinct control parameters inducing the exciton current: electric fields, strain gradients, surface plasmon polaritons, and photonic cavities. For each approach, the underlying principles are introduced in conjunction with its progression through recent studies, gradually expanding their accessibility, efficiency, and functionality. Finally, we outline the prevailing challenges to fully harness the potential of excitonic quasiparticles and implement practical exciton-based optoelectronic devices.

Multi-scale time-resolved electron diffraction: A case study in moiré materials

Ultrafast-optical-pump - structural-probe measurements, including ultrafast electron and x-ray scattering, provide direct experimental access to the fundamental timescales of atomic motion, and are thus foundational techniques for studying matter out of equilibrium. High-performance detectors are needed in scattering experiments to obtain maximum scientific value from every probe particle. We deploy a hybrid pixel array direct electron detector to perform ultrafast electron diffraction experiments on a WSe2/MoSe2 2D heterobilayer, resolving the weak features of diffuse scattering and moiré superlattice structure without saturating the zero order peak. Enabled by the detector's high frame rate, we show that a chopping technique provides diffraction difference images with signal-to-noise at the shot noise limit. Finally, we demonstrate that a fast detector frame rate coupled with a high repetition rate probe can provide continuous time resolution from femtoseconds to seconds, enabling us to perform a scanning ultrafast electron diffraction experiment that maps thermal transport in WSe2/MoSe2 and resolves distinct diffusion mechanisms in space and time.

Strong Dipolar Repulsion of One-Dimensional Interfacial Excitons in Monolayer Lateral Heterojunctions

Repulsive and long-range exciton-exciton interactions are crucial for the exploration of one-dimensional (1D) correlated quantum phases in the solid state. However, the experimental realization of nanoscale confinement of a 1D dipolar exciton has thus far been limited. Here, we demonstrate atomically precise lateral heterojunctions based at transitional-metal dichalcogenides (TMDCs) as a platform for 1D dipolar excitons. The dynamics and transport of the interfacial charge transfer excitons in a type II WSe2-WS1.16Se0.84 lateral heterostructure were spatially and temporally imaged using ultrafast transient reflection microscopy. The expansion of the exciton cloud driven by dipolar repulsion was found to be strongly density dependent and highly anisotropic. The interaction strength between the 1D excitons was determined to be ∼3.9 × 10-14 eV cm-2, corresponding to a dipolar length of 310 nm, which is a factor of 2-3 larger than the interlayer excitons at two-dimensional van der Waals vertical interfaces. These results suggest 1D dipolar excitons with large static in-plane dipole moments in lateral TMDC heterojunctions as an exciting system for investigating quantum many-body physics.

Electrically tunable dipolar interactions between layer-hybridized excitons

Transition-metal dichalcogenide bilayers exhibit a rich exciton landscape including layer-hybridized excitons, i.e. excitons which are of partly intra- and interlayer nature. In this work, we study hybrid exciton-exciton interactions in naturally stacked WSe2 homobilayers. In these materials, the exciton landscape is electrically tunable such that the low-energy states can be rendered more or less interlayer-like depending on the strength of the external electric field. Based on a microscopic and material-specific many-particle theory, we reveal two intriguing interaction regimes: a low-dipole regime at small electric fields and a high-dipole regime at larger fields, involving interactions between hybrid excitons with a substantially different intra- and interlayer composition in the two regimes. While the low-dipole regime is characterized by weak inter-excitonic interactions between intralayer-like excitons, the high-dipole regime involves mostly interlayer-like excitons which display a strong dipole-dipole repulsion and give rise to large spectral blue-shifts and a highly anomalous diffusion. Overall, our microscopic study sheds light on the remarkable electrical tunability of hybrid exciton-exciton interactions in atomically thin semiconductors and can guide future experimental studies in this growing field of research.

Bosonic Delocalization of Dipolar Moiré Excitons

In superlattices of twisted semiconductor monolayers, tunable moiré potentials emerge, trapping excitons into periodic arrays. In particular, spatially separated interlayer excitons are subject to a deep potential landscape and they exhibit a permanent dipole providing a unique opportunity to study interacting bosonic lattices. Recent experiments have demonstrated density-dependent transport properties of moiré excitons, which could play a key role for technological applications. However, the intriguing interplay between exciton-exciton interactions and moiré trapping has not been well understood yet. In this work, we develop a microscopic theory of interacting excitons in external potentials allowing us to tackle this highly challenging problem. We find that interactions between moiré excitons lead to a delocalization at intermediate densities, and we show how this transition can be tuned via twist angle and temperature. The delocalization is accompanied by a modification of optical moiré resonances, which gradually merge into a single free exciton peak.

