Composite super-moiré lattices in double-aligned graphene heterostructures

Correlated Charge Density Wave Insulators in Chirally Twisted Triple Bilayer Graphene

Electrons residing in a flat-band system can play a vital role in triggering spectacular phenomenology due to relatively large interactions and spontaneous breaking of different degeneracies. In this work, we demonstrate chirally twisted triple bilayer graphene, a new moiré structure formed by three pieces of helically stacked Bernal bilayer graphene, as a highly tunable flat-band system. In addition to the correlated insulators showing at integer moiré fillings, commonly attributed to interaction induced symmetry broken isospin flavors in graphene, we observe abundant insulating states at half-integer moiré fillings, suggesting a longer-range interaction and the formation of charge density wave insulators which spontaneously break the moiré translation symmetry. With weak out-of-plane magnetic field applied, as observed half-integer filling states are enhanced and more quarter-integer filling states appear, pointing toward further quadrupling moiré unit cells. The insulating states at fractional fillings combined with Hartree-Fock calculations demonstrate the observation of a new type of correlated charge density wave insulators in graphene and points to a new accessible twist manner engineering correlated moiré electronics.

High-Mobility Compensated Semimetals, Orbital Magnetization, and Umklapp Scattering in Bilayer Graphene Moiré Superlattices

Twist-controlled moiré superlattices (MSs) have emerged as a versatile platform for realizing artificial systems with complex electronic spectra. The combination of Bernal-stacked bilayer graphene (BLG) and hexagonal boron nitride (hBN) can give rise to an interesting MS, which has recently featured a set of unexpected behaviors, such as unconventional ferroelectricity and the electronic ratchet effect. Yet, the understanding of the electronic properties of BLG/hBN MS has, at present, remained fairly limited. Here, we combine magneto-transport and low-energy sub-THz excitation to gain insights into the properties of this MS. We demonstrate that the alignment between BLG and hBN crystal lattices results in the emergence of compensated semimetals at some integer fillings of the moiré bands, separated by van Hove singularities where the Lifshitz transition occurs. A particularly pronounced semimetal develops when eight holes reside in the moiré unit cell, where coexisting high-mobility electron and hole systems feature strong magnetoresistance reaching 2350% already at B = 0.25 T. Next, by measuring the THz-driven Nernst effect in remote bands, we observe valley splitting, indicating an orbital magnetization characterized by a strongly enhanced effective gv-factor of 340. Finally, using THz photoresistance measurements, we show that the high-temperature conductivity of the BLG/hBN MS is limited by electron-electron umklapp processes. Our multifaceted analysis introduces THz-driven magnetotransport as a convenient tool to probe the band structure and interaction effects in van der Waals materials and provides a comprehensive understanding of the BLG/hBN MS.

Topological Flat Bands in Graphene Super-Moiré Lattices

Moiré-pattern-based potential engineering has become an important way to explore exotic physics in a variety of two-dimensional condensed matter systems. While these potentials have induced correlated phenomena in almost all commonly studied 2D materials, monolayer graphene has remained an exception. We demonstrate theoretically that a single layer of graphene, when placed between two bulk boron nitride crystal substrates with the appropriate twist angles, can support a robust topological ultraflat band emerging as the second hole band. This is one of the simplest platforms to design and exploit topological flat bands.

Layer-polarized ferromagnetism in rhombohedral multilayer graphene

Flat-band systems with strongly correlated electrons can exhibit a variety of phenomena, such as correlated insulating and topological states, unconventional superconductivity, and ferromagnetism. Rhombohedral multilayer graphene has recently emerged as a promising platform for investigating exotic quantum states due to its hosting of topologically protected surface flat bands at low energy, which have a layer-dependent energy dispersion. However, the complex relationship between the surface flat bands and the highly dispersive high-energy bands makes it difficult to study correlated surface states. In this study, we introduce moiré superlattices as a method to isolate the surface flat bands of rhombohedral multilayer graphene. The observed pronounced screening effects in the moiré potential-modulated rhombohedral multilayer graphene indicate that the two surface states are electronically decoupled. The flat bands that are isolated promote correlated surface states in areas that are distant from the charge neutrality points. Notably, we observe tunable layer-polarized ferromagnetism, which is evidenced by a hysteretic anomalous Hall effect. This is achieved by polarizing the surface states with finite displacement fields.

