Interlayer Phonon Coupling and Enhanced Electron-Phonon Interactions in Doubly Aligned hBN/Graphene/hBN Heterostructures

Engineering the band structure via moiré superlattices plays a crucial role in tailoring the electronic and phononic spectra of hBN/graphene heterostructures, enabling a range of emergent properties. While moiré heterostructures have been extensively studied through transport measurements to investigate electronic spectra, their influence on the phononic spectrum, particularly on phonon-phonon and electron-phonon interactions, remains less explored. In this study, we examine the temperature-dependent (8 K-300 K) frequency and line width responses of the phonon near the K-point of graphene in hBN/graphene/hBN heterostructures for nonaligned, partially aligned, singly aligned, and doubly aligned configurations. The nonaligned samples, where the graphene is rotated by 30° with respect to both top and bottom hBN, exhibit pristine graphene behavior, characterized by minimal frequency variation with temperature and a typical line width increase with increasing temperature. In contrast, doubly aligned samples, where graphene and both hBN are perfectly aligned, display anomalous behavior, with the Raman frequency decreasing linearly and the lifetime increasing with increasing temperature. This anomalous anharmonic response could not be explained by the existing models considering only intralayer (within the graphene) phonon-phonon interactions, but rather indicates the role of strong interlayer phonon-phonon coupling (between hBN and graphene phonons), hitherto not observed. Furthermore, the enhanced electron-phonon interactions due to the resonant condition of phonon decay into electronic channels of doubly aligned hBN/graphene/hBN heterostructures explain the observed line width behavior. Our findings demonstrate the ability to engineer phonon-phonon and electron-phonon interactions through the precise alignment of hBN and graphene lattices, with implications for thermal management and carrier transport optimization in hBN/graphene/hBN heterostructures.

Synthesis of Highly Anisotropic 2D Insulator CrOCl Nanosheets for Interfacial Symmetry Breaking in Isotropic 2D Semiconductors

Chromium oxychloride (CrOCl), a van der Waals antiferromagnetic insulator, has attracted significant interest in 2D optoelectronic, ferromagnetic, and quantum devices. However, the bottom-up preparation of 2D CrOCl remains challenging, limiting its property exploration and device application. Herein, the controllable synthesis of 2D CrOCl crystals by chemical vapor deposition is demonstrated. The combination reaction of precursors together with the space-confined growth strategy, providing stable and stoichiometric growth conditions, enable a robust synthesis of high-crystallinity CrOCl nanosheets with regular rhombus-like morphology and uniform thickness. By tuning the growth temperature from 675 to 800 °C, the thickness of CrOCl nanosheets can be continuously modulated from 10.2 to 30.8 nm, with the domain size increasing from 16.9 to 25.5 µm. The as-grown CrOCl nanosheets exhibit significant structural/optical anisotropy, ultrahigh insulativity, and superior air stability. Furthermore, a MoS2/CrOCl heterostructure with single-mirror symmetry stacking and ultrastrong interfacial coupling is built to realize interfacial symmetry breaking, a novel interface phenomenon that converts MoS2 from isotropy to anisotropy. Consequently, the MoS2/CrOCl heterostructure device achieves polarization-sensitive photodetection and bulk photovoltaic effect, which are nonexistent in high-symmetry 2D materials. This work paves the way for the future exploration of CrOCl-based 2D physics and devices via symmetry engineering.

Moiré-driven topological electronic crystals in twisted graphene

In a dilute two-dimensional electron gas, Coulomb interactions can stabilize the formation of a Wigner crystal1-3. Although Wigner crystals are topologically trivial, it has been predicted that electrons in a partially filled band can break continuous translational symmetry and time-reversal symmetry spontaneously, resulting in a type of topological electron crystal known as an anomalous Hall crystal4-11. Here we report signatures of a generalized version of the anomalous Hall crystal in twisted bilayer-trilayer graphene, whose formation is driven by the moiré potential. The crystal forms at a band filling of one electron per four moiré unit cells (ν = 1/4) and quadruples the unit-cell area, coinciding with an integer quantum anomalous Hall effect. The Chern number of the state is exceptionally tunable, and it can be switched reversibly between +1 and -1 by electric and magnetic fields. Several other topological electronic crystals arise in a modest magnetic field, originating from ν = 1/3, 1/2, 2/3 and 3/2. The quantum geometry of the interaction-modified bands is likely to be very different from that of the original parent band, which enables possible future discoveries of correlation-driven topological phenomena.

Electronic ferroelectricity in monolayer graphene moiré superlattices

Extending ferroelectric materials to two-dimensional limit provides versatile applications for the development of next-generation nonvolatile devices. Conventional ferroelectricity requires materials consisting of at least two constituent elements associated with polar crystalline structures. Monolayer graphene as an elementary two-dimensional material unlikely exhibits ferroelectric order due to its highly centrosymmetric hexagonal lattices. Here, we report the observations of electronic ferroelectricity in monolayer graphene by introducing asymmetric moiré superlattice at the graphene/h-BN interface, in which the electric polarization stems from electron-hole dipoles. The polarization switching is probed through the measurements of itinerant Hall carrier density up to room temperature, manifesting as standard polarization-electric field hysteresis loops. We find ferroelectricity in graphene moiré systems exhibits generally similar characteristics in monolayer, bilayer, and trilayer graphene, which indicates layer polarization is not essential to observe the ferroelectricity. Furthermore, we demonstrate the applications of this ferroelectric moiré structures in multi-state nonvolatile data storage with high retention and the emulation of versatile synaptic behaviors. Our work not only provides insights into the fundamental understanding of ferroelectricity, but also demonstrates the potential of graphene for high-speed and multi-state nonvolatile memory applications.