Fermi Pressure and Coulomb Repulsion Driven Rapid Hot Plasma Expansion in a van der Waals Heterostructure

Transition metal dichalcogenide heterostructures provide a versatile platform to explore electronic and excitonic phases. As the excitation density exceeds the critical Mott density, interlayer excitons are ionized into an electron-hole plasma phase. The transport of the highly non-equilibrium plasma is relevant for high-power optoelectronic devices but has not been carefully investigated previously. Here, we employ spatially resolved pump-probe microscopy to investigate the spatial-temporal dynamics of interlayer excitons and hot-plasma phase in a MoSe₂/WSe₂ twisted bilayer. At the excitation density of ∼10¹⁴ cm^-2, well exceeding the Mott density, we find a surprisingly rapid initial expansion of hot plasma to a few microns away from the excitation source within ∼0.2 ps. Microscopic theory reveals that this rapid expansion is mainly driven by Fermi pressure and Coulomb repulsion, while the hot carrier effect has only a minor effect in the plasma phase.

Lattice Reconstruction in MoSe2-WSe2 Heterobilayers Synthesized by Chemical Vapor Deposition

Vertical van der Waals heterostructures of semiconducting transition metal dichalcogenides realize moiré systems with rich correlated electron phases and moiré exciton phenomena. For material combinations with small lattice mismatch and twist angles as in MoSe₂-WSe₂, however, lattice reconstruction eliminates the canonical moiré pattern and instead gives rise to arrays of periodically reconstructed nanoscale domains and mesoscopically extended areas of one atomic registry. Here, we elucidate the role of atomic reconstruction in MoSe₂-WSe₂ heterostructures synthesized by chemical vapor deposition. With complementary imaging down to the atomic scale, simulations, and optical spectroscopy methods, we identify the coexistence of moiré-type cores and extended moiré-free regions in heterostacks with parallel and antiparallel alignment. Our work highlights the potential of chemical vapor deposition for applications requiring laterally extended heterosystems of one atomic registry or exciton-confining heterostack arrays.

Ultrafast hot electron-hole plasma photoluminescence in two-dimensional semiconductors

The transition metal dichalcogenide family of semiconducting two-dimensional materials has recently shown a prominent potential to be an ideal platform to study the exciton Mott transition into electron-hole plasma and liquid phases due to their strong Coulomb interactions. Here, we show that pulsed laser excitation at high pump fluences can induce this exciton Mott transition to an electron-hole plasma in mono and few-layer transition metal dichalcogenides at room temperature. The formation of an electron-hole plasma leads to a broadband light emission spanning from the near infrared to the visible region. In agreement with our theoretical calculations, the photoluminescence emission at high energies displays an exponential decay that directly reflects the electronic temperature - a characteristic fingerprint of unbound electron-hole pair recombination. Furthermore, two-pulse excitation correlation measurements were performed to study the dynamics of electronic cooling, which shows two decay time components, one of less than 100 fs and a slower component of few ps associated with the electron-phonon and phonon-lattice bath thermalizations, respectively. Our work may shed light on further studies of the exciton Mott transition into other two-dimensional materials and their heterostructures and its applications in nanolasers and other optoelectronic devices.

Enhanced interactions of interlayer excitons in free-standing heterobilayers

Strong, long-range dipole-dipole interactions between interlayer excitons (IXs) can lead to new multiparticle correlation regimes^1,2, which drive the system into distinct quantum and classical phases^2-5, including dipolar liquids, crystals and superfluids. Both repulsive and attractive dipole-dipole interactions have been theoretically predicted between IXs in a semiconductor bilayer^2,6-8, but only repulsive interactions have been reported experimentally so far^3,9-16. This study investigated free-standing, twisted (51°, 53°, 45°) tungsten diselenide/tungsten disulfide (WSe₂/WS₂) heterobilayers, in which we observed a transition in the nature of dipolar interactions among IXs, from repulsive to attractive. This was caused by quantum-exchange-correlation effects, leading to the appearance of a robust interlayer biexciton phase (formed by two IXs), which has been theoretically predicted^6-8 but never observed before in experiments. The reduced dielectric screening in a free-standing heterobilayer not only resulted in a much higher formation efficiency of IXs, but also led to strongly enhanced dipole-dipole interactions, which enabled us to observe the many-body correlations of pristine IXs at the two-dimensional quantum limit. In addition, we firstly observed several emission peaks from moiré-trapped IXs at room temperature in a well-aligned, free-standing WSe₂/WS₂ heterobilayer. Our findings open avenues for exploring new quantum phases with potential for applications in non-linear optics.