Higher order gaps in the renormalized band structure of doubly aligned hBN/bilayer graphene moiré superlattice

This paper presents our findings on the recursive band gap engineering of chiral fermions in bilayer graphene doubly aligned with hBN. Using two interfering moiré potentials, we generate a supermoiré pattern that renormalizes the electronic bands of the pristine bilayer graphene, resulting in higher order fractal gaps even at very low energies. These Bragg gaps can be mapped using a unique linear combination of periodic areas within the system. To validate our findings, we use electronic transport measurements to identify the position of these gaps as a function of the carrier density. We establish their agreement with the predicted carrier densities and corresponding quantum numbers obtained using the continuum model. Our study provides strong evidence of the quantization of the momentum-space area of quasi-Brillouin zones in a minimally incommensurate lattice. It fills important gaps in the understanding of band structure engineering of Dirac fermions with a doubly periodic superlattice spinor potential.

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.

Electrostatic moiré potential from twisted hexagonal boron nitride layers

Moiré superlattices host a rich variety of correlated electronic phases. However, the moiré potential is fixed by interlayer coupling, and it is dependent on the nature of carriers and valleys. In contrast, it has been predicted that twisted hexagonal boron nitride (hBN) layers can impose a periodic electrostatic potential capable of engineering the properties of adjacent functional layers. Here, we show that this potential is described by a theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. This enables controllability of the potential depth and profile by controlling the twist angles between the two interfaces. Employing this approach, we further demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in semiconductor monolayers, suggesting opportunities for engineering the properties of adjacent functional layers using the surface potential of a twisted hBN substrate.

Toward Edge Engineering of Two-Dimensional Layered Transition-Metal Dichalcogenides by Chemical Vapor Deposition

The manipulation of edge configurations and structures in atomically-thin transition metal dichalcogenides (TMDs) for versatile functionalization has attracted intensive interest in recent years. The chemical vapor deposition (CVD) approach has shown promise for TMD edge engineering of atomic edge configurations (1H, 1T or 1T'-zigzag or armchair edges) as well as diverse edge morphologies (1D nanoribbons, 2D dendrites, 3D spirals, etc.). These edge-rich TMD layers offer versatile candidates for probing the physical and chemical properties and exploring potential applications in electronics, optoelectronics, catalysis, sensing, and quantum technologies. In this Review, we present an overview of the current state-of-the-art in the manipulation of TMD atomic edges and edge-rich structures using CVD. We highlight the vast range of distinct properties associated with these edge configurations and structures and provide insights into the opportunities afforded by such edge-functionalized crystals. The objective of this Review is to motivate further research and development efforts to use CVD as a scalable approach to harness the benefits of such crystal-edge engineering.

Superconductivity and strong interactions in a tunable moiré quasicrystal

Electronic states in quasicrystals generally preclude a Bloch description1, rendering them fascinating and enigmatic. Owing to their complexity and scarcity, quasicrystals are underexplored relative to periodic and amorphous structures. Here we introduce a new type of highly tunable quasicrystal easily assembled from periodic components. By twisting three layers of graphene with two different twist angles, we form two mutually incommensurate moiré patterns. In contrast to many common atomic-scale quasicrystals2,3, the quasiperiodicity in our system is defined on moiré length scales of several nanometres. This 'moiré quasicrystal' allows us to tune the chemical potential and thus the electronic system between a periodic-like regime at low energies and a strongly quasiperiodic regime at higher energies, the latter hosting a large density of weakly dispersing states. Notably, in the quasiperiodic regime, we observe superconductivity near a flavour-symmetry-breaking phase transition4,5, the latter indicative of the important role that electronic interactions play in that regime. The prevalence of interacting phenomena in future systems with in situ tunability is not only useful for the study of quasiperiodic systems but may also provide insights into electronic ordering in related periodic moiré crystals6-12. We anticipate that extending this platform to engineer quasicrystals by varying the number of layers and twist angles, and by using different two-dimensional components, will lead to a new family of quantum materials to investigate the properties of strongly interacting quasicrystals.

