Maximally localized Wannier functions, interaction models, and fractional quantum anomalous Hall effect in twisted bilayer MoTe2.

We investigate the moiré band structures and the strong correlation effects in twisted bilayer MoTe[Formula: see text] for a wide range of twist angles, employing a combination of various techniques. Using large-scale first-principles calculations, we pinpoint realistic continuum modeling parameters, subsequently deriving the maximally localized Wannier functions for the top three moiré bands. Simplifying our model with reasonable assumptions, we obtain a minimal two-band model, encompassing Coulomb repulsion, correlated hopping, and spin exchange. Our minimal interaction models pave the way for further exploration of the rich many-body physics in twisted MoTe[Formula: see text]. Furthermore, we explore the phase diagrams of the system through Hartree-Fock approximation and exact diagonalization (ED). Our two-band ED analysis underscores significant band-mixing effects in this system, which enlarge the optimal twist angle for fractional quantum anomalous Hall states.

Programming the morphology of DNA origami crystals by magnesium ion strength.

Harnessing the programmable nature of DNA origami for controlling structural features in crystalline materials affords opportunities to bring crystal engineering to a remarkable level. However, the challenge of crystallizing a single type of DNA origami unit into varied structural outcomes remains, given the requirement for specific DNA designs for each targeted structure. Here, we show that crystals with distinct equilibrium phases and shapes can be realized using a single DNA origami morphology with an allosteric factor to modulate the binding coordination. As a result, origami crystals undergo phase transitions from a simple cubic lattice to a simple hexagonal (SH) lattice and eventually to a face-centered cubic (FCC) lattice. After selectively removing internal nanoparticles from DNA origami building blocks, the body-centered tetragonal and chalcopyrite lattice are derived from the SH and FCC lattices, respectively, revealing another phase transition involving crystal system conversions. The rich phase space was realized through the de novo synthesis of crystals under varying solution environments, followed by the individual characterizations of the resulting products. Such phase transitions can lead to associated transitions in the shape of the resulting products. Hexagonal prism crystals, crystals characterized by triangular facets, and twinned crystals are observed to form from SH and FCC systems, which have not previously been experimentally realized by DNA origami crystallization. These findings open a promising pathway toward accessing a rich phase space with a single type of building block and wielding other instructions as tools to develop crystalline materials with tunable properties.

Emergence of Optical Anisotropy in Moiré Superlattice via Heterointerface Engineering.

The interaction between light and moiré superlattices presents a platform for exploring unique light-matter phenomena. Tailoring these optical properties holds immense potential for advancing the utilization of moiré superlattices in photonics, optoelectronics, and valleytronics. However, the control of the optical polarization state in moiré superlattices, particularly in the presence of moiré effects, remains elusive. Here, we unveil the emergence of optical anisotropy in moiré superlattices by constructing twisted WSe2/WSe2/SiP heterostructures. We report a linear polarization degree of ∼70% for moiré excitons, attributed to the spatially nonuniform charge distribution, corroborated by first-principles calculations. Furthermore, we demonstrate the modulation of this linear polarization state via the application of a magnetic field, resulting in polarization angle rotation and a magnetic-field-dependent linear polarization degree, influenced by valley coherence and moiré potential effects. Our findings demonstrate an efficient strategy for tuning the optical polarization state of moiré superlattices using heterointerface engineering.

Predictive Modeling of Nanocrystal Orientation in Superlattices: Insights from Ligand Entropy.

The self-assembly of nanocrystals (NCs) into close-packed, ordered superlattices (SLs) is of broad, engineering interest. The coherent orientation of polyhedral nanocrystals within NC SLs enhances electronic, magnetic, and vibrational coupling, leading to a variety of emergent phenomena. Here, we show that coherent orientation of polyhedral NCs in many SLs can be understood simply by considering its effect on the conformational entropy of surface ligands. We report the predicted nanocrystal orientations and entropic driving force to orient for a broad range of nanocrystal shapes and superlattice unit cells, and we show that ligand entropy is sufficient to reproduce a host of reported experimental and computational observations. We additionally use this framework to predict the expected distribution of interstitial species such as solvent or unbound ligands in an oriented NC SL. This work offers intuition for understanding the orientation of NCs in superlattices and a future framework for analyzing multinary structures.

Controlled Self-Assembly of Nanoscale Superstructures in Phase-Change Ge-Sb-Te Nanowires.

