Atomic Registry Research Articles

Constructing Slip Stacking Diversity in Van der Waals Homobilayers.

The van der Waals (vdW) interface provides two important degrees of freedom-twist and slip-to tune interlayer structures and inspire unique physics. However, constructing diversified high-quality slip stackings (i.e., lattice orientations between layers are parallel with only interlayer sliding) is more challenging than twisted stackings due to angstrom-scale structural discrepancies between different slip stackings, sparsity of thermodynamically stable candidates and insufficient mechanism understanding. Here, using transition metal dichalcogenide (TMD) homobilayers as a model system, this work theoretically elucidates that vdW materials with low lattice symmetry and weak interlayer coupling allow the creation of multifarious thermodynamically advantageous slip stackings, and experimentally achieves13 and 9 slip stackings in 1T″-ReS2 and 1T″-ReSe2 bilayers via direct growth, which are systematically revealed by atomic-resolution scanning transmission electron microscopy (STEM), angle-resolved polarization Raman spectroscopy, and second harmonic generation (SHG) measurements. This work also develops modulation strategies to switch the stacking via grain boundaries (GBs) and to expand the slip stacking library from thermodynamic to kinetically favored structures via in situ thermal treatment. Finally, density functional theory (DFT) calculations suggest a prominent dependence of the pressure-induced electronic band structure transition on stacking configurations. These studies unveil a unique vdW epitaxy and offer a viable means for manipulating interlayer atomic registries.

Van der Waals Engineering of Charge Density Waves in One-Dimensional Nb6Te6 Nanowires.

One-dimensional (1D) systems have played a crucial role in the development of fundamental physics and practical applications. Recently, transition metal monochalcogenide (TMM) wires based on molybdenum (Mo) and tungsten (W) have emerged as promising platforms for investigating 1D physics in pure van der Waals (vdW) platforms. Here, we report on the bottom-up fabrication of Nb6Te6 wires down to the single-wire limit. The unique properties of Nb6Te6 single wire enable the realization of 1D charge density wave (CDW) phases in an isolated single TMM wire. Moreover, we revealed the appealing regulation of 1D CDW orders by van der Waals interactions at either the 1D-2D interface (i.e., rotation of a single wire along its wire axis) or the 1D-1D interface. Two rotation angles (30° and 0°) give rise to 3 × 1 and zigzag chain CDW morphologies, respectively, which exhibit pronounced differences in atomic displacement by a factor of 2. The interwire vdW coupling overwhelms its counterpart at the 1D-2D interface, thus locking the rotation angle (at 0°) as well as the interwire atomic registries. In contrast, interestingly, the phases of the charge oscillations are independent of the adjacent wires. The ability to tailor 1D charge orders provides a crucial addition to the toll set of vdW integrations beyond two-dimensional materials.

Correlation-driven nonequilibrium exciton site transition in a WSe2/WS2 moiré supercell

Moiré superlattices of transition metal dichalcogenides offer a unique platform to explore correlated exciton physics with optical spectroscopy. Whereas the spatially modulated potentials evoke that the exciton resonances are distinct depending on a site in a moiré supercell, there have been no clear demonstration how the moiré excitons trapped in different sites dynamically interact with the doped carriers; so far the exciton-electron dynamic interactions were presumed to be site-dependent. Thus, the transient emergence of nonequilibrium correlations are open questions, but existing studies are limited to steady-state optical measurements. Here we report experimental fingerprints of site-dependent exciton correlations under continuous-wave as well as ultrashort optical excitations. In near-zero angle-aligned WSe2/WS2 heterobilayers, we observe intriguing polarization switching and strongly enhanced Pauli blocking near the Mott insulating state, dictating the dominant correlation-driven effects. When the twist angle is near 60°, no such correlations are observed, suggesting the strong dependence of atomic registry in moiré supercell configuration. Our studies open the door to largely unexplored nonequilibrium correlations of excitons in moiré superlattices.