Controlled alignment of supermoiré lattice in double-aligned graphene heterostructures

The supermoiré lattice, built by stacking two moiré patterns, provides a platform for creating flat mini-bands and studying electron correlations. An ultimate challenge in assembling a graphene supermoiré lattice is in the deterministic control of its rotational alignment, which is made highly aleatory due to the random nature of the edge chirality and crystal symmetry. Employing the so-called "golden rule of three", here we present an experimental strategy to overcome this challenge and realize the controlled alignment of double-aligned hBN/graphene/hBN supermoiré lattice, where the twist angles between graphene and top/bottom hBN are both close to zero. Remarkably, we find that the crystallographic edge of neighboring graphite can be used to better guide the stacking alignment, as demonstrated by the controlled production of 20 moiré samples with an accuracy better than ~ 0.2°. Finally, we extend our technique to low-angle twisted bilayer graphene and ABC-stacked trilayer graphene, providing a strategy for flat-band engineering in these moiré materials.

Interlayer Electron-Hole Friction in Tunable Twisted Bilayer Graphene Semimetal

Charge-neutral conducting systems represent a class of materials with unusual properties governed by electron-hole (e-h) interactions. Depending on the quasiparticle statistics, band structure, and device geometry these semimetallic phases of matter can feature unconventional responses to external fields that often defy simple interpretations in terms of single-particle physics. Here we show that small-angle twisted bilayer graphene (SA TBG) offers a highly tunable system in which to explore interactions-limited electron conduction. By employing a dual-gated device architecture we tune our devices from a nondegenerate charge-neutral Dirac fluid to a compensated two-component e-h Fermi liquid where spatially separated electrons and holes experience strong mutual friction. This friction is revealed through the T^{2} resistivity that accurately follows the e-h drag theory we develop. Our results provide a textbook illustration of a smooth transition between different interaction-limited transport regimes and clarify the conduction mechanisms in charge-neutral SA TBG.

2+δ-Dimensional Materials via Atomistic Z-Welding

Pivotal to functional van der Waals stacked flexible electronic/excitonic/spintronic/thermoelectric chips is the synergy amongst constituent layers. However; the current techniques viz. sequential chemical vapor deposition, micromechanical/wet-chemical transfer are mostly limited due to diffused interfaces, and metallic remnants/bubbles at the interface. Inter-layer-coupled 2+δ-dimensional materials, as a new class of materials can be significantly suitable for out-of-plane carrier transport and hence prompt response in prospective devices. Here, the discovery of the use of exotic electric field ≈10⁶  V cm^{- 1} (at microwave hot-spot) and 2 thermomechanical conditions i.e. pressure ≈1 MPa, T ≈ 200 °C (during solvothermal reaction) to realize 2+δ-dimensional materials is reported. It is found that P_z P_z chemical bonds form between the component layers, e.g., CB and CN in G-BN, MoN and MoB in MoS₂ -BN hybrid systems as revealed by X-ray photoelectron spectroscopy. New vibrational peaks in Raman spectra (BC ≈1320 cm^-1 for the G-BN system and MoB ≈365 cm^-1 for the MoS₂ -BN system) are recorded. Tunable mid-gap formation, along with diodic behavior (knee voltage ≈0.7 V, breakdown voltage ≈1.8 V) in the reduced graphene oxide-reduced BN oxide (RGO-RBNO) hybrid system is also observed. Band-gap tuning in MoS₂ -BN system is observed. Simulations reveal stacking-dependent interfacial charge/potential drops, hinting at the feasibility of next-generation functional devices/sensors.

Research progress of ferroptosis in glaucoma and optic nerve damage

Unlike other death forms, such as autophagy, necrosis, and apoptosis, ferroptosis is a novel type of programmed cell death with iron-dependent properties. Esteroxygenase affects the content of unsaturated fatty acids and promotes lipid peroxidation. In addition, GSH can cause the reduction of GPX4, which can cause ferroptosis. P53 and its signaling pathways also regulate ferroptosis. Recent studies have confirmed that ferroptosis also promotes the death of RGC. The progressive loss of RGC is one of the pathological features of glaucoma, indicating that ferroptosis may be related to the onset of glaucoma. Down-regulation of GPX4 leads to the loss of nerve cells, which suggests that ferroptosis may also be related to diseases related to optic nerve damage. At present, ferroptosis has been extensively researched and advanced in systemic diseases, such as cardiovascular diseases, gastrointestinal tumors such as stomach, liver, and pancreas, and brain diseases. This review focuses on the research progress of ferroptosis in ophthalmic diseases, especially glaucoma and optic nerve damage.