Controlled growth of semiconductor nanowires with atomic precision offers the potential to tune the material properties for integration into scalable functional devices. Despite significant progress in understanding the nanowire growth mechanism, definitive control over atomic positions of its constituents, structure, and morphology via self-assembly remains challenging. Here, we demonstrate an exquisite control over synthesis of cation-ordered nanoscale superstructures in Ge-Sb-Te nanowires with the ability to deterministically vary the nanowire growth direction, crystal facets, and periodicity of cation ordering by tuning the relative precursor flux during synthesis. Furthermore, the role of anisotropy on material properties in cation-ordered nanowire superstructures is illustrated by fabricating phase-change memory (PCM) devices, which show significantly different growth direction dependent amorphization current density. This level of control in synthesizing chemically ordered nanoscale superstructures holds potential to precisely modulate fundamental material properties such as the electronic and thermal transport, which may have implications for PCM, thermoelectrics, and other nanoelectronic devices.

Tuning Topology Phases by Controlling Effective Screening and Depolarization in Oxide Superlattices.

Polar topological phases in oxide superlattices attracted significant attention due to their unique properties. Previous work revealed that a polar vortex and polar skyrmions exist in (PTO)/(STO) superlattices under different elastic constraints, i.e., on different substrates. Here, our phase-field simulation demonstrates that manipulating the PTO and STO layers' thickness can control the effective screening provided by STO and the depolarization degree in PTO, thus switching the system among the polar skyrmions, vortex labyrinth, or paraelectric phase without changing elastic constraints. Additionally, reducing the STO thickness creates interlayer coupling among PTO layers, generating the long-range order of topological phases within superlattices. Furthermore, we construct a PTO-STO thickness topological phase diagram. These findings offer insights into the polar topological phases' formation in oxide superlattices, elucidating the roles of ferroelectric and paraelectric layers in their formation.

Manipulation of Moiré Superlattice in Twisted Monolayer-multilayer Graphene by Moving Nanobubbles.

In the heterostructure of two-dimensional (2D) materials, many novel physics phenomena are strongly dependent on the Moiré superlattice. How to achieve the continuous manipulation of the Moiré superlattice in the same sample is very important to study the evolution of various physical properties. Here, in minimally twisted monolayer-multilayer graphene, we found that bubble-induced strain has a huge impact on the Moiré superlattice. By employing the AFM tip to dynamically and continuously move the nanobubble, we realized the modulation of the Moiré superlattice, like the evolution of regular triangular domains into long strip domain structures with single or double domain walls. We also achieved controllable modulation of the Moiré superlattice by moving multiple nanobubbles and establishing the coupling of nanobubbles. Our work presents a flexible method for continuous and controllable manipulation of Moiré superlattices, which will be widely used to study novel physical properties in 2D heterostructures.

Interlayer Coupling Controlled Ordering and Phases in Polar Vortex Superlattices.

The recent discovery of polar topological structures has opened the door for exciting physics and emergent properties. There is, however, little methodology to engineer stability and ordering in these systems, properties of interest for engineering emergent functionalities. Notably, when the surface area is extended to arbitrary thicknesses, the topological polar texture becomes unstable. Here we show that this instability of the phase is due to electrical coupling between successive layers. We demonstrate that this electrical coupling is indicative of an effective screening length in the dielectric, similar to the conductor-ferroelectric interface. Controlling the electrostatics of the superlattice interfaces, the system can be tuned between a pure topological vortex state and a mixed classical-topological phase. This coupling also enables engineering coherency among the vortices, not only tuning the bulk phase diagram but also enabling the emergence of a 3D lattice of polar textures.

Nonlinear Landau Fan Diagram for Graphene Electrons Exposed to a Moiré Potential.

Due to Landau quantization, the conductance of two-dimensional electrons exposed to a perpendicular magnetic field exhibits oscillations that generate a fan of linear trajectories when plotted in the parameter space spanned by density and field. This fan looks identical, irrespective of the dispersion and field dependence of the Landau level energy. This is no surprise because the position of conductance minima depends solely on the level degeneracy that is linear in flux. The fractal energy spectrum that emerges within each Landau band when electrons are also exposed to a two-dimensional superlattice potential produces numerous additional oscillations, but they also create just linear fans for identical reasons. Here, we report conductance oscillations of graphene electrons exposed to a moiré potential that defy this general rule and form nonlinear trajectories in the density-field plane. We attribute this anomalous behavior to the simultaneous occupation of multiple minibands and magnetic breakdown-induced open orbits.

Patterned Gold Nanoparticle Superlattice Film for Wearable Sweat Sensors.