Optical Microcavity‐Induced Moiré Exciton Localization in Twisted WSe2 Homobilayer

Abstract2D moiré superlattices offer a versatile platform for manipulating quantum materials, exploiting their spatially varying atomic registry to modify electronic structures, resulting in the emergence of flat electronic minibands, enhanced electronic interactions, and the onset of novel quantum phenomena. Despite extensive investigations into moiré excitons within twisted bilayer moiré superlattices, the interplay between moiré superlattices and optical microcavities remains elusive. Here, a WSe2 homobilayer with a small twist angle positioned on optical microcavities atop a SiO2 (285 nm)/Si substrate is investigated. Utilizing low‐temperature photoluminescence (PL) spectroscopy, it is observed that the twisted homobilayer at the edge of the optical cavity (Edge‐THB) exhibits enhanced localization of moiré excitons and a deeper moiré potential. This behavior is attributed to the combined influence of strain induced by the optical microcavity structure on the moiré superlattice and the amplification of the electromagnetic field. Furthermore, the existence of moiré excitons through a comprehensive analysis, encompassing temperature‐dependent PL spectra, circularly polarized PL spectra, and Landé g‐factor measurements for Edge‐THB is validated. These findings provide valuable insights into the intricate interaction between moiré superlattices and optical microcavities, paving the way for future applications in quantum technologies.

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.

Revealing intrinsic domains and fluctuations of moiré magnetism by a wide-field quantum microscope

Moiré magnetism featured by stacking engineered atomic registry and lattice interactions has recently emerged as an appealing quantum state of matter at the forefront of condensed matter physics research. Nanoscale imaging of moiré magnets is highly desirable and serves as a prerequisite to investigate a broad range of intriguing physics underlying the interplay between topology, electronic correlations, and unconventional nanomagnetism. Here we report spin defect-based wide-field imaging of magnetic domains and spin fluctuations in twisted double trilayer (tDT) chromium triiodide CrI3. We explicitly show that intrinsic moiré domains of opposite magnetizations appear over arrays of moiré supercells in low-twist-angle tDT CrI3. In contrast, spin fluctuations measured in tDT CrI3 manifest little spatial variations on the same mesoscopic length scale due to the dominant driving force of intralayer exchange interaction. Our results enrich the current understanding of exotic magnetic phases sustained by moiré magnetism and highlight the opportunities provided by quantum spin sensors in probing microscopic spin related phenomena on two-dimensional flatland.

Programming twist angle and strain profiles in 2D materials.

Moiré superlattices in twisted two-dimensional materials have generated tremendous excitement as a platform for achieving quantum properties on demand. However, the moiré pattern is highly sensitive to the interlayer atomic registry, and current assembly techniques suffer from imprecise control of the average twist angle, spatial inhomogeneity in the local twist angle, and distortions caused by random strain. We manipulated the moiré patterns in hetero- and homobilayers through in-plane bending of monolayer ribbons, using the tip of an atomic force microscope. This technique achieves continuous variation of twist angles with improved twist-angle homogeneity and reduced random strain, resulting in moiré patterns with tunable wavelength and ultralow disorder. Our results may enable detailed studies of ultralow-disorder moiré systems and the realization of precise strain-engineered devices.

Interfacial Reconstructed Layer Controls the Orientation of Monolayer Transition-Metal Dichalcogenides.

Growing continuous monolayer films of transition-metal dichalcogenides (TMDs) without the disruption of grain boundaries is essential to realize the full potential of these materials for future electronics and optoelectronics, but it remains a formidable challenge. It is generally believed that controlling the TMDs orientations on epitaxial substrates stems from matching the atomic registry, symmetry, and penetrable van der Waals forces. Interfacial reconstruction within the exceedingly narrow substrate-epilayer gap has been anticipated. However, its role in the growth mechanism has not been intensively investigated. Here, we report the experimental conformation of an interfacial reconstructed (IR) layer within the substrate-epilayer gap. Such an IR layer profoundly impacts the orientations of nucleating TMDs domains and, thus, affects the materials' properties. These findings provide deeper insights into the buried interface that could have profound implications for the development of TMD-based electronics and optoelectronics.

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.

Atomic structure evolution and linear regression fitting models for pre-breakdown electric field strength of FCC, BCC and HCP metal nano-emitters under high electric field from PIC-ED–MD simulations

Multi-scale and multi-physics simulations are carried out for nano-emitters consisting of FCC (Al, Cu and Au), BCC (V, Mo and W) and HCP (Ti, Zn and Zr) metals, using hybrid electrodynamics coupled with molecular dynamics-particle in cell simulations (PIC-ED–MD). We show that the tilting of the nano-emitter at low temperature and small electric field (E-field) is mainly caused either by the movement of partial dislocations at the apex of the nanotip or by the elastic local distortions of atomic registries away from their ideal lattice sites (FCC/BCC/HCP). At high E-field, the intense resistive heating due to the strong electron emission leads to the direct melting of the apex of nano-emitters. For nano-emitters consisting of low melting point metals such as Al, Zn and Au, the thermal runaway is driven by the elongation, thinning and necking of the molten region. Meanwhile, the elongation, thinning and sharpening produce the nano-protrusion at the apex of metal nano-emitters, and the detachment of atoms or atomic clusters from the nano-protrusion mainly contributes to the thermal runaway event for refractor metals such as Ti, Zr, Mo and W. The critical E-field strength of metal nano-emitters is found to be strongly correlated with structural parameters (atomic coordination number of liquid and equilibrium lattice constant), thermodynamic quantities (cohesive energy and enthalpy of evaporation) and phase transition temperatures (melting point and boiling point). These correlations enable us to establish either single-variable linear fitting models or multi-variable linear regression models to predict the critical E-field value for metal nano-emitters with good credibility.