Strain Quantum Sensing with Spin Defects in Hexagonal Boron Nitride

Hexagonal boron nitride is not only a promising functional material for the development of two-dimensional optoelectronic devices but also a good candidate for quantum sensing thanks to the presence of quantum emitters in the form of atom-like defects. Their exploitation in quantum technologies necessitates understanding their coherence properties as well as their sensitivity to external stimuli. In this work, we probe the strain configuration of boron vacancy centers (VB^-) created by ion implantation in h-BN flakes thanks to wide-field spatially resolved optically detected magnetic resonance and submicro Raman spectroscopy. Our experiments demonstrate the ability of VB^- for quantum sensing of strain and, given the omnipresence of h-BN in 2D-based devices, open the door for in situ imaging of strain under working conditions.

Nano-engineering and nano-manufacturing in 2D materials: marvels of nanotechnology

Two-dimensional materials have attracted significant interest and investigation since the marvellous discovery of graphene. Due to their unique physical, mechanical and optical properties, van der Waals (vdW) materials possess extraordinary potential for application in future optoelectronics devices. Nano-engineering and nano-manufacturing in the atomically thin regime has further opened multifarious avenues to explore novel physical properties. Among them, moiré heterostructures, strain engineering and substrate manipulation have created numerous exotic and topological phenomena such as unconventional superconductivity, orbital magnetism, flexible nanoelectronics and highly efficient photovoltaics. This review comprehensively summarizes the three most influential techniques of nano-engineering in 2D materials. The latest development in the marvels of moiré structures in vdW materials is discussed; in addition, topological structures in layered materials and substrate engineering on the nanoscale are thoroughly scrutinized to highlight their significance in micro- and nano-devices. Finally, we conclude with remarks on challenges and possible future directions in the rapidly expanding field of nanotechnology and nanomaterial.

Moiré-Induced Transport in CVD-Based Small-Angle Twisted Bilayer Graphene

To realize the applicative potential of 2D twistronic devices, scalable synthesis and assembly techniques need to meet stringent requirements in terms of interface cleanness and twist-angle homogeneity. Here, we show that small-angle twisted bilayer graphene assembled from separated CVD-grown graphene single-crystals can ensure high-quality transport properties, determined by a device-scale-uniform moiré potential. Via low-temperature dual-gated magnetotransport, we demonstrate the hallmarks of a 2.4°-twisted superlattice, including tunable regimes of interlayer coupling, reduced Fermi velocity, large interlayer capacitance, and density-independent Brown-Zak oscillations. The observation of these moiré-induced electrical transport features establishes CVD-based twisted bilayer graphene as an alternative to "tear-and-stack" exfoliated flakes for fundamental studies, while serving as a proof-of-concept for future large-scale assembly.

Simple low-cost 3D metal printing via plastic skeleton burning

Additive manufacturing of complex volumetric structures opened new frontiers in many technological fields, turning previously inconceivable designs into a practical reality. Electromagnetic components, including antenna and waveguiding elements, can benefit from exploring the third dimension. While fused deposition modeling (FDM) polymer printers become widely accessible, they manufacture structures with moderately low electromagnetic permittivities, compared to metals. However, metal 3D printers, being capable of producing complex volumetric constructions, remain extremely expensive and hard to maintain apparatus, suitable for high-end market applications. Here we develop a new metal printing technique, based on a low-cost and simple FDM device and subsequent electrochemical deposition. For testing the new method, we fabricated several antenna devices and compared their performances to standard printed FeCl₃ etched board-based counterparts, demonstrating clear advantages of the new technique. Our new metal printing can be applied to manufacture electromagnetic devices as well as metallic structures for other applications.