Nanoparticle superlattices are beneficial in terms of providing strong and uniform signals in analysis owing to their closely packed uniform structures. However, nanoparticle superlattices are prone to cracking during physical activities because of stress concentrations, which hinders their detection performance and limits their analytical applications. In this work, template printing methods were used in this study to prepare a patterned gold nanoparticle (AuNP) superlattice film. By adjustment of the size of the AuNP superlattice domain below the critical size of fracture, the mechanical stability of the AuNP superlattice domain is improved. Thus, long-term sustainable high-performance signal output is achieved. The patterned AuNP superlattice film was used to construct a wearable sweat sensor based on surface-enhanced Raman scattering (SERS). The designed sensor showed promise for long-term reliable use in actual scenarios in terms of recommending water replenishment, monitoring hydration states, and tracking the intensity of activity.

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.

Topotactic Syntopogenous Sodium Vanadium Fluoride for High-Performance Sodium-Ion Batteries: Electron and Sodium-Ion Reservoirs in Perovskite/Diperovskite Superlattice.

In order to simultaneously accelerate ion and electron transfer in sodium-ion battery (SIB) cathodes, a topotactic superlattice was utilized, in which the atomically intrinsic lattice-matching effect from inner to external surface can boost the charge transfer due to the disappearance of the heterojunction interface. Herein, a topotactic syntopogenous Na3VF6/NaVF3 superlattice formulated as Na2.9V1.1F6 (NVF) was synthesized by a facile one-step low-temperature hydrothermal reaction. NVF nanoparticles show an excellent Na+ storage capacity (∼205 mAh g-1) in a high voltage window up to 4.2 V with ultralong cycling stability. That is associated with the mixed occupancy of V and Na in NVF. The multivalent V centers serve as electron reservoirs to inhibit phase transformation, and the Na-enriched Na3VF6 with better electron conductivity acts as a Na+ reservoir for effective electron transfer. Highly reversible (de)intercalation of Na+ is achieved in the channel of perovskite-type NaVF3 with structural integrity.

Tuning Displacement Fields in a Two-Dimensional Topological Insulator Using Nanopatterned Gates.

Epitaxial heterostructures with topological insulators enable novel quantum phases and practical device applications. Their topological electronic states are sensitive to the microscopic parameters, including structural inversion asymmetry (SIA), which is an inherent feature of many real heterostructures. Controlling SIA is challenging, because it requires the ability to tune the displacement field across the topological film. Here, using nanopatterned gates, we demonstrate a tunable displacement field in a heterostructure of the two-dimensional topological insulator cadmium arsenide. Transport studies in magnetic fields reveal an extreme sensitivity of the band inversion to SIA. We show that a relatively small displacement field (∼50 mV/nm) converts the crossing of the two zeroth Landau levels in magnetic field to an avoided crossing, signaling a change to trivial band order. This work demonstrates a universal methodology for tuning electronic states in topological thin films.

Emergent Inhomogeneity and Nonlocality in a Graphene Field-Effect Transistor on a Near-Parallel Moiré Superlattice of Transition Metal Dichalcogenides.

At near-parallel orientation, twisted bilayers of transition metal dichalcogenides exhibit interlayer charge transfer-driven out-of-plane ferroelectricity. Here, we report detailed electrical transport in a dual-gated graphene field-effect transistor placed on a 2.1° twisted bilayer WSe2. We observe hysteretic transfer characteristics and an emergent charge inhomogeneity with multiple local Dirac points evolving with an increasing electric displacement field (D). Concomitantly, we also observe a strong nonlocal voltage signal at D ∼ 0 V/nm that decreases rapidly with increasing D. A linear scaling of the nonlocal signal with longitudinal resistance suggests edge mode transport, which we attribute to the breaking of valley symmetry of graphene due to the spatially fluctuating electric field from the underlying polarized moiré domains. A quantitative analysis suggests the emergence of finite-size domains in graphene that modulate the charge and the valley currents simultaneously. This work underlines the impact of interfacial ferroelectricity that can trigger a new generation of devices.

Structural Complexities in Sodium Ion Conductive Antiperovskite Revealed by Cryogenic Transmission Electron Microscopy.

We use low-dose cryogenic transmission electron microscopy (cryo-TEM) to investigate the atomic-scale structure of antiperovskite Na2NH2BH4 crystals by preserving the room-temperature cubic phase and carefully monitoring the electron dose. Via quantitative analysis of electron beam damage using selected area electron diffraction, we find cryogenic imaging provides 6-fold improvement in beam stability for this solid electrolyte. Cryo-TEM images obtained from flat crystals revealed the presence of a new, long-range-ordered supercell with a cubic phase. The supercell exhibits doubled unit cell dimensions of 9.4 Å × 9.4 Å as compared to the cubic lattice structure revealed by X-ray crystallography of 4.7 Å × 4.7 Å. The comparison between the experimental image and simulated potential map indicates the origin of the supercell is a vacancy ordering of sodium atoms. This work demonstrates the potential of using cryo-TEM imaging to study the atomic-scale structure of air- and electron-beam-sensitive antiperovskite-type solid electrolytes.