Coulomb Drag in Graphene/h-BN/Graphene Moiré Heterostructures

We report on the observation of Coulomb drag between graphene-hexagonal boron nitride (h-BN) moiré heterostructure with a moiré wavelength of ∼14  nm and an intrinsic graphene with a lattice constant of ∼0.25  nm. By tuning carrier densities of each graphene layer independently, we find that charge carriers in moiré minibands, i.e., near satellite Dirac point (sDP), can be coupled with massless Fermions near the original Dirac point (oDP), strongly enough to generate a finite drag resistivity. At high temperature (T) and large density (n), the drag resistivities near both oDP and sDP follow a typical n^{-α} (α=1.3-1.7) and T^{2} power law dependence as expected for the momentum transfer process and it also satisfies the layer reciprocity. In contrast, at low T, the layer reciprocity is broken in both oDP-oDP and sDP-oDP coupled regions that suggest dominant energy drag. Furthermore, quantitatively, the drag resistivities near sDPs are smaller than those near oDP and they deviate from T^{2} dependence below ∼100  K. Our work demonstrates that the drag experiment can be used to investigate the coupling between the carriers in moiré minibands and those in original Dirac bands which can be extended to other moiré materials.

Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene

In Bernal-stacked bilayer graphene (BBG), the Landau levels give rise to an intimate connection between valley and layer degrees of freedom. Adding a moiré superlattice potential enriches the BBG physics with the formation of topological minibands - potentially leading to tunable exotic quantum transport. Here, we present magnetotransport measurements of a high-quality bilayer graphene-hexagonal boron nitride (hBN) heterostructure. The zero-degree alignment generates a strong moiré superlattice potential for the electrons in BBG and the resulting Landau fan diagram of longitudinal and Hall resistance displays a Hofstadter butterfly pattern with a high level of detail. We demonstrate that the intricate relationship between valley and layer degrees of freedom controls the topology of moiré-induced bands, significantly influencing the energetics of interacting quantum phases in the BBG superlattice. We further observe signatures of field-induced correlated insulators, helical edge states and clear quantizations of interaction-driven topological quantum phases, such as symmetry broken Chern insulators.

Modulating electronic structure by interlayer spacing and twist on bilayer bismuthene

Modulation of the electronic structure has played a crucial role in advancing the field of two-dimensional materials, but there are still many unexplored directions, such as the twist angle for a novel degree of freedom, for modulating the properties of heterostructures. We observed a distinct pattern in the energy bands of bilayer bismuthene, demonstrating that modulating the twist angle and interlayer spacing significantly influences interlayer interactions. Our study of various interlayer spacings and twist angles revealed a close relationship between bandgap size and interlayer spacing, while the twist angle notably affects the shape of the energy bands. Furthermore, we observed a synergistic effect between these two factors. As the twist angle decreases, the energy bands become flat, and flat bands can be generated without requiring a specific angle on bilayer bismuthene. Our results suggest a promising way to tailor the energy band structure of bilayer 2D materials by varying the interlayer spacing and twist angle.

Non-identical moiré twins in bilayer graphene

The superlattice obtained by aligning a monolayer graphene and boron nitride (BN) inherits from the hexagonal lattice a sixty degrees periodicity with the layer alignment. It implies that, in principle, the properties of the heterostructure must be identical for 0° and 60° of layer alignment. Here, we demonstrate, using dynamically rotatable van der Waals heterostructures, that the moiré superlattice formed in a bilayer graphene/BN has different electronic properties at 0° and 60° of alignment. Although the existence of these non-identical moiré twins is explained by different relaxation of the atomic structures for each alignment, the origin of the observed valley Hall effect remains to be explained. A simple Berry curvature argument is not sufficient to explain the 120° periodicity of this observation. Our results highlight the complexity of the interplay between mechanical and electronic properties in moiré structures and the importance of taking into account atomic structure relaxation to understand their electronic properties.

An anisotropic van der Waals dielectric for symmetry engineering in functionalized heterointerfaces

Van der Waals dielectrics are fundamental materials for condensed matter physics and advanced electronic applications. Most dielectrics host isotropic structures in crystalline or amorphous forms, and only a few studies have considered the role of anisotropic crystal symmetry in dielectrics as a delicate way to tune electronic properties of channel materials. Here, we demonstrate a layered anisotropic dielectric, SiP2, with non-symmorphic twofold-rotational C2 symmetry as a gate medium which can break the original threefold-rotational C3 symmetry of MoS2 to achieve unexpected linearly-polarized photoluminescence and anisotropic second harmonic generation at SiP2/MoS2 interfaces. In contrast to the isotropic behavior of pristine MoS2, a large conductance anisotropy with an anisotropy index up to 1000 can be achieved and modulated in SiP2-gated MoS2 transistors. Theoretical calculations reveal that the anisotropic moiré potential at such interfaces is responsible for the giant anisotropic conductance and optical response. Our results provide a strategy for generating exotic functionalities at dielectric/semiconductor interfaces via symmetry engineering.

Signatures of hot carriers and hot phonons in the re-entrant metallic and semiconducting states of Moiré-gapped graphene

Stacking of graphene with hexagonal boron nitride (h-BN) can dramatically modify its bands from their usual linear form, opening a series of narrow minigaps that are separated by wider minibands. While the resulting spectrum offers strong potential for use in functional (opto)electronic devices, a proper understanding of the dynamics of hot carriers in these bands is a prerequisite for such applications. In this work, we therefore apply a strategy of rapid electrical pulsing to drive carriers in graphene/h-BN heterostructures deep into the dissipative limit of strong electron-phonon coupling. By using electrical gating to move the chemical potential through the "Moiré bands", we demonstrate a cyclical evolution between metallic and semiconducting states. This behavior is captured in a self-consistent model of non-equilibrium transport that considers the competition of electrically driven inter-band tunneling and hot-carrier scattering by strongly non-equilibrium phonons. Overall, our results demonstrate how a treatment of the dynamics of both hot carriers and hot phonons is essential to understanding the properties of functional graphene superlattices.