Lattice-Mismatch-Driven Small-Angle Moiré Twists in Epitaxially Grown 2D Vertical Layered Heterostructures

Artificially introduced small twist angles at the interfaces of vertical layered heterostructures (VLHs) have allowed deterministic tuning of electronic and optical properties such as strongly correlated electronic phases and Moiré excitons. But creating a Moiré twist in van der Waals (vdWs) systems by manual stacking is challenging in reproducibility, uniformity, and accuracy of the twist angle, which hinders future studies. Here, it is demonstrated that contrary to the commonly believed 0°-orientation in vdWs epitaxy, these VLHs show small twist angles controlled by the low-order commensurate phase with low energy and local atomic relaxation. A commensurate multilevel map is proposed to predict possible orientations. Remarkably, high-mismatch VLHs show discrete and sometimes non-zero twist angles dependent on their natural mismatch value. Such framework is experimentally confirmed in five epitaxially grown VLHs under high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM), and can provide significant insights for large-scale engineering of twist angle in VLHs.

Ultralocalized Optoelectronic Properties of Nanobubbles in 2D Semiconductors

The optical properties of transition-metal dichalcogenides have previously been modified at the nanoscale by using mechanical and electrical nanostructuring. However, a clear experimental picture relating the local electronic structure with emission properties in such structures has so far been lacking. Here, we use a combination of scanning tunneling microscopy (STM) and near-field photoluminescence (nano-PL) to probe the electronic and optical properties of single nanobubbles in bilayer heterostructures of WSe₂ on MoSe₂. We show from tunneling spectroscopy that there are electronic states deeply localized in the gap at the edge of such bubbles, which are independent of the presence of chemical defects in the layers. We also show a significant change in the local band gap on the bubble, with a continuous evolution to the edge of the bubble over a length scale of ∼20 nm. Nano-PL measurements observe a continuous redshift of the interlayer exciton on entering the bubble, in agreement with the band-to-band transitions measured by STM. We use self-consistent Schrödinger-Poisson simulations to capture the essence of the experimental results and find that strong doping in the bubble region is a key ingredient to achieving the observed localized states, together with mechanical strain.

Twist Angle-Dependent Interlayer Exciton in MoS2 Bilayers Revealed by Room-Temperature Reflectance

In 2H stacking bilayer MoS2, the exciton with an interlayer nature has been evidenced due to the hybridization of hole states among both layers. The transition energy of this interlayer exciton is located between the A and B excitons. In this work, we investigate the evolution of optical properties in stacking MoS2 bilayers with the twisted angles ranging from 0° to 60°, especially focusing on the interlayer exciton. The clear modulations of the exciton responses are observed by the room-temperature reflectance. The interlayer exciton transition is observed in the artificial stacking bilayer MoS2 with the twisted angle around 60°. We found that the interlayer exciton is very sensitive to the twisted angle. Once the stacking angle deviates the 2H stacking by a few degrees, the interlayer transition is quenched. This is due to the bilayer symmetry and interlayer coupling of this unique system.

Self-Trapped Interlayer Excitons in van der Waals Heterostructures

The self-trapped state (STS) of the interlayer exciton (IX) has aroused enormous interest owing to its significant impact on the fundamental properties of the van der Waals heterostructures (vdWHs). Nevertheless, the microscopic mechanisms of STS are still controversial. Herein, we study the corrections of the binding energies of the IXs stemming from the exciton-interface optical phonon coupling in four kinds of vdWHs and find that these IXs are in the STS for the appropriate ratio of the electron and hole effective masses. We show that these self-trapped IXs could be classified into type I with the increasing binding energy in the tens of millielectronvolts range, which are very agreement with the red-shift of the IX spectra in experiments, and type II with the decreasing binding energy, which provides a possible explanation for the blue-shift and broad line width of the IX's spectra at low temperatures. Moreover, these two types of exciton states could be transformed into each other by adjusting the structural parameters of vdWHs. These results not only provide an in-depth understanding for the self-trapped mechanism but also shed light on the modulations of IXs in vdWHs.