Excitons in mesoscopically reconstructed moiré heterostructures

Moiré effects in vertical stacks of two-dimensional crystals give rise to new quantum materials with rich transport and optical phenomena that originate from modulations of atomic registries within moiré supercells. Due to finite elasticity, however, the superlattices can transform from moiré-type to periodically reconstructed patterns. Here we expand the notion of such nanoscale lattice reconstruction to the mesoscopic scale of laterally extended samples and demonstrate rich consequences in optical studies of excitons in MoSe2–WSe2 heterostructures with parallel and antiparallel alignments. Our results provide a unified perspective on moiré excitons in near-commensurate semiconductor heterostructures with small twist angles by identifying domains with exciton properties of distinct effective dimensionality, and establish mesoscopic reconstruction as a compelling feature of real samples and devices with inherent finite size effects and disorder. Generalized to stacks of other two-dimensional materials, this notion of mesoscale domain formation with emergent topological defects and percolation networks will instructively expand the understanding of fundamental electronic, optical and magnetic properties of van der Waals heterostructures.

Unconventional ferroelectricity in half-filling states of antiparallel stacking of twisted WSe<sub>2</sub>

<p indent="0mm">We report on emergence of an abnormal electronic polarization in twisted double bilayer WSe₂ in antiparallel interface stacking geometry, where local centrosymmetry of atomic registries at the twist interface does not favor the spontaneous electronic polarizations as recently observed in the parallel interface stacking geometry. The unconventional ferroelectric behaviors probed by electronic transport measurement occur at half filling insulating states at <sc>1.5 K</sc> and gradually disappear at about <sc>40 K.</sc> Single band Hubbard model based on the triangular moiré lattice and the interlayer charge transfer controlled by insulating phase transition are proposed to interpret the formation of electronic polarization states near half filling in twisted WSe₂ devices. Our work highlights the prominent role of many-body electronic interaction in fostering novel quantum states in moiré-structured systems.

Deep-Learning Pipeline for Statistical Quantification of Amorphous Two-Dimensional Materials

Aberration-corrected transmission electron microscopy enables imaging of two-dimensional (2D) materials with atomic resolution. However, dissecting the short-range-ordered structures in radiation-sensitive and amorphous 2D materials remains a significant challenge due to low atomic contrast and laborious manual evaluation. Here, we imaged carbon-based 2D materials with strong contrast, which is enabled by chromatic and spherical aberration correction at a low acceleration voltage. By constructing a deep-learning pipeline, atomic registry in amorphous 2D materials can be precisely determined, providing access to a full spectrum of quantitative data sets, including bond length/angle distribution, pair distribution function, and real-space polygon mapping. Accurate segmentation of micropores and surface contamination, together with robustness against background inhomogeneity, guaranteed the quantification validity in complex experimental images. The automated image analysis provides quantitative metrics with high efficiency and throughput, which may shed light on the structural understanding of short-range-ordered structures. In addition, the convolutional neural network can be readily generalized to crystalline materials, allowing for automatic defect identification and strain mapping.

Nanophotonic control of thermal emission under extreme temperatures in air.

Nanophotonic materials offer spectral and directional control over thermal emission, but in high-temperature oxidizing environments, their stability remains low. This limits their applications in technologies such as solid-state energy conversion and thermal barrier coatings. Here we show an epitaxial heterostructure of perovskite BaZr0.5Hf0.5O3 (BZHO) and rocksalt MgO that is stable up to 1,100 °C in air. The heterostructure exhibits coherent atomic registry and clearly separated refractive-index-mismatched layers after prolonged exposure to this extreme environment. The immiscibility of the two materials is corroborated by the high formation energy of substitutional defects from density functional theory calculations. The epitaxy of immiscible refractory oxides is, therefore, an effective method to avoid prevalent thermal instabilities in nanophotonic materials, such as grain-growth degradation, interlayer mixing and oxidation. As a functional example, a BZHO/MgO photonic crystal is implemented as a filter to suppress long-wavelength thermal emission from the leading bulk selective emitter and effectively raise its cutoff energy by 20%, which can produce a corresponding gain in the efficiency of mobile thermophotovoltaic systems. Beyond BZHO/MgO, computational screening shows that hundreds of potential cubic oxide pairs fit the design principles of immiscible refractory photonics. Extending the concept to other material systems could enable further breakthroughs in a wide range of photonic and energy conversion applications.