Heterostrain and temperature-tuned twist between graphene/h-BN bilayers

Two-dimensional materials stacked atomically at small twist angles enable the modification of electronic states, motivating twistronics. Here, we demonstrate that heterostrain can rotate the graphene flake on monolayer h-BN within a few degrees (- 4° to 4°), and the twist angle stabilizes at specific values with applied constant strains, while the temperature effect is negligible in 100-900 K. The band gaps of bilayers can be modulated from ~ 0 to 37 meV at proper heterostrain and twist angles. Further analysis shows that the heterostrain modulates the interlayer energy landscape by regulating Moiré pattern evolution. The energy variation is correlated with the dynamic instability of different stacking modes of bilayers, and arises from the fluctuation of interlayer repulsive interaction associated with p-orbit electrons. Our results provide a mechanical strategy to manipulate twist angles of graphene/h-BN bilayers, and may facilitate the design of rotatable electronic nanodevices.

Defect engineering of two-dimensional materials for advanced energy conversion and storage

In the global trend towards carbon neutrality, sustainable energy conversion and storage technologies are of vital significance to tackle the energy crisis and climate change. However, traditional electrode materials gradually reach their property limits. Two-dimensional (2D) materials featuring large aspect ratios and tunable surface properties exhibit tremendous potential for improving the performance of energy conversion and storage devices. To rationally control the physical and chemical properties for specific applications, defect engineering of 2D materials has been investigated extensively, and is becoming a versatile strategy to promote the electrode reaction kinetics. Simultaneously, exploring the in-depth mechanisms underlying defect action in electrode reactions is crucial to provide profound insight into structure tailoring and property optimization. In this review, we highlight the cutting-edge advances in defect engineering in 2D materials as well as their considerable effects in energy-related applications. Moreover, the confronting challenges and promising directions are discussed for the development of advanced energy conversion and storage systems.

Unconventional self-similar Hofstadter superconductivity from repulsive interactions

Fractal Hofstadter bands have become widely accessible with the advent of moiré superlattices, opening the door to studies of the effect of interactions in these systems. In this work we employ a renormalization group (RG) analysis to demonstrate that the combination of repulsive interactions with the presence of a tunable manifold of Van Hove singularities provides a new mechanism for driving unconventional superconductivity in Hofstadter bands. Specifically, the number of Van Hove singularities at the Fermi energy can be controlled by varying the flux per unit cell and the electronic filling, leading to instabilities toward nodal superconductivity and chiral topological superconductivity with Chern number [Formula: see text]. The latter is characterized by a self-similar fixed trajectory of the RG flow and an emerging self-similarity symmetry of the order parameter. Our results establish Hofstadter quantum materials such as moiré heterostructures as promising platforms for realizing novel reentrant Hofstadter superconductors.

Direct growth of hBN/Graphene heterostructure via surface deposition and segregation for independent thickness regulation

Hexagonal boron nitride/graphene (hBN/G) vertical heterostructures have attracted extensive attention, owing to the unusual physical properties for basic research and electronic device applications. Here we report a facile deposition-segregation technique to synthesize hBN/G heterostructures on recyclable platinum (Pt) foil via low pressure chemical vapor deposition. The growth mechanism of the vertical hBN/G is demonstrated to be the surface deposition of hBN on top of the graphene segregated from the Pt foil with pre-dissolved carbon. The thickness of hBN and graphene can be controlled separately from sub-monolayer to multilayer through the fine control of the growth parameters. Further investigations by Raman, scanning Kelvin probe microscopy and transmission electron microscope show that the hBN/G inclines to form a heterostructure with strong interlayer coupling and with interlayer twist angle smaller than 1.5°. This deposition-segregation approach paves a new pathway for large-scale production of hBN/G heterostructures and could be applied to synthesize of other van der Waals heterostructures.

A Simple Evolutionary Model of Genetic Robustness After Gene Duplication

When a dispensable gene is duplicated (referred to the ancestral dispensability denoted by O⁺), genetic buffering and duplicate compensation together maintain the duplicate redundancy, whereas duplicate compensation is the only mechanism when an essential gene is duplicated (referred to the ancestral essentiality denoted by O^-). To investigate these evolutionary scenarios of genetic robustness, I formulated a simple mixture model for analyzing duplicate pairs with one of the following states: double dispensable (DD), semi-dispensable (one dispensable one essential, DE), or double essential (EE). This model was applied to the yeast duplicate pairs from a whole-genome duplication (WGD) occurred about 100 million years ago (mya), and the mouse duplicate pairs from a WGD occurred about more than 500 mya. Both case studies revealed that the proportion of essentiality for those duplicates with ancestral essentiality [P_E(O^-)] was much higher than that for those with ancestral dispensability [P_E(O⁺)]. While it was negligible in the yeast duplicate pairs, P_E(O⁺) (about 20%) was shown statistically significant in the mouse duplicate pairs. These findings, together, support the hypothesis that both sub-functionalization and neo-functionalization may play some roles after gene duplication, though the former may be much faster than the later.

Highly Tunable Carrier Tunneling in Vertical Graphene-WS2-Graphene van der Waals Heterostructures

Owing to the fascinating properties, the emergence of two-dimensional (2D) materials brings various important applications of electronic and optoelectronic devices from field-effect transistors (FETs) to photodetectors. As a zero-band-gap material, graphene has excellent electric conductivity and ultrahigh carrier mobility, while the ON/OFF ratio of the graphene FET is severely low. Semiconducting 2D transition metal chalcogenides (TMDCs) exhibit an appropriate band gap, realizing FETs with high ON/OFF ratio and compensating for the disadvantages of graphene transistors. However, a Schottky barrier often forms at the interface between the TMDC and metallic contact, which limits the on-state current of the devices. Here, we lift the two limits of the 2D-FET by demonstrating highly tunable field-effect tunneling transistors based on vertical graphene-WS₂-graphene van der Waals heterostructures. Our devices show a low off-state current below 1 pA and a high ON/OFF ratio exceeding 10⁶ at room temperature. Moreover, the carrier transport polarity of the device can be effectively tuned from n-type under small bias voltage to bipolar under large bias by controlling the crossover from a direct tunneling region to the Fowler-Nordheim tunneling region. Further, we find that the effective barrier height can be controlled by an external gate voltage. The temperature dependence of carrier transport demonstrates that both tunneling and thermionic emission contribute to the operation current at elevated temperature, which significantly enhances the on-state current of the tunneling transistors.

