Cloning of Dirac fermions in graphene superlattices

Direct Growth of van der Waals Tin Diiodide Monolayers

Two-dimensional (2D) van der Waals (vdW) materials have garnered considerable attention for their unique properties and potentials in a wide range of fields, which include nano-electronics/optoelectronics, solar energy, and catalysis. Meanwhile, challenges in the approaches toward achieving high-performance devices still inspire the search for new 2D vdW materials with precious properties. In this study, via molecular beam epitaxy, for the first time, the vdW SnI2 monolayer is successfully fabricated with a new structure. Scanning tunneling microscopy/spectroscopy characterization, as corroborated by the density functional theory calculation, indicates that this SnI2 monolayer exhibits a band gap of ≈2.9 eV in the visible purple range, and an indirect- to direct-band gap transition occurs in the SnI2 bilayer. This study provides a new semiconducting 2D material that is promising as a building block in future electronics/optoelectronics.

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.

Direct imaging of interlayer-coupled symmetric and antisymmetric plasmon modes in graphene/hBN/graphene heterostructures

Much of the richness and variety of physics today are based on coupling phenomena where multiple interacting systems hybridize into new ones with completely distinct attributes. Recent development in building van der Waals (vdWs) heterostructures from different 2D materials provides exciting possibilities in realizing novel coupling phenomena in a designable manner. Here, with a graphene/hBN/graphene heterostructure, we report near-field infrared nano-imaging of plasmon-plasmon coupling in two vertically separated graphene layers. Emergent symmetric and anti-symmetric coupling modes are directly observed simultaneously. Coupling and decoupling processes are systematically investigated with experiment, simulation and theory. The reported interlayer plasmon-plasmon coupling could serve as an extra degree of freedom to control light propagation at the deep sub-wavelength scale with low loss and provide exciting opportunities for optical chip integration.

Ultrafast Electron Tunneling Devices-From Electric-Field Driven to Optical-Field Driven

The search for ever higher frequency information processing has become an area of intense research activity within the micro, nano, and optoelectronics communities. Compared to conventional semiconductor-based diffusive transport electron devices, electron tunneling devices provide significantly faster response times due to near-instantaneous tunneling that occurs at sub-femtosecond timescales. As a result, the enhanced performance of electron tunneling devices is demonstrated, time and again, to reimagine a wide variety of traditional electronic devices with a variety of new "lightwave electronics" emerging, each capable of reducing the electron transport channel transit time down to attosecond timescales. In response to unprecedented rapid progress within this field, here the current state-of-the-art in electron tunneling devices is reviewed, current challenges and opportunities are highlighted, and possible future research directions are identified.

Criteria for Assessing the Interlayer Coupling of van der Waals Heterostructures Using Ultrafast Pump-Probe Photoluminescence Spectroscopy

van der Waals (vdW) heterostructures of transition metal dichalcogenides (TMDCs) provide an excellent paradigm for next-generation electronic and optoelectronic applications. However, the reproducible fabrications of vdW heterostructure devices and the boosting of practical applications are severely hindered by their unstable performance, due to the lack of criteria to assess the interlayer coupling in heterostructures. Here we propose a physical model involving ultrafast electron transfer in the heterostructures and provide two criteria, η (the ratio of the transferred electrons to the total excited electrons) and ζ (the relative photoluminescence variation), to evaluate the interlayer coupling by considering the electron transfer in TMDC heterostructures and numerically simulating the corresponding rate equations. We have proved the effectiveness and robustness of two criteria by measuring the pump-probe photoluminescence intensity of monolayer WS₂ in the WS₂/WSe₂ heterostructures. During thermal annealing of WS₂/WSe₂, ζ varies from negative to positive values and η changes between 0 and 4.5 × 10^-3 as the coupling strength enhanced; both of them can well characterize the tuning of interlayer coupling. We also design a scheme to image the interlayer coupling by performing PL imaging at two time delays. Our scheme offers powerful criteria to assess the interlayer coupling in TMDC heterostructures, offering opportunities for the implementation of vdW heterostructures for broadband and high-performance electronic and optoelectronic applications.