2D Heterostructures for Ubiquitous Electronics and Optoelectronics: Principles, Opportunities, and Challenges

A grand family of two-dimensional (2D) materials and their heterostructures have been discovered through the extensive experimental and theoretical efforts of chemists, material scientists, physicists, and technologists. These pioneering works contribute to realizing the fundamental platforms to explore and analyze new physical/chemical properties and technological phenomena at the micro-nano-pico scales. Engineering 2D van der Waals (vdW) materials and their heterostructures via chemical and physical methods with a suitable choice of stacking order, thickness, and interlayer interactions enable exotic carrier dynamics, showing potential in high-frequency electronics, broadband optoelectronics, low-power neuromorphic computing, and ubiquitous electronics. This comprehensive review addresses recent advances in terms of representative 2D materials, the general fabrication methods, and characterization techniques and the vital role of the physical parameters affecting the quality of 2D heterostructures. The main emphasis is on 2D heterostructures and 3D-bulk (3D) hybrid systems exhibiting intrinsic quantum mechanical responses in the optical, valley, and topological states. Finally, we discuss the universality of 2D heterostructures with representative applications and trends for future electronics and optoelectronics (FEO) under the challenges and opportunities from physical, nanotechnological, and material synthesis perspectives.

Science of 2.5 dimensional materials: paradigm shift of materials science toward future social innovation

The past decades of materials science discoveries are the basis of our present society - from the foundation of semiconductor devices to the recent development of internet of things (IoT) technologies. These materials science developments have depended mainly on control of rigid chemical bonds, such as covalent and ionic bonds, in organic molecules and polymers, inorganic crystals and thin films. The recent discovery of graphene and other two-dimensional (2D) materials offers a novel approach to synthesizing materials by controlling their weak out-of-plane van der Waals (vdW) interactions. Artificial stacks of different types of 2D materials are a novel concept in materials synthesis, with the stacks not limited by rigid chemical bonds nor by lattice constants. This offers plenty of opportunities to explore new physics, chemistry, and engineering. An often-overlooked characteristic of vdW stacks is the well-defined 2D nanospace between the layers, which provides unique physical phenomena and a rich field for synthesis of novel materials. Applying the science of intercalation compounds to 2D materials provides new insights and expectations about the use of the vdW nanospace. We call this nascent field of science '2.5 dimensional (2.5D) materials,' to acknowledge the important extra degree of freedom beyond 2D materials. 2.5D materials not only offer a new field of scientific research, but also contribute to the development of practical applications, and will lead to future social innovation. In this paper, we introduce the new scientific concept of this science of '2.5D materials' and review recent research developments based on this new scientific concept.

Developing Graphene-Based Moiré Heterostructures for Twistronics

Graphene-based moiré heterostructures are strongly correlated materials, and they are considered to be an effective platform to investigate the challenges of condensed matter physics. This is due to the distinct electronic properties that are unique to moiré superlattices and peculiar band structures. The increasing research on strongly correlated physics via graphene-based moiré heterostructures, especially unconventional superconductors, greatly promotes the development of condensed matter physics. Herein, the preparation methods of graphene-based moiré heterostructures on both in situ growth and assembling monolayer 2D materials are discussed. Methods to improve the quality of graphene and optimize the transfer process are presented to mitigate the limitations of low-quality graphene and damage caused by the transfer process during the fabrication of graphene-based moiré heterostructures. Then, the topological properties in various graphene-based moiré heterostructures are reviewed. Furthermore, recent advances regarding the factors that influence physical performances via a changing twist angle, the exertion of strain, and regulation of the dielectric environment are presented. Moreover, various unique physical properties in graphene-based moiré heterostructures are demonstrated. Finally, the challenges faced during the preparation and characterization of graphene-based moiré heterostructures are discussed. An outlook for the further development of moiré heterostructures is also presented.

Correlated states in doubly-aligned hBN/graphene/hBN heterostructures

Interfacial moiré superlattices in van der Waals vertical assemblies effectively reconstruct the crystal symmetry, leading to opportunities for investigating exotic quantum states. Notably, a two-dimensional nanosheet has top and bottom open surfaces, allowing the specific case of doubly aligned super-moiré lattice to serve as a toy model for studying the tunable lattice symmetry and the complexity of related electronic structures. Here, we show that by doubly aligning a graphene monolayer to both top and bottom encapsulating hexagonal boron nitride (h-BN), multiple conductivity minima are observed away from the main Dirac point, which are sensitively tunable with respect to the small twist angles. Moreover, our experimental evidences together with theoretical calculations suggest correlated insulating states at integer fillings of -5, -6, -7 electrons per moiré unit cell, possibly due to inter-valley coherence. Our results provide a way to construct intriguing correlations in 2D electronic systems in the weak interaction regime.