Scalable Synthesis of Monolayer Hexagonal Boron Nitride on Graphene with Giant Bandgap Renormalization

Monolayer hexagonal boron nitride (hBN) has been widely considered a fundamental building block for 2D heterostructures and devices. However, the controlled and scalable synthesis of hBN and its 2D heterostructures has remained a daunting challenge. Here, an hBN/graphene (hBN/G) interface-mediated growth process for the controlled synthesis of high-quality monolayer hBN is proposed and further demonstrated. It is discovered that the in-plane hBN/G interface can be precisely controlled, enabling the scalable epitaxy of unidirectional monolayer hBN on graphene, which exhibits a uniform moiré superlattice consistent with single-domain hBN, aligned to the underlying graphene lattice. Furthermore, it is identified that the deep-ultraviolet emission at 6.12 eV stems from the 1s-exciton state of monolayer hBN with a giant renormalized direct bandgap on graphene. This work provides a viable path for the controlled synthesis of ultraclean, wafer-scale, atomically ordered 2D quantum materials, as well as the fabrication of 2D quantum electronic and optoelectronic devices.

Correlated States in Strained Twisted Bilayer Graphenes Away from the Magic Angle

Graphene moiré superlattice formed by rotating two graphene sheets can host strongly correlated and topological states when flat bands form at so-called magic angles. Here, we report that, for a twisting angle far away from the magic angle, the heterostrain induced during stacking heterostructures can also create flat bands. Combining a direct visualization of strain effect in twisted bilayer graphene moiré superlattices and transport measurements, features of correlated states appear at "non-magic" angles in twisted bilayer graphene under the heterostrain. Observing correlated states in these "non-standard" conditions can enrich the understanding of the possible origins of the correlated states and widen the freedom in tuning the moiré heterostructures and the scope of exploring the correlated physics in moiré superlattices.

Recent Advances on Tuning the Interlayer Coupling and Properties in van der Waals Heterostructures

2D van der Waals (vdW) heterostructures are receiving increasing research attention due to the theoretically amazing properties and unprecedented application potential. However, the as-synthesized heterostructures are generally underperforming due to the weak interlayer coupling, which inspires the researchers to find ways to modulate the interlayer coupling and properties, realizing the tailored performance for actual applications. There have been a lot of publications regarding the controllable regulation of the structures and properties of 2D vdW heterostructures in the past few years, while a review work summarizing the current advances is not yet available, though it is significant. This paper conducts a state-of-the-art review regarding the current research progress of performance modulation of vdW heterostructures by different techniques. First, the general synthesis methods of vdW heterostructures are summarized. Then, different performance modulation techniques, that is, mechanical-based, external fields-assisted, and particle beam irradiation-based methods, are discussed and compared in detail. Some of the newly proposed concepts are described. Thereafter, applications of vdW heterostructures with tailored properties are reviewed for the application prospects of the topic around this area. Moreover, the future research challenges and prospects are discussed, aiming at triggering more research interest and device applications around this topic.

Interlayer Interactions in 1D Van der Waals Moiré Superlattices

Studying two-dimensional (2D) van der Waals (vdW) moiré superlattices and their interlayer interactions have received surging attention after recent discoveries of many new phases of matter that are highly tunable. Different atomistic registry between layers forming the inner and outer nanotubes can also form one-dimensional (1D) vdW moiré superlattices. In this review, experimental observations and theoretical perspectives related to interlayer interactions in 1D vdW moiré superlattices are summarized. The discussion focuses on double-walled carbon nanotubes (DWNTs), a model 1D vdW moiré system, and the authors highlight the new optical features emerging from the non-trivial strong interlayer coupling effect and the unique physics in 1D DWNTs. Future directions and questions in probing the intriguing physical phenomena in 1D vdW moiré superlattices such as, correlated physics in different 1D moiré systems beyond DWNTs are proposed and discussed.

Direct growth of hexagonal boron nitride on non-metallic substrates and its heterostructures with graphene

Hexagonal boron nitride (h-BN) and its heterostructures with graphene are widely investigated van der Waals (vdW) quantum materials for electronics, photonics, sensing, and energy storage/transduction. However, their metal catalyst-based growth and transfer-based heterostructure assembly approaches present impediments to obtaining high-quality and wafer-scale quantum material. Here, we have presented our perspective on the synthetic strategies that involve direct nucleation of h-BN on various dielectric substrates and its heterostructures with graphene. Mechanistic understanding of direct growth of h-BN via bottom-up approaches such as (a) the chemical-interaction guided nucleation on silicon-based dielectrics, (b) surface nitridation and N+ sputtering of h-BN target on sapphire, and (c) epitaxial growth of h-BN on sapphire, among others, are reviewed. Several design methodologies are presented for the direct growth of vertical and lateral vdW heterostructures of h-BN and graphene. These complex 2D heterostructures exhibit various physical phenomena and could potentially have a range of practical applications.

Epitaxial Intercalation Growth of Scalable Hexagonal Boron Nitride/Graphene Bilayer Moiré Materials with Highly Convergent Interlayer Angles

Vertically stacked two-dimensional van der Waals (vdW) heterostructures with specific interlayer angles exhibit peculiar physical properties. Nowadays, most of the stacked layers are fabricated by mechanical exfoliation followed by precise transfer and alignment with micrometer spatial accuracy. This stringent ingredient of sample preparation limits the productivity of device fabrication and the reproducibility of device performance. Here, we demonstrate the one-pot chemical vapor deposition growth of hexagonal boron nitride (hBN)/graphene bilayers with a high-purity moiré phase. The epitaxial intercalation of graphene under a hydrogen-terminated hBN template leads to convergent interlayer angles of less than 0.5°. The near 0° stacking angle shows almost 2 orders of magnitude higher likelihood of occurrence compared with angles larger than 0.5°. The bilayers show a substantial enhancement of carrier mobility compared with monolayer graphene owing to protection from the top hBN layer. Our work proposes a large-scale fabrication method of hBN/graphene bilayers with a high uniformity and controlled interlayer rotation and will promote the production development for high-quality vdW heterostructures.