The optical response of artificially twisted MoS[Formula: see text] bilayers

Two-dimensional layered materials offer the possibility to create artificial vertically stacked structures possessing an additional degree of freedom-the interlayer twist. We present a comprehensive optical study of artificially stacked bilayers (BLs) MoS[Formula: see text] encapsulated in hexagonal BN with interlayer twist angle ranging from 0[Formula: see text] to 60[Formula: see text] using Raman scattering and photoluminescence spectroscopies. It is found that the strength of the interlayer coupling in the studied BLs can be estimated using the energy dependence of indirect emission versus the A[Formula: see text]-E[Formula: see text] energy separation. Due to the hybridization of electronic states in the valence band, the emission line related to the interlayer exciton is apparent in both the natural (2H) and artificial (62[Formula: see text]) MoS[Formula: see text] BLs, while it is absent in the structures with other twist angles. The interlayer coupling energy is estimated to be of about 50 meV. The effect of temperature on energies and intensities of the direct and indirect emission lines in MoS[Formula: see text] BLs is also quantified.

When graphene meets white graphene - recent advances in the construction of graphene and h-BN heterostructures

2D heterostructures have very recently witnessed a boom in scientific and technological activities owing to the customized spatial orientation and tailored physical properties. A large amount of 2D heterostructures have been constructed on the basis of the combination of mechanical exfoliation and located transfer method, opening wide possibilities for designing novel hybrid systems with tuned structures, properties, and applications. Among the as-developed 2D heterostructures, in-plane graphene and h-BN heterostructures have drawn the most attention in the past few decades. The controllable synthesis, the investigation of properties, and the expansion of applications have been widely explored. Herein, the fabrication of graphene and h-BN heterostructures is mainly focused on. Then, the spatial configurations for the heterostructures are systematically probed to identify the highly related unique features. Moreover, as a most promising approach for the scaled production of 2D materials, the in situ CVD fabrication of the heterostructures is summarized, demonstrating a significant potential in the controllability of size, morphology, and quality. Further, the recent applications of the 2D heterostructures are discussed. Finally, the concerns and challenges are fully elucidated and a bright future has been envisioned.

Engineering of Numerous Moiré Superlattices in Twisted Multilayer Graphene for Twistronics and Straintronics Applications

Because of their unique atomic structure, 2D materials are able to create an up-to-date paradigm in fundamental science and technology on the way to engineering the band structure and electronic properties of materials on the nanoscale. One of the simplest methods along this path is the superposition of several 2D nanomaterials while simultaneously specifying the twist angle between adjacent layers (θ), which leads to the emergence of Moiré superlattices. The key challenge in 2D nanoelectronics is to obtain a nanomaterial with numerous Moiré superlattices in addition to a high carrier mobility in a stable and easy-to-fabricate material. Here, we demonstrate the possibility of synthesizing twisted multilayer graphene (tMLG) with a number of monolayers N_L = 40-250 and predefined narrow ranges of θ = 3-8°, θ = 11-15°, and θ = 26-30°. A 2D nature of the electron transport is observed in the tMLG, and its carrier mobilities are close to those of twisted bilayer graphene (tBLG) (with θ = 30°) between h-BN layers. We demonstrate an undoubtful presence of numerous Moiré superlattices simultaneously throughout the entire tMLG thickness, while the periods of these superlattices are rather close to each other. This offers a challenge of producing a next generation of devices for nanoelectronics, twistronics, and neuromorphic computing for large data applications.

Multiple flat bands and topological Hofstadter butterfly in twisted bilayer graphene close to the second magic angle

Moiré superlattices in two-dimensional van der Waals heterostructures provide an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has made this moiré system one of the most renowned condensed matter platforms. So far studies of tBLG have been mostly focused on the lowest two flat moiré bands at the first magic angle θ_m1 ∼ 1.1°, leaving high-order moiré bands and magic angles largely unexplored. Here we report an observation of multiple well-isolated flat moiré bands in tBLG close to the second magic angle θ_m2 ∼ 0.5°, which cannot be explained without considering electron-election interactions. With high magnetic field magnetotransport measurements we further reveal an energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band gaps. The connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moiré bands. Overall, our work provides a perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.