Strain Engineering of Low-Dimensional Materials for Emerging Quantum Phenomena and Functionalities

Recent discoveries of exotic physical phenomena, such as unconventional superconductivity in magic-angle twisted bilayer graphene, dissipationless Dirac fermions in topological insulators, and quantum spin liquids, have triggered tremendous interest in quantum materials. The macroscopic revelation of quantum mechanical effects in quantum materials is associated with strong electron-electron correlations in the lattice, particularly where materials have reduced dimensionality. Owing to the strong correlations and confined geometry, altering atomic spacing and crystal symmetry via strain has emerged as an effective and versatile pathway for perturbing the subtle equilibrium of quantum states. This review highlights recent advances in strain-tunable quantum phenomena and functionalities, with particular focus on low-dimensional quantum materials. Experimental strategies for strain engineering are first discussed in terms of heterogeneity and elastic reconfigurability of strain distribution. The nontrivial quantum properties of several strain-quantum coupled platforms, including 2D van der Waals materials and heterostructures, topological insulators, superconducting oxides, and metal halide perovskites, are next outlined, with current challenges and future opportunities in quantum straintronics followed. Overall, strain engineering of quantum phenomena and functionalities is a rich field for fundamental research of many-body interactions and holds substantial promise for next-generation electronics capable of ultrafast, dissipationless, and secure information processing and communications.

Correlated Insulating States and Transport Signature of Superconductivity in Twisted Trilayer Graphene Superlattices

Layers of two-dimensional materials stacked with a small twist angle give rise to beating periodic patterns on a scale much larger than the original lattice, referred to as a "moiré superlattice." Here, we demonstrate a higher-order "moiré of moiré" superlattice in twisted trilayer graphene with two consecutive small twist angles. We report correlated insulating states near the half filling of the moiré of moiré superlattice at an extremely low carrier density (∼10^{10}  cm^{-2}), near which we also report a zero-resistance transport behavior typically expected in a 2D superconductor. The full-occupancy (ν=-4 and ν=4) states are semimetallic and gapless, distinct from the twisted bilayer systems.

Parity-Dependent Moiré Superlattices in Graphene/h-BN Heterostructures: A Route to Mechanomutable Metamaterials

The superlattice of alternating graphene/h-BN few-layered heterostructures is found to exhibit strong dependence on the parity of the number of layers within the stack. Odd-parity systems show a unique flamingolike pattern, whereas their even-parity counterparts exhibit regular hexagonal or rectangular superlattices. When the alternating stack consists of 7 layers or more, the flamingo pattern becomes favorable, regardless of parity. Notably, the out-of-plane corrugation of the system strongly depends on the shape of the superstructure resulting in significant parity dependence of its mechanical properties. The predicted phenomenon originates in an intricate competition between moiré patterns developing at the interface of consecutive layers. This mechanism is of general nature and is expected to occur in other alternating stacks of closely matched rigid layered materials as demonstrated for homogeneous alternating junctions of twisted graphene and h-BN. Our findings thus allow for the rational design of mechanomutable metamaterials based on van der Waals heterostructures.

Imaging Dual-Moiré Lattices in Twisted Bilayer Graphene Aligned on Hexagonal Boron Nitride Using Microwave Impedance Microscopy

Moiré superlattices (MSLs) formed in van der Waals materials have become a promising platform to realize novel two-dimensional electronic states. Angle-aligned trilayer structures can form two sets of MSLs which could potentially interfere. In this work, we directly image the moiré patterns in both monolayer and twisted bilayer graphene aligned on hexagonal boron nitride (hBN), using combined scanning microwave impedance microscopy and conductive atomic force microscopy. Correlation of the two techniques reveals the contrast mechanism for the achieved ultrahigh spatial resolution (<2 nm). We observe two sets of MSLs with different periodicities in the trilayer stack. The smaller MSL breaks the 6-fold rotational symmetry and exhibits abrupt discontinuities at the boundaries of the larger MSL. Using a rigid atomic-stacking model, we demonstrate that the hBN layer considerably modifies the MSL of twisted bilayer graphene. We further analyze its effect on the reciprocal space spectrum of the dual-moiré system.