Hyperbolic band theory under magnetic field and Dirac cones on a higher genus surface

We explore the hyperbolic band theory under a magnetic field for the first time. Our theory is a general extension of the conventional band theory defined on a Euclidean lattice into the band theory on a general hyperbolic lattice/Riemann surface. Our methods and results can be confirmed experimentally by circuit quantum electrodynamics, which enables us to create novel materials in a hyperbolic space. To investigate the band structures, we construct directly the hyperbolic magnetic Bloch states and find that they form Dirac cones on a coordinate neighborhood. They can be regarded as a global quantum gravity solution detectable in a laboratory. Besides this is the first explicit example of a massless Dirac state on a higher genus surface. Moreover we show that the energy spectrum exhibits an unusual fractal structure refracting the negative curvature, when plotted as a function of a magnetic flux.

Accurate Measurement of the Gap of Graphene/h-BN Moiré Superlattice through Photocurrent Spectroscopy

Monolayer graphene aligned with hexagonal boron nitride (h-BN) develops a gap at the charge neutrality point (CNP). This gap has previously been extensively studied by electrical transport through thermal activation measurements. Here, we report the determination of the gap size at the CNP of graphene/h-BN superlattice through photocurrent spectroscopy study. We demonstrate two distinct measurement approaches to extract the gap size. A maximum of ∼14  meV gap is observed for devices with a twist angle of less than 1°. This value is significantly smaller than that obtained from thermal activation measurements, yet larger than the theoretically predicted single-particle gap. Our results suggest that lattice relaxation and moderate electron-electron interaction effects may enhance the CNP gap in graphene/h-BN superlattice.

Atomically Thin Hexagonal Boron Nitride and Its Heterostructures

Atomically thin hexagonal boron nitride (h-BN) is an emerging star of 2D materials. It is taken as an optimal substrate for other 2D-material-based devices owing to its atomical flatness, absence of dangling bonds, and excellent stability. Specifically, h-BN is found to be a natural hyperbolic material in the mid-infrared range, as well as a piezoelectric material. All the unique properties are beneficial for novel applications in optoelectronics and electronics. Currently, most of these applications are merely based on exfoliated h-BN flakes at their proof-of-concept stages. Chemical vapor deposition (CVD) is considered as the most promising approach for producing large-scale, high-quality, atomically thin h-BN films and heterostructures. Herein, CVD synthesis of atomically thin h-BN is the focus. Also, the growth kinetics are systematically investigated to point out general strategies for controllable and scalable preparation of single-crystal h-BN film. Meanwhile, epitaxial growth of 2D materials onto h-BN and at its edge to construct heterostructures is summarized, emphasizing that the specific orientation of constituent parts in heterostructures can introduce novel properties. Finally, recent applications of atomically thin h-BN and its heterostructures in optoelectronics and electronics are summarized.

Correlation-driven topological phases in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene (MATBG) exhibits a range of correlated phenomena that originate from strong electron-electron interactions. These interactions make the Fermi surface highly susceptible to reconstruction when ±1, ±2 and ±3 electrons occupy each moiré unit cell, and lead to the formation of various correlated phases^1-4. Although some phases have been shown to have a non-zero Chern number^5,6, the local microscopic properties and topological character of many other phases have not yet been determined. Here we introduce a set of techniques that use scanning tunnelling microscopy to map the topological phases that emerge in MATBG in a finite magnetic field. By following the evolution of the local density of states at the Fermi level with electrostatic doping and magnetic field, we create a local Landau fan diagram that enables us to assign Chern numbers directly to all observed phases. We uncover the existence of six topological phases that arise from integer fillings in finite fields and that originate from a cascade of symmetry-breaking transitions driven by correlations^7,8. These topological phases can form only for a small range of twist angles around the magic angle, which further differentiates them from the Landau levels observed near charge neutrality. Moreover, we observe that even the charge-neutrality Landau spectrum taken at low fields is considerably modified by interactions, exhibits prominent electron-hole asymmetry, and features an unexpectedly large splitting between zero Landau levels (about 3 to 5 millielectronvolts). Our results show how strong electronic interactions affect the MATBG band structure and lead to correlation-enabled topological phases.

Band Engineering of Large-Twist-Angle Graphene/h-BN Moiré Superlattices with Pressure

Graphene interfacing hexagonal boron nitride (h-BN) forms lateral moiré superlattices that host a wide range of new physical effects such as the creation of secondary Dirac points and band gap opening. A delicate control of the twist angle between the two layers is required as the effects weaken or disappear at large twist angles. In this Letter, we show that these effects can be reinstated in large-angle (∼1.8°) graphene/h-BN moiré superlattices under high pressures. A graphene/h-BN moiré superlattice microdevice is fabricated directly on the diamond culet of a diamond anvil cell, where pressure up to 8.3 GPa is applied. The band gap at the primary Dirac point is opened by 40-60 meV, and fingerprints of the second Dirac band gap are also observed in the valence band. Theoretical calculations confirm the band engineering with pressure in large-angle graphene/h-BN bilayers.

Moiré Fringe Induced Gauge Field in Photonics

We realize moiré fringe induced gauge field in a double-layer photonic honeycomb metacrystal with mismatched lattice constants. Benefitting from the generated strong effective gauge field, we report direct measurement of the band diagrams of both Landau level flat bands and intermagnetic-domain edge states. Importantly, we observe the correlation between the momentum and orbital position of the Landau modes, serving as an evidence of the noncommuteness between orthogonal components of the momentum. Without complicated time driving mechanics and careful site-by-site engineering, moiré superlattices could emerge as a powerful means to generate effective gauge fields for photonics benefiting from its simplicity and reconfigurability, which can be applied to nonlinearity enhancement and lasing applications at optical frequencies.