Modulating the microscopic lattice distortions through the Al-rich layers for boosting the ferroelectricity in Al:HfO2 nanofilms

Combining the experimental characterization with the large-scale density functional theory calculations based on finite-element discretization (DFT-FE), we address the stabilization of polar orthorhombic phases (o-HfO2) in Al:HfO2 nanofilms by means of the atomic registry distortions and lattice deformation caused by Al substitutional defects (AlHf) and Schottky defects (2AlHf + VO) in tetragonal phases (t-HfO2) or monoclinic phases (m-HfO2). The phase transformation directly from the t-HfO2 into polar o-HfO2 are also elucidated within a heterogeneous distribution of Al dopants in both t-HfO2 bulk crystal structure and Al:HfO2 nanofilm. It is revealed using large-scale DFT calculations that the Al substitutional defects (AlHf) or the Schottky defect (2AlHf + VO) could induce the highly extended atomic registry distortions or lattice deformation in the t- and m-HfO2 phases, but such effects are greatly diminished in ferroelectric orthorhombic phase. By purposely engineering the multiple AlHf defects to form dopant-rich layers in paraelectric t-HfO2 nanofilm or bulk crystal, the induced extended lattice distortions surrounding the defect sites exhibit the shearing-like atomic displacement vector field. The large-scale DFT calculations further predicted that the shearing-like microscopic lattice distortions could directly induce the phase transformation from the t-HfO2 into polar orthorhombic phase in both Al:HfO2 bulk crystal and nanofilms, leading to the large remanent polarization observed in Al:HfO2 nanofilms with the presence of Al-rich layers. The current study demonstrates that the ferroelectricity of HfO2 bulk crystal or thin film can be optimized and tuned by delicately engineering both the distribution and concentration of Al dopants in atomic layer deposition without applying the top capping electrode, providing the extra flexibility for designing the HfO2 based electronic devices in the future.

Nanoscale Electronic Transparency of Wafer-Scale Hexagonal Boron Nitride.

Monolayer hexagonal boron nitride (hBN) has attracted interest as an ultrathin tunnel barrier or environmental protection layer. Recently, wafer-scale hBN growth on Cu(111) was developed for semiconductor chip applications. For basic research and technology, understanding how hBN perturbs underlying electronically active layers is critical. Encouragingly, hBN/Cu(111) has been shown to preserve the Cu(111) surface state (SS), but it was unknown how tunneling into this SS through hBN varies spatially. Here, we demonstrate that the Cu(111) SS under wafer-scale hBN is homogeneous in energy and spectral weight over nanometer length scales and across atomic terraces. In contrast, a new spectral feature─not seen on bare Cu(111)─varies with atomic registry and shares the spatial periodicity of the hBN/Cu(111) moiré. This work demonstrates that, for some 2D electron systems, an hBN overlayer can act as a protective yet remarkably transparent window on fragile low-energy electronic structure below.

Dative Epitaxy of Commensurate Monocrystalline Covalent van der Waals Moiré Supercrystal.

Realizing van der Waals (vdW) epitaxy in the 1980s represents a breakthrough that circumvents the stringent lattice matching and processing compatibility requirements in conventional covalent heteroepitaxy. However, due to the weak vdW interactions, there is little control over film qualities by the substrate. Typically, discrete domains with a spread of misorientation angles are formed, limiting the applicability of vdW epitaxy. Here, the epitaxial growth of monocrystalline, covalent Cr5 Te8 2D crystals on monolayer vdW WSe2 by chemical vapor deposition is reported, driven by interfacial dative bond formation. The lattice of Cr5 Te8 , with a lateral dimension of a few tens of micrometers, is fully commensurate with that of WSe2 via 3 × 3 (Cr5 Te8 )/7 × 7 (WSe2 ) supercell matching, forming a single-crystalline moiré superlattice. This work establishes a conceptually distinct paradigm of thin-film epitaxy, termed "dative epitaxy", which takes full advantage of covalent epitaxy with chemical bonding for fixing the atomic registry and crystal orientation, while circumventing its stringent lattice matching and processing compatibility requirements; conversely, it ensures the full flexibility of vdW epitaxy, while avoiding its poor orientation control. Cr5 Te8 2D crystals grown by dative epitaxy exhibit square magnetic hysteresis, suggesting minimized interfacial defects that can serve as pinning sites.