Moiré Patterns in 2D Materials: A Review

Quantum materials have attracted much attention in recent years due to their exotic and incredible properties. Among them, van der Waals materials stand out due to their weak interlayer coupling, providing easy access to manipulating electrical and optical properties. Many fascinating electrical, optical, and magnetic properties have been reported in the moiré superlattices, such as unconventional superconductivity, photonic dispersion engineering, and ferromagnetism. In this review, we summarize the methods to prepare moiré superlattices in the van der Waals materials and focus on the current discoveries of moiré pattern-modified electrical properties, recent findings of atomic reconstruction, as well as some possible future directions in this field.

Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride

When two-dimensional crystals are brought into close proximity, their interaction results in reconstruction of electronic spectrum and crystal structure. Such reconstruction strongly depends on the twist angle between the crystals, which has received growing attention due to interesting electronic and optical properties that arise in graphene and transitional metal dichalcogenides. Here we study two insulating crystals of hexagonal boron nitride stacked at small twist angle. Using electrostatic force microscopy, we observe ferroelectric-like domains arranged in triangular superlattices with a large surface potential. The observation is attributed to interfacial elastic deformations that result in out-of-plane dipoles formed by pairs of boron and nitrogen atoms belonging to opposite interfacial surfaces. This creates a bilayer-thick ferroelectric with oppositely polarized (BN and NB) dipoles in neighbouring domains, in agreement with our modeling. These findings open up possibilities for designing van der Waals heterostructures and offer an alternative probe to study moiré-superlattice electrostatic potentials.

Ultrahigh-resolution scanning microwave impedance microscopy of moiré lattices and superstructures

Two-dimensional heterostructures composed of layers with slightly different lattice vectors exhibit new periodic structure known as moiré lattices, which, in turn, can support novel correlated and topological phenomena. Moreover, moiré superstructures can emerge from multiple misaligned moiré lattices or inhomogeneous strain distributions, offering additional degrees of freedom in tailoring electronic structure. High-resolution imaging of the moiré lattices and superstructures is critical for understanding the emerging physics. Here, we report the imaging of moiré lattices and superstructures in graphene-based samples under ambient conditions using an ultrahigh-resolution implementation of scanning microwave impedance microscopy. Although the probe tip has a gross radius of ~100 nm, spatial resolution better than 5 nm is achieved, which allows direct visualization of the structural details in moiré lattices and the composite super-moiré. We also demonstrate artificial synthesis of novel superstructures, including the Kagome moiré arising from the interplay between different layers.

In situ manipulation of van der Waals heterostructures for twistronics

In van der Waals heterostructures, electronic bands of two-dimensional (2D) materials, their nontrivial topology, and electron-electron interactions can be markedly changed by a moiré pattern induced by twist angles between different layers. This process is referred to as twistronics, where the tuning of twist angle can be realized through mechanical manipulation of 2D materials. Here, we demonstrate an experimental technique that can achieve in situ dynamical rotation and manipulation of 2D materials in van der Waals heterostructures. Using this technique, we fabricated heterostructures where graphene is perfectly aligned with both top and bottom encapsulating layers of hexagonal boron nitride. Our technique enables twisted 2D material systems in one single stack with dynamically tunable optical, mechanical, and electronic properties.

Long-range ballistic transport of Brown-Zak fermions in graphene superlattices

In quantizing magnetic fields, graphene superlattices exhibit a complex fractal spectrum often referred to as the Hofstadter butterfly. It can be viewed as a collection of Landau levels that arise from quantization of Brown-Zak minibands recurring at rational (p/q) fractions of the magnetic flux quantum per superlattice unit cell. Here we show that, in graphene-on-boron-nitride superlattices, Brown-Zak fermions can exhibit mobilities above 10⁶ cm² V⁻¹ s⁻¹ and the mean free path exceeding several micrometers. The exceptional quality of our devices allows us to show that Brown-Zak minibands are 4q times degenerate and all the degeneracies (spin, valley and mini-valley) can be lifted by exchange interactions below 1 K. We also found negative bend resistance at 1/q fractions for electrical probes placed as far as several micrometers apart. The latter observation highlights the fact that Brown-Zak fermions are Bloch quasiparticles propagating in high fields along straight trajectories, just like electrons in zero field.

Here, the authors show that Brown-Zak fermions in graphene-on-boron-nitride superlattices exhibit mobilities above 10⁶ cm²/V s and micrometer scale ballistic transport.