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.

Magnetic field detection limits for ultraclean graphene Hall sensors

Solid-state magnetic field sensors are important for applications in commercial electronics and fundamental materials research. Most magnetic field sensors function in a limited range of temperature and magnetic field, but Hall sensors in principle operate over a broad range of these conditions. Here, we evaluate ultraclean graphene as a material platform for high-performance Hall sensors. We fabricate micrometer-scale devices from graphene encapsulated with hexagonal boron nitride and few-layer graphite. We optimize the magnetic field detection limit under different conditions. At 1 kHz for a 1 μm device, we estimate a detection limit of 700 nT Hz^−1/2 at room temperature, 80 nT Hz^−1/2 at 4.2 K, and 3 μT Hz^−1/2 in 3 T background field at 4.2 K. Our devices perform similarly to the best Hall sensors reported in the literature at room temperature, outperform other Hall sensors at 4.2 K, and demonstrate high performance in a few-Tesla magnetic field at which the sensors exhibit the quantum Hall effect.

The development of high-performance magnetic field sensors is important for magnetic sensing and imaging. Here, the authors fabricate Hall sensors from graphene encapsulated in hBN and few-layer graphite, demonstrating high performance over a wide range of temperature and background magnetic field.

Versatile construction of van der Waals heterostructures using a dual-function polymeric film

The proliferation of van der Waals (vdW) heterostructures formed by stacking layered materials can accelerate scientific and technological advances. Here, we report a strategy for constructing vdW heterostructures through the interface engineering of the exfoliation substrate using a sub-5 nm polymeric film. Our construction method has two main features that distinguish it from existing techniques. First is the consistency of its exfoliation process in increasing the yield and in producing large (>10,000 μm²) monolayer graphene. Second is the applicability of its layer transfer process to different layered materials without requiring a specialized stamp—a feature useful for generalizing the assembly process. We demonstrate vdW graphene devices with peak carrier mobility of 200,000 and 800,000 cm² V⁻¹ s⁻¹ at room temperature and 9 K, respectively. The simplicity of our construction method and its versatility to different layered materials may open doors for automating the fabrication process of vdW heterostructures.

Heterostructure stacking of 2D materials is crucial for fundamental studies and device applications. Here, the authors report heterostructures based on exfoliated flakes of graphene with large lateral area sizes and record high mobility of 200,000 cm2/Vs at room temperature.

Excitonic Effect Drives Ultrafast Dynamics in van der Waals Heterostructures

Recent experiments revealed stacking-configuration-independent and ultrafast charge transfer in transition metal dichalcogenides van der Waals (vdW) heterostructures, which is surprising given strong exciton binding energies and large momentum mismatch across the heterojunctions. Previous theories failed to provide a comprehensive physical picture for the charge transfer mechanisms. To address this challenge, we developed a first-principles framework which can capture exciton-phonon interaction in extended systems. We find that excitonic effect does not impede, but actually drives ultrafast charge transfer in vdW heterostructures. The many-body electron-hole interaction affords cooperation among the electrons, which relaxes the constraint on momentum conservation and reduces energy gaps for charge transfer. We uncover a two-step process in exciton dynamics: ultrafast hole transfer followed by much longer relaxation of intermediate "hot" excitons. This work establishes that many-body excitonic effect is crucial to the ultrafast dynamics and provides a basis to understand relevant phenomena in vdW heterostructures.

Nano-photocurrent Mapping of Local Electronic Structure in Twisted Bilayer Graphene

We report a combined nano-photocurrent and infrared nanoscopy study of twisted bilayer graphene (TBG) enabling access to the local electronic phenomena at length scales as short as 20 nm. We show that the photocurrent changes sign at carrier densities tracking the local superlattice density of states of TBG. We use this property to identify domains of varying local twist angle by local photothermoelectric effect. Consistent with the photocurrent study, infrared nanoimaging experiments reveal optical conductivity features dominated by twist-angle-dependent interband transitions. Our results provide a fast and robust method for mapping the electronic structure of TBG and suggest that similar methods can be broadly applied to probe electronic inhomogeneities of Moiré superlattices in other van der Waals heterostructures.

30°-Twisted Bilayer Graphene Quasicrystals from Chemical Vapor Deposition

The artificial stacking of atomically thin crystals suffers from intrinsic limitations in terms of control and reproducibility of the relative orientation of exfoliated flakes. This drawback is particularly severe when the properties of the system critically depends on the twist angle, as in the case of the dodecagonal quasicrystal formed by two graphene layers rotated by 30°. Here we show that large-area 30°-rotated bilayer graphene can be grown deterministically by chemical vapor deposition on Cu, eliminating the need of artificial assembly. The quasicrystals are easily transferred to arbitrary substrates and integrated in high-quality hexagonal boron nitride-encapsulated heterostructures, which we process into dual-gated devices exhibiting carrier mobility up to 10⁵ cm²/(V s). From low-temperature magnetotransport, we find that the graphene quasicrystals effectively behave as uncoupled graphene layers, showing 8-fold degenerate quantum Hall states. This result indicates that the Dirac cones replica detected by previous photoemission experiments do not contribute to the electrical transport.

Research on the correlation of mechanical properties of BN-graphene-BN/BN vertically-stacked nanostructures in the presence of interlayer sp3 bonds and nanopores with temperature

In this study, we investigate the coupling of an internal field (defect field-sp³ bonds and nanopores) and an external field (strain and temperature). Simultaneously, we provide a design idea of hybrid materials. The mechanical properties of hybrid materials under the condition of internal and external field coupling were studied. When nanopores and sp³ bonds are considered simultaneously, we found that internal (sp³ bonds and defects) and external field (temperature and strain fields) have a negative chain reaction on the mechanical properties of BN-graphene-BN/BN vertically-stacked nanostructures, and the negative chain reaction will gradually increase with the change in parameters (such as the increase in temperature). The sp³ bonds can be regarded as a special defect, which will increase the initial strain of the system. In addition, the mechanical properties of the nanostructure, containing square nanopores in the boron nitride region are most sensitive to temperature change, relative to the nanopore in the other two regions. Atoms (around square nanopores) are more likely to overcome the binding energy and lose stability from the inherent equilibrium position, relative to that of circular nanopores.