Intrinsic Room-Temperature Ferromagnetism in V2C MXene Nanosheets

Two-dimensional (2D) materials with intrinsic magnetic properties are intensively explored due to their potential applications in low-power-consumption electronics and spintronics. To date, only a handful of intrinsic magnetic 2D materials have been reported. Here, we report a realization of intrinsic ferromagnetic behavior in 2D V₂C MXene nanosheets through layer mismatch engineering. The V₂C MXene nanosheets with a small-angle twisting show a robust intrinsic ferromagnetic response with a saturation magnetic moment of 0.013 emu/g at room temperature. An in-depth study has been performed by X-ray absorption spectroscopy as well as electron paramagnetic resonance (EPR) and photoelectron spectroscopy analyses. It has been revealed that the symmetry-broken interlayer twisting reduced the degeneracy of V 3d states and the van Hove singularity. This led to a redistribution of the density of electronic states near the Fermi level and consequently activated the Stoner ferromagnetism with improved density of itinerant d electrons. This work highlights V₂C MXene as a promising intrinsic room-temperature ferromagnetic material with potential applications in spintronics or spin-based electronics.

Localization transitions and mobility edges in quasiperiodic ladder

We investigate localization properties of two-coupled uniform chains (ladder) with quasiperiodic modulation on interchain coupling strength. We demonstrate that this ladder is equivalent to two Aubry-André chains when two legs are symmetric. Analytical and numerical results indicate the appearance of mobility edges in asymmetric ladder systems. We propose an easy-to-engineer quasiperiodic Moiré superlattice ladder system comprising two-coupled uniform chains. An irrational lattice constant difference results in a quasiperiodic structure. Numerical simulations indicate that such a system supports the existence of mobility edges. Furthermore, we demonstrate that the mobility edges can be detected through a dynamical method, that is based on the measurement of survival probability in the presence of a single imaginary negative potential. The results provide insights into localization transitions and mobility edges in experiments.

Efficient Fizeau drag from Dirac electrons in monolayer graphene

Fizeau demonstrated in 1850 that the speed of light can be modified when it is propagating in moving media¹. However, such control of the light speed has not been achieved efficiently with a fast-moving electron media by passing an electrical current. Because the strong electromagnetic coupling between the electron and light leads to the collective excitation of plasmon polaritons, it is hypothesized that Fizeau drag in electron flow systems manifests as a plasmonic Doppler effect. Experimental observation of the plasmonic Doppler effect in electronic systems has been challenge because the plasmon propagation speed is much faster than the electron drift velocity in conventional noble metals. Here we report direct observation of Fizeau drag of plasmon polaritons in strongly biased monolayer graphene by exploiting the high electron mobility and the slow plasmon propagation of massless Dirac electrons. The large bias current in graphene creates a fast-drifting Dirac electron medium hosting the plasmon polariton. This results in non-reciprocal plasmon propagation, where plasmons moving with the drifting electron media propagate at an enhanced speed. We measure the Doppler-shifted plasmon wavelength using cryogenic near-field infrared nanoscopy, which directly images the plasmon polariton mode in the biased graphene at low temperature. We observe a plasmon wavelength difference of up to 3.6 per cent between a plasmon moving with and a plasmon moving against the drifting electron media. Our findings on the plasmonic Doppler effect provide opportunities for electrical control of non-reciprocal surface plasmon polaritons in non-equilibrium systems.