Ultrafast Nanoscopy of High-Density Exciton Phases in WSe2

The density-driven transition of an exciton gas into an electron-hole plasma remains a compelling question in condensed matter physics. In two-dimensional transition metal dichalcogenides, strongly bound excitons can undergo this phase change after transient injection of electron-hole pairs. Unfortunately, unavoidable nanoscale inhomogeneity in these materials has impeded quantitative investigation into this elusive transition. Here, we demonstrate how ultrafast polarization nanoscopy can capture the Mott transition through the density-dependent recombination dynamics of electron-hole pairs within a WSe₂ homobilayer. For increasing carrier density, an initial monomolecular recombination of optically dark excitons transitions continuously into a bimolecular recombination of an unbound electron-hole plasma above 7 × 10¹² cm^-2. We resolve how the Mott transition modulates over nanometer length scales, directly evidencing the strong inhomogeneity in stacked monolayers. Our results demonstrate how ultrafast polarization nanoscopy could unveil the interplay of strong electronic correlations and interlayer coupling within a diverse range of stacked and twisted two-dimensional materials.

Excitons in semiconductor moiré superlattices

Semiconductor moiré superlattices represent a rapidly developing area of engineered photonic materials and a new platform to explore correlated electron states and quantum simulation. In this Review, we briefly introduce early experiments that identified new exciton resonances in transition metal dichalcogenide heterobilayers and discuss several topics including two types of transition metal dichalcogenide moiré superlattice, new optical selection rules, early evidence of moiré excitons, and how the resonant energy, dynamics and diffusion properties of moiré excitons can be controlled via the twist angle. To interpret optical spectra, it is important to measure the energy modulation within a moiré supercell. In this context, we describe a few scanning tunnelling microscopy experiments that measure the moiré potential landscape directly. Finally, we review a few recent experiments that applied excitonic optical spectroscopy to probe correlated electron phenomena in transition metal dichalcogenide moiré superlattices.

Excitonic transport driven by repulsive dipolar interaction in a van der Waals heterostructure

Dipolar bosonic gases are currently the focus of intensive research due to their interesting many-body physics in the quantum regime. Their experimental embodiments range from Rydberg atoms to GaAs double quantum wells and van der Waals heterostructures built from transition metal dichalcogenides. Although quantum gases are very dilute, mutual interactions between particles could lead to exotic many-body phenomena such as Bose-Einstein condensation and high-temperature superfluidity. Here, we report the effect of repulsive dipolar interactions on the dynamics of interlayer excitons in the dilute regime. By using spatial and time-resolved photoluminescence imaging, we observe the dynamics of exciton transport, enabling a direct estimation of the exciton mobility. The presence of interactions significantly modifies the diffusive transport of excitons, effectively acting as a source of drift force and enhancing the diffusion coefficient by one order of magnitude. The repulsive dipolar interactions combined with the electrical control of interlayer excitons opens up appealing new perspectives for excitonic devices.

Signatures of moiré trions in WSe2/MoSe2 heterobilayers

Moiré superlattices formed by van der Waals materials can support a wide range of electronic phases, including Mott insulators^1-4, superconductors^5-10 and generalized Wigner crystals². When excitons are confined by a moiré superlattice, a new class of exciton emerges, which holds promise for realizing artificial excitonic crystals and quantum optical effects^11-16. When such moiré excitons are coupled to charge carriers, correlated states may arise. However, no experimental evidence exists for charge-coupled moiré exciton states, nor have their properties been predicted by theory. Here we report the optical signatures of trions coupled to the moiré potential in tungsten diselenide/molybdenum diselenide heterobilayers. The moiré trions show multiple sharp emission lines with a complex charge-density dependence, in stark contrast to the behaviour of conventional trions. We infer distinct contributions to the trion emission from radiative decay in which the remaining carrier resides in different moiré minibands. Variation of the trion features is observed in different devices and sample areas, indicating high sensitivity to sample inhomogeneity and variability. The observation of these trion features motivates further theoretical and experimental studies of higher-order electron correlation effects in moiré superlattices.

Moiré metrology of energy landscapes in van der Waals heterostructures

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe2/WSe2. Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.