Heteromoiré Engineering on Magnetic Bloch Transport in Twisted Graphene Superlattices

Localized electrons subject to applied magnetic fields can restart to propagate freely through the lattice in delocalized magnetic Bloch states (MBSs) when the lattice periodicity is commensurate with the magnetic length. Twisted graphene superlattices with moiré wavelength tunability enable experimental access to the unique delocalization in a controllable fashion. Here, we report the observation and characterization of high-temperature Brown-Zak (BZ) oscillations which come in two types, 1/B and B periodicity, originating from the generation of integer and fractional MBSs, in the twisted bilayer and trilayer graphene superlattices, respectively. Coexisting periodic-in-1/B oscillations assigned to different moiré wavelengths are dramatically observed in small-angle twisted bilayer graphene, which may arise from angle-disorder-induced in-plane heteromoiré superlattices. Moreover, the vertical stacking of heteromoiré supercells in double-twisted trilayer graphene results in a mega-sized superlattice. The exotic superlattice contributes to the periodic-in-B oscillation and dominates the magnetic Bloch transport.

Cyclotron Resonance Study of Monolayer Graphene under Double Moiré Potentials

We report the first cyclotron resonance study of monolayer graphene under double-moiré potentials in which the crystal axis of graphene is nearly aligned to those of both the top and bottom hexagonal boron nitride (h-BN) layers. Under mid-infrared light irradiation, we observe cyclotron resonance absorption with the following unique features: (1) cyclotron resonance magnetic field B_CR is entirely different from that of nonaligned monolayer graphene, (2) B_CR exhibits strong electron-hole asymmetry, and (3) splitting of B_CR is observed for |ν| < 1, with the split maximum at |ν| = 1, resulting in eyeglass-shaped trajectories. These features are well explained by considering the large bandgap induced by the double moiré potentials, the electron-hole asymmetry in the Fermi velocity, and the Fermi-level-dependent enhancement of spin gaps, which suggests a large electron-electron correlation contribution in this system.

Proximity Spin-Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI3

The recently discovered two-dimensional magnetic insulator CrI₃ is an intriguing case for basic research and spintronic applications since it is a ferromagnet in the bulk but an antiferromagnet in bilayer form, with its magnetic ordering amenable to external manipulations. Using the first-principles quantum transport approach, we predict that injecting unpolarized charge current parallel to the interface of the bilayer-CrI₃/monolayer-TaSe₂ van der Waals (vdW) heterostructure will induce spin-orbit torque and thereby drive the dynamics of magnetization on the first monolayer of CrI₃ in direct contact with TaSe₂. By combining the calculated complex angular dependence of spin-orbit torque with the Landau-Lifshitz-Gilbert equation for classical dynamics of magnetization, we demonstrate that current pulses can switch the direction of magnetization on the first monolayer to become parallel to that of the second monolayer, thereby converting CrI₃ from antiferromagnet to ferromagnet while not requiring any external magnetic field. We explain the mechanism of this reversible current-driven nonequilibrium phase transition by showing that first monolayer of CrI₃ carries current due to evanescent wave functions injected by metallic transition metal dichalcogenide TaSe₂, while concurrently acquiring strong spin-orbit coupling via such a proximity effect, whereas the second monolayer of CrI₃ remains insulating. The transition can be detected by passing vertical read current through the vdW heterostructure, encapsulated by a bilayer of hexagonal boron nitride and sandwiched between graphite electrodes, where we find a tunneling magnetoresistance of ≃240%.

Double Moiré with a Twist: Supermoiré in Encapsulated Graphene

A periodic spatial modulation, as created by a moiré pattern, has been extensively studied with the view to engineer and tune the properties of graphene. Graphene encapsulated by hexagonal boron nitride (hBN) when slightly misaligned with the top and bottom hBN layers experiences two interfering moiré patterns, resulting in a so-called supermoiré (SM). This leads to a lattice and electronic spectrum reconstruction. A geometrical construction of the nonrelaxed SM patterns allows us to indicate qualitatively the induced changes in the electronic properties and to locate the SM features in the density of states and in the conductivity. To emphasize the effect of lattice relaxation, we report band gaps at all Dirac-like points in the hole doped part of the reconstructed spectrum, which are expected to be enhanced when including interaction effects. Our result is able to distinguish effects due to lattice relaxation and due to the interfering SM and provides a clear picture on the origin of recently experimentally observed effects in such trilayer heterostuctures.