Moiré superlattices and related moiré excitons in twisted van der Waals heterostructures

Recent advances in moiré superlattices and moiré excitons, such as quantum emission arrays, low-energy flat bands, and Mott insulators, have rapidly attracted attention in the fields of optoelectronics, materials, and energy research. The interlayer twist turns into a degree of freedom that alters the properties of the systems of materials, and the realization of moiré excitons also offers the feasibility of making artificial exciton crystals. Moreover, moiré excitons exhibit many exciting properties under the regulation of various external conditions, including spatial polarisation, alternating dipolar to alternating dipolar moments and gate-dependence to gate voltage dependence; all are pertinent to their applications in nano-photonics and quantum information. But the lag in theoretical development and the low-efficiency of processing technologies significantly limit the potential of moiré superlattice applications. In this review, we systematically summarise and discuss the recent progress in moiré superlattices and moiré excitons, and analyze the current challenges, and put forward relevant recommendations. There is no doubt that further research will lead to breakthroughs in their application and promote reforms and innovations in traditional solid-state physics and materials science.

Trigonal quasicrystalline states in [Formula: see text] rotated double moiré superlattices

We study the lattice configuration and electronic structure of a double moiré superlattice, which is composed of a graphene layer encapsulated by two other layers in a way such that the two hexagonal moiré patterns are arranged in a dodecagonal quasicrystalline configuration. We show that there are between 0 and 4 such configurations depending on the lattice mismatch between graphene and the encapsulating layer. We then reveal the resonant interaction, which is distinct from the conventional 2-, 3-, 4-wave mixing of moiré superlattices, that brings together and hybridizes twelve degenerate Bloch states of monolayer graphene. These states do not fully satisfy the dodecagonal quasicrystalline rotational symmetry due to the symmetry of the wave vectors involved. Instead, their wave functions exhibit trigonal quasicrystalline order, which lacks inversion symmetry, at the energies much closer to the charge neutrality point of graphene.

Stacking-engineered ferroelectricity in bilayer boron nitride

2D ferroelectrics with robust polarization down to atomic thicknesses provide building blocks for functional heterostructures. Experimental realization remains challenging because of the requirement of a layered polar crystal. Here, we demonstrate a rational design approach to engineering 2D ferroelectrics from a non-ferroelectric parent compound via employing van der Waals assembly. Parallel-stacked bilayer boron nitride exhibits out-of-plane electric polarization that reverses depending on the stacking order. The polarization switching is probed via the resistance of an adjacently stacked graphene sheet. Twisting the boron nitride sheets by a small angle changes the dynamics of switching thanks to the formation of moiré ferroelectricity with staggered polarization. The ferroelectricity persists to room temperature while keeping the high mobility of graphene, paving the way for potential ultrathin nonvolatile memory applications.

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.

Electronic spectrum of Kekulé patterned graphene considering second neighbor-interactions

The effects of second-neighbor interactions in Kekulé-Y patterned graphene electronic properties are studied starting from a tight-binding Hamiltonian. Thereafter, a low-energy effective Hamiltonian is obtained by projecting the high energy bands at the Γ point into the subspace defined by the Kekulé wave vector. The spectrum of the low energy Hamiltonian is in excellent agreement with the one obtained from a numerical diagonalization of the full tight-binding Hamiltonian. The main effect of the second-neighbour interaction is that a set of bands gains an effective mass and a shift in energy, thus lifting the degeneracy of the conduction bands at the Dirac point. This band structure is akin to a 'pseudo spin-one Dirac cone', a result expected for honeycomb lattices with a distinction between one third of the atoms in one sublattice. Finally, we present a study of Kekulé patterned graphene nanoribbons. This shows that the previous effects are enhanced as the width decreases. Moreover, edge states become dispersive, as expected due to second neighbors interaction, but here the Kek-Y bond texture results in an hybridization of both edge states. The present study shows the importance of second neighbors in realistic models of Kekulé patterned graphene, specially at surfaces.