Reliable Postprocessing Improvement of van der Waals Heterostructures

The successful assembly of heterostructures consisting of several layers of different 2D materials in arbitrary order by exploiting van der Waals forces has truly been a game changer in the field of low-dimensional physics. For instance, the encapsulation of graphene or MoS₂ between atomically flat hexagonal boron nitride (hBN) layers with strong affinity and graphitic gates that screen charge impurity disorder provided access to a plethora of interesting physical phenomena by drastically boosting the device quality. The encapsulation is accompanied by a self-cleansing effect at the interfaces. The otherwise predominant charged impurity disorder is minimized, and random strain fluctuations ultimately constitute the main source of residual disorder. Despite these advances, the fabricated heterostructures still vary notably in their performance. Although some achieve record mobilities, others only possess mediocre quality. Here, we report a reliable method to improve fully completed van der Waals heterostructure devices with a straightforward postprocessing surface treatment based on thermal annealing and contact mode atomic force microscopy (AFM). The impact is demonstrated by comparing magnetotransport measurements before and after the AFM treatment on one and the same device as well as on a larger set of treated and untreated devices to collect device statistics. Both the low-temperature properties and the room temperature electrical characteristics, as relevant for applications, improve on average substantially. We surmise that the main beneficial effect arises from reducing nanometer scale corrugations at the interfaces, that is, the detrimental impact of random strain fluctuations.

Tunable crystal symmetry in graphene-boron nitride heterostructures with coexisting moiré superlattices

In van der Waals (vdW) heterostructures consisting of atomically thin crystals layered on top of one another, lattice mismatch and rotation between the layers can result in long-wavelength moiré superlattices. These moiré patterns can drive notable band structure reconstruction of the composite material, leading to a wide range of emergent phenomena including superconductivity^1-3, magnetism⁴, fractional Chern insulating states⁵ and moiré excitons^6-9. Here, we investigate devices consisting of monolayer graphene encapsulated between two crystals of boron nitride (BN), in which the rotational alignment of all three components is controlled. We find that bandgaps in the graphene arising from perfect rotational alignment with both BN layers can be modified considerably depending on whether the relative orientation of the two BN layers is 0° or 60°, suggesting a tunable transition between the absence or presence of inversion symmetry in the heterostructure. Small deviations (<1°) from perfect alignment of all three layers leads to coexisting long-wavelength moiré potentials, resulting in a highly reconstructed graphene band structure featuring multiple secondary Dirac points. Our results demonstrate that the interplay between multiple moiré patterns can be utilized to controllably modify the symmetry and electronic properties of the composite heterostructure.

Bottom-up growth of homogeneous Moiré superlattices in bismuth oxychloride spiral nanosheets

Moiré superlattices (MSLs) are modulated structures produced from homogeneous or heterogeneous 2D layers stacked with a twist angle and/or lattice mismatch. Expanding the range of available materials, methods for fabricating MSL, and realization of unique emergent properties are key challenges. Here we report a facile bottom-up synthesis of homogeneous MSL based on a wide-gap 2D semiconductor, BiOCl, using a one-pot solvothermal approach with robust reproducibility. Unlike previous MSLs usually prepared by directly stacking two monolayers, our BiOCl MSLs are realized in a scalable, direct way through chemical growth of spiral-type nanosheets driven by screw-dislocations. We find emergent properties including large band gap reduction (∼0.6 eV), two-fold increase in carrier lifetime, and strongly enhanced photocatalytic activity. First-principles calculations reveal that such unusual properties can be ascribed to the locally enhanced inter-layer coupling associated with the Moiré potential modulation. Our results demonstrate the promise of MSL materials for chemical and physical functions.

Expanding the range of available materials, methods for fabricating Moiré superlattices, and realization of new emergent properties are key challenges. Here the authors report a facile bottom-up synthesis of homogeneous Moiré superlattices based on a wide-gap 2D semiconductor, bismuth oxychloride.

Superlattices based on van der Waals 2D materials

Two-dimensional (2D) materials exhibit a number of improved mechanical, optical, and electronic properties compared to their bulk counterparts. The absence of dangling bonds in the cleaved surfaces of these materials allows combining different 2D materials into van der Waals heterostructures to fabricate p-n junctions, photodetectors, and 2D-2D ohmic contacts that show unexpected performances. These intriguing results are regularly summarized in comprehensive reviews. A strategy to tailor their properties even further and to observe novel quantum phenomena consists in the fabrication of superlattices whose unit cell is formed either by two dissimilar 2D materials or by a 2D material subjected to a periodic perturbation, each component contributing with different characteristics. Furthermore, in a 2D material-based superlattice, the interlayer interaction between the layers mediated by van der Waals forces constitutes a key parameter to tune the global properties of the superlattice. The above-mentioned factors reflect the potential to devise countless combinations of van der Waals 2D material-based superlattices. In the present feature article, we explain in detail the state-of-the-art of 2D material-based superlattices and describe the different methods to fabricate them, classified as vertical stacking, intercalation with atoms or molecules, moiré patterning, strain engineering and lithographic design. We also aim to highlight some of the specific applications of each type of superlattices.

Quantum Electrodynamical Bloch Theory with Homogeneous Magnetic Fields

We propose a solution to the problem of Bloch electrons in a homogeneous magnetic field by including the quantum fluctuations of the photon field. A generalized quantum electrodynamical (QED)-Bloch theory from first principles is presented. In the limit of vanishing quantum fluctuations, we recover the standard results of solid-state physics: the fractal spectrum of the Hofstadter butterfly. As a further application, we show how the well-known Landau physics is modified by the photon field and that Landau polaritons emerge. This shows that our QED-Bloch theory does not only allow us to capture the physics of solid-state systems in homogeneous magnetic fields but also novel features that appear at the interface of condensed matter physics and quantum optics.