Electronic Quantum Materials Simulated with Artificial Model Lattices.

The band structure and electronic properties of a material are defined by the sort of elements, the atomic registry in the crystal, the dimensions, the presence of spin–orbit coupling, and the electronic interactions. In natural crystals, the interplay of these factors is difficult to unravel, since it is usually not possible to vary one of these factors in an independent way, keeping the others constant. In other words, a complete understanding of complex electronic materials remains challenging to date. The geometry of two- and one-dimensional crystals can be mimicked in artificial lattices. Moreover, geometries that do not exist in nature can be created for the sake of further insight. Such engineered artificial lattices can be better controlled and fine-tuned than natural crystals. This makes it easier to vary the lattice geometry, dimensions, spin–orbit coupling, and interactions independently from each other. Thus, engineering and characterization of artificial lattices can provide unique insights. In this Review, we focus on artificial lattices that are built atom-by-atom on atomically flat metals, using atomic manipulation in a scanning tunneling microscope. Cryogenic scanning tunneling microscopy allows for consecutive creation, microscopic characterization, and band-structure analysis by tunneling spectroscopy, amounting in the analogue quantum simulation of a given lattice type. We first review the physical elements of this method. We then discuss the creation and characterization of artificial atoms and molecules. For the lattices, we review works on honeycomb and Lieb lattices and lattices that result in crystalline topological insulators, such as the Kekulé and “breathing” kagome lattice. Geometric but nonperiodic structures such as electronic quasi-crystals and fractals are discussed as well. Finally, we consider the option to transfer the knowledge gained back to real materials, engineered by geometric patterning of semiconductor quantum wells.

Intralayer Phonons in Multilayer Graphene Moiré Superlattices

Moiré pattern in twisted multilayers (tMLs) induces many emergent phenomena by subtle variation of atomic registry to modulate quasiparticles and their interactions, such as superconductivity, moiré excitons, and moiré phonons. The periodic superlattice potential introduced by moiré pattern also underlies patterned interlayer coupling at the interface of tMLs. Although this arising patterned interfacial coupling is much weaker than in-plane atomic interactions, it is crucial in moiré systems, as captured by the renormalized interlayer phonons in twisted bilayer transitional metal dichalcogenides. Here, we determine the quantitative relationship between the lattice dynamics of intralayer out-of-plane optical (ZO) phonons and patterned interfacial coupling in multilayer graphene moiré superlattices (MLG-MS) by the proposed perturbation model, which is previously challenging for MLGs due to their out-of-phase displacements of adjacent atoms in one atomic plane. We unveil that patterned interfacial coupling introduces profound modulations on Davydov components of nonfolded ZO phonon that are localized within the AB-stacked constituents, while the coupling results in layer-extended vibrations with symmetry of moiré pattern for moiré ZO phonons. Our work brings further degrees of freedom to engineer moiré physics according to the modulations imprinted on the phonon frequency and wavefunction.

Visualizing band structure hybridization and superlattice effects in twisted MoS2/WS2 heterobilayers

A mismatch of atomic registries between single-layer transition metal dichalcogenides (TMDs) in a two-dimensional (2D) van der Waals heterostructure produces a moiré superlattice with a periodic potential, which can be fine-tuned by introducing a twist angle between the materials. This approach is promising both for controlling the interactions between the TMDs and for engineering their electronic band structures, yet direct observation of the changes to the electronic structure introduced with varying twist angle has so far been missing. Here, we probe heterobilayers comprised of single-layer MoS2 and WS2 with twist angles ranging from 2∘ to 20∘ and determine the twist angle-dependent evolution of the electronic band structure using micro-focused angle-resolved photoemission spectroscopy. We find strong interlayer hybridization between MoS2 and WS2 electronic states at the -point of the Brillouin zone, leading to a shift of the valence band maximum in the heterostructure. Replicas of the hybridized states are observed at the center of twist angle-dependent moiré mini Brillouin zones. We confirm that these replica features arise from the inherent moiré potential by comparing our experimental observations with density functional theory calculations of the superlattice dispersion. Our direct visualization of these features underscores the potential of using twisted heterobilayer semiconductors to engineer hybrid electronic states and superlattices that alter the electronic and optical properties of 2D heterostructures for a wide range of twist angles.