Creation of moiré bands in a monolayer semiconductor by spatially periodic dielectric screening

Moiré superlattices of two-dimensional van der Waals materials have emerged as a powerful platform for designing electronic band structures and discovering emergent physical phenomena. A key concept involves the creation of long-wavelength periodic potential and moiré bands in a crystal through interlayer electronic hybridization or atomic corrugation when two materials are overlaid. Here we demonstrate a new approach based on spatially periodic dielectric screening to create moiré bands in a monolayer semiconductor. This approach relies on reduced dielectric screening of the Coulomb interactions in monolayer semiconductors and their environmental dielectric-dependent electronic band structure. We observe optical transitions between moiré bands in monolayer WSe₂ when it is placed close to small-angle-misaligned graphene on hexagonal boron nitride. The moiré bands are a result of long-range Coulomb interactions, which are strongly gate tunable, and can have versatile superlattice symmetries independent of the crystal lattice of the host material. Our result also demonstrates that monolayer semiconductors are sensitive local dielectric sensors.

Anisotropic band flattening in graphene with one-dimensional superlattices

Patterning graphene with a spatially periodic potential provides a powerful means to modify its electronic properties^1-3. In particular, in twisted bilayers, coupling to the resulting moiré superlattice yields an isolated flat band that hosts correlated many-body phases^4,5. However, both the symmetry and strength of the effective moiré potential are constrained by the constituent crystals, limiting its tunability. Here, we have exploited the technique of dielectric patterning⁶ to subject graphene to a one-dimensional electrostatic superlattice (SL)¹. We observed the emergence of multiple Dirac cones and found evidence that with increasing SL potential the main and satellite Dirac cones are sequentially flattened in the direction parallel to the SL basis vector, behaviour resulting from the interaction between the one-dimensional SL electric potential and the massless Dirac fermions hosted by graphene. Our results demonstrate the ability to induce tunable anisotropy in high-mobility two-dimensional materials, a long-desired property for novel electronic and optical applications^7,8. Moreover, these findings offer a new approach to engineering flat energy bands where electron interactions can lead to emergent properties⁹.

Growth of h-BN/graphene heterostructure using proximity catalysis

In this study, a proximity catalysis route was developed for the fast growth of graphene/h-BN vertical heterostructures on Cu foils, which shows much improved synthesis efficiency (500 times faster than other routes) and good crystalline quality graphene (large single crystalline length up to 10μm). The key advantage of our synthesis route is the introduction of fresh Cu foil (or Cu foam) into the high-temperature zone using a turntable. At high temperatures, Cu vapor acts as a gaseous catalyst, which can reduce the energy barrier of graphene growth and promote the decomposition of carbon sources. Therefore, after the first layer of hexagonal boron nitride is grown on the Cu substrate, another layer of graphene can be grown by introducing a fresh catalyst. Our calculations have revealed the catalytic effect and graphene growth contribution of Cu vapor evaporated by the suspended catalyst. We also investigated the growth sequence of graphene from 1 to 24 carbon atoms on h-BN/Cu and determined the morphology evolution of these carbon clusters. In this regard, multilayer stacked heterogeneous structures can be synthesized, thus increasing their potential applications in high performance electronic devices and energy harvesting/transition directions.

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.

Fermi Velocity Reduction of Dirac Fermions around the Brillouin Zone Center in In2 Se3 -Bilayer Graphene Heterostructures

Emergent phenomena such as unconventional superconductivity, Mott-like insulators, and the peculiar quantum Hall effect in graphene-based heterostructures are proposed to stem from the superlattice-induced renormalization of (moiré) Dirac fermions at the graphene Brillouin zone corners. Understanding the corresponding band structure commonly demands photoemission spectroscopy with both sub-meV resolution and large-momentum coverage, beyond the capability of the current state-of-the-art. Here the realization of moiré Dirac cones around the Brillouin zone center in monolayer In₂ Se₃ /bilayer graphene heterostructure is reported. The renormalization is evidenced by reduced Fermi velocity (≈23%) of the moiré Dirac cones and the reshaped Dirac point at the Γ point where they intersect. While there have been many theoretical predictions and much indirect experimental evidence, the findings here are the first direct observation of Fermi velocity reduction of the moiré Dirac cones. These features suggest strong In₂ Se₃ /graphene interlayer coupling, which is comparable with that in twisted bilayer graphene. The strategy expands the choice of materials in the heterostructure design and stimulates subsequent broad investigations of emergent physics at the sub-meV energy scale.