Engineering the Band Topology in a Rhombohedral Trilayer Graphene Moiré Superlattice.

Moiré superlattices have become a fertile playground for topological Chern insulators, where the displacement field can tune the quantum geometry and Chern number of the topological band. However, in experiments, displacement field engineering of spontaneous symmetry-breaking Chern bands has not been demonstrated. Here in a rhombohedral trilayer graphene moiré superlattice, we use a thermodynamic probe and transport measurement to monitor the Chern number evolution as a function of the displacement field. At a quarter filling of the moiré band, a novel Chern number of three is unveiled to compete with the well-established number of two upon turning on the electric field and survives when the displacement field is sufficiently strong. The transition can be reconciled by a nematic instability on the Fermi surface due to the pseudomagnetic vector field potentials associated with moiré strain patterns. Our work opens more opportunities to active control of Chern numbers in van der Waals moiré systems.

Chern Insulator States with Tunable Chern Numbers in a Graphene Moiré Superlattice.

Moiré superlattices, constituted by two-dimensional materials, demonstrate a variety of strongly correlated and topological phenomena including correlated insulators, superconductivity, and integer/fractional Chern insulators. In the realm of topological nontrivial Chern insulators within specific moiré superlattices, previous studies usually observe a single Chern number at a given filling factor in a device. Here we present the observation of gate-tunable Chern numbers within the Chern insulator state of an ABC-stacked trilayer graphene/hexagonal boron nitride moiré superlattice device. Near quarter filling, the moiré superlattice exhibits spontaneous valley polarization and distinct ferromagnetism associated with the Chern insulator states over a range of the displacement field. Surprisingly we find a transition of the Chern number from C = 3 to 4 as the displacement field is increased. Our observation of gate-tunable correlated Chern insulators suggests new ways to control and manipulate topological states in a moiré superlattice device.

Experimental Demonstration of High-Efficiency Harmonic Generation in Photonic Moiré Superlattice Microcavities.

Integrated photonic microcavities have demonstrated powerful enhancement of nonlinear effects, but they face a challenge in achieving critical coupling for sufficient use of incident pump power. In this work, we first experimentally demonstrate that highly efficient third-harmonic generation (THG) and detectable second-harmonic generation (SHG) can be produced from high-Q photonic moiré superlattice microcavities, where a critical coupling condition can be achieved via selecting a magic angle. Furthermore, at the magic angle of 13.17°, critical coupling is satisfied, resulting in a normalized THG conversion efficiency of 136%/W2 at a relatively low peak pump power of 6.8 MW/cm2, which is 3 orders of magnitude higher than the best results reported previously. Our work shows the power of photonic moiré superlattices in enhancing nonlinear optical performances through flexible and feasible engineering resonant modes, which can be applied in integrated frequency conversion and generation of quantum light sources.

Kagome Quantum Oscillations in Graphene Superlattices.

Electronic spectra of solids subjected to a magnetic field are often discussed in terms of Landau levels and Hofstadter-butterfly-style Brown-Zak minibands manifested by magneto-oscillations in two-dimensional electron systems. Here, we present the semiclassical precursors of these quantum magneto-oscillations which appear in graphene superlattices at low magnetic field near the Lifshitz transitions and persist at elevated temperatures. These oscillations originate from Aharonov-Bohm interference of electron waves following open trajectories that belong to a kagome-shaped network of paths characteristic for Lifshitz transitions in the moire superlattice minibands of twistronic graphenes.

Controlling Umklapp Scattering in a Bilayer Graphene Moiré Superlattice.

We present experimental findings on electron-electron scattering in two-dimensional moiré heterostructures with a tunable Fermi wave vector, reciprocal lattice vector, and band gap. We achieve this in high-mobility aligned heterostructures of bilayer graphene (BLG) and hBN. Around the half-full point, the primary contribution to the resistance of these devices arises from Umklapp electron-electron (Uee) scattering, making the resistance of graphene/hBN moiré devices significantly larger than that of non-aligned devices (where Uee is forbidden). We find that the strength of Uee scattering follows a universal scaling with Fermi energy and is nonmonotonically dependent on the superlattice period. The Uee scattering can be tuned with the electric field and is affected by layer polarization of BLG. It has a strong particle-hole asymmetry; the resistance when the chemical potential is in the conduction band is significantly lower than when it is in the valence band, making the electron-doped regime more practical for potential applications.