Fractional and Symmetry-Broken Chern Insulators in Tunable Moiré Superlattices

We study dual-gated graphene bilayer/hBN moiré superlattices. Under zero magnetic field, we observe additional resistance peaks as the charge density varies. The peaks' resistivities vary approximately quadratically with an applied perpendicular displacement field D. Data fit to a continuum model yield a bilayer/hBN interaction energy scale ∼30 ± 10 meV. Under a perpendicular magnetic field, we observe Hofstadter butterfly spectra as well as symmetry-broken and fractional Chern insulator states. Their topology and lattice symmetry breaking is D-tunable, enabling the realization of new topological states in this system.

Disorder in van der Waals heterostructures of 2D materials

Realizing the full potential of any materials system requires understanding and controlling disorder, which can obscure intrinsic properties and hinder device performance. Here we examine both intrinsic and extrinsic disorder in two-dimensional (2D) materials, in particular graphene and transition metal dichalcogenides (TMDs). Minimizing disorder is crucial for realizing desired properties in 2D materials and improving device performance and repeatability for practical applications. We discuss the progress in disorder control for graphene and TMDs, as well as in van der Waals heterostructures realized by combining these materials with hexagonal boron nitride. Furthermore, we showcase how atomic defects or disorder can also be harnessed to provide useful electronic, optical, chemical and magnetic functions.

New Generation of Moiré Superlattices in Doubly Aligned hBN/Graphene/hBN Heterostructures

The specific rotational alignment of two-dimensional lattices results in a moiré superlattice with a larger period than the original lattices and allows one to engineer the electronic band structure of such materials. So far, transport signatures of such superlattices have been reported for graphene/hBN and graphene/graphene systems. Here we report moiré superlattices in fully hBN encapsulated graphene with both the top and the bottom hBN aligned to the graphene. In the graphene, two different moiré superlattices form with the top and the bottom hBN, respectively. The overlay of the two superlattices can result in a third superlattice with a period larger than the maximum period (14 nm) in the graphene/hBN system, which we explain in a simple model. This new type of band structure engineering allows one to artificially create an even wider spectrum of electronic properties in two-dimensional materials.

Effects of site asymmetry and valley mixing on Hofstadter-type spectra of bilayer graphene in a square-scatter array potential

Under a magnetic field perpendicular to an monolayer graphene, the existence of a two-dimensional periodic scatter array can not only mix Landau levels of the same valley for displaying split electron-hole Hofstadter-type energy spectra, but also couple two sets of Landau subbands from different valleys in a bilayer graphene. Such a valley mixing effect with a strong scattering strength has been found observable and studied thoroughly in this paper by using a Bloch-wave expansion approach and a projected [Formula: see text] effective Hamiltonian including interlayer effective mass, interlayer coupling and asymmetrical on-site energies due to a vertically-applied electric field. For bilayer graphene, we find two important characteristics, i.e. mixing and interference of intervalley scatterings in the presence of a scatter array, as well as a perpendicular-field induced site-energy asymmetry which deforms severely or even destroys completely the Hofstadter-type band structures due to the dependence of Bloch-wave expansion coefficients on the applied electric field.

Topological Insulators in Twisted Transition Metal Dichalcogenide Homobilayers

We show that moiré bands of twisted homobilayers can be topologically nontrivial, and illustrate the tendency by studying valence band states in ±K valleys of twisted bilayer transition metal dichalcogenides, in particular, bilayer MoTe_{2}. Because of the large spin-orbit splitting at the monolayer valence band maxima, the low energy valence states of the twisted bilayer MoTe_{2} at the +K (-K) valley can be described using a two-band model with a layer-pseudospin magnetic field Δ(r) that has the moiré period. We show that Δ(r) has a topologically nontrivial skyrmion lattice texture in real space, and that the topmost moiré valence bands provide a realization of the Kane-Mele quantum spin-Hall model, i.e., the two-dimensional time-reversal-invariant topological insulator. Because the bands narrow at small twist angles, a rich set of broken symmetry insulating states can occur at integer numbers of electrons per moiré cell.

Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene

We present a theory of phonon-mediated superconductivity in near magic angle twisted bilayer graphene. Using a microscopic model for phonon coupling to moiré band electrons, we find that phonons generate attractive interactions in both s- and d-wave pairing channels and that the attraction is strong enough to explain the experimental superconducting transition temperatures. Before including Coulomb repulsion, the s-wave channel is more favorable; however, on-site Coulomb repulsion can suppress s-wave pairing relative to d wave. The pair amplitude varies spatially with the moiré period, and is identical in the two layers in the s-wave channel but phase shifted by π in the d-wave channel. We discuss experiments that can distinguish the two pairing states.

Accurate Gap Determination in Monolayer and Bilayer Graphene/ h-BN Moiré Superlattices

High mobility single and few-layer graphene sheets are in many ways attractive as nanoelectronic circuit hosts but lack energy gaps, which are essential to the operation of field-effect transistors. One of the methods used to create gaps in the spectrum of graphene systems is to form long period moiré patterns by aligning the graphene and hexagonal boron nitride ( h-BN) substrate lattices. Here, we use planar tunneling devices with thin h-BN barriers to obtain direct and accurate tunneling spectroscopy measurements of the energy gaps in single-layer and bilayer graphene- h-BN superlattice structures at charge neutrality (first Dirac point) and at integer moiré band occupancies (second Dirac point, SDP) as a function of external electric and magnetic fields and the interface twist angle. In single-layer graphene, we find, in agreement with previous work, that gaps are formed at neutrality and at the hole-doped SDP, but not at the electron-doped SDP. Both primary and secondary gaps can be determined accurately by extrapolating Landau fan patterns to a zero magnetic field and are as large as ≈17 meV for devices in near-perfect alignment. For bilayer graphene, we find that gaps occur only at charge neutrality where they can be modified by an external electric field.