Nano-imaging photoresponse in a moiré unit cell of minimally twisted bilayer graphene

Graphene-based moiré superlattices have recently emerged as a unique class of tuneable solid-state systems that exhibit significant optoelectronic activity. Local probing at length scales of the superlattice should provide deeper insight into the microscopic mechanisms of photoresponse and the exact role of the moiré lattice. Here, we employ a nanoscale probe to study photoresponse within a single moiré unit cell of minimally twisted bilayer graphene. Our measurements reveal a spatially rich photoresponse, whose sign and magnitude are governed by the fine structure of the moiré lattice and its orientation with respect to measurement contacts. This results in a strong directional effect and a striking spatial dependence of the gate-voltage response within the moiré domains. The spatial profile and carrier-density dependence of the measured photocurrent point towards a photo-thermoelectric induced response that is further corroborated by good agreement with numerical simulations. Our work shows sub-diffraction photocurrent spectroscopy is an exceptional tool for uncovering the optoelectronic properties of moiré superlattices.

Spontaneous Folding Growth of Graphene on h-BN

Graphene has been the subject of much research, with structural engineering frequently used to harness its various properties. In particular, the concepts of graphene origami and kirigami have inspired the design of quasi-three-dimensional graphene structures, which possess intriguing mechanical, electronic, and optical properties. However, accurate controlling the folding process remains a big challenge. Here, we report the discovery of spontaneous folding growth of graphene on the h-BN substrate via adopting a simple chemical vapor deposition method. Folded edges are formed when two stacked graphene layers share a joint edge at a growth temperature up to 1300 °C. Using first-principles density functional theory calculations, the bilayer graphene with folded edges is demonstrated to be more stable than that with open edges. Utilizing this novel growth mode, hexagram bilayer graphene containing entirely sealed edges is eventually realized. Our findings provide a route for designing graphene devices with a new folding dimension.

Moiré-Potential-Induced Band Structure Engineering in Graphene and Silicene

A moiré pattern results from the projection of one periodic pattern to another with relative lattice constant or misalignment and provides great periodic potential to modify the electronic properties of pristine materials. In this Review, recent research on the effect of the moiré superlattice on the electronic structures of graphene and silicene, both of which possess a honeycomb lattice, is focused on. The moiré periodic potential is introduced by the interlayer interaction to realize abundant phenomena, including new generation of Dirac cones, emergence of Van Hove singularities (vHs) at the cross point of two sets of Dirac cones, Mott-like insulating behavior at half-filling state, unconventional superconductivity, and electronic Kagome lattice and flat band with nontrivial edge state. The role of interlayer coupling strength, which is determined by twist angle and buckling degree, in these exotic properties is discussed in terms of both the theoretical prediction and experimental measurement, and finally, the challenges and outlook for this field are discussed.

Large-area integration of two-dimensional materials and their heterostructures by wafer bonding

Integrating two-dimensional (2D) materials into semiconductor manufacturing lines is essential to exploit their material properties in a wide range of application areas. However, current approaches are not compatible with high-volume manufacturing on wafer level. Here, we report a generic methodology for large-area integration of 2D materials by adhesive wafer bonding. Our approach avoids manual handling and uses equipment, processes, and materials that are readily available in large-scale semiconductor manufacturing lines. We demonstrate the transfer of CVD graphene from copper foils (100-mm diameter) and molybdenum disulfide (MoS2) from SiO2/Si chips (centimeter-sized) to silicon wafers (100-mm diameter). Furthermore, we stack graphene with CVD hexagonal boron nitride and MoS2 layers to heterostructures, and fabricate encapsulated field-effect graphene devices, with high carrier mobilities of up to [Formula: see text]. Thus, our approach is suited for backend of the line integration of 2D materials on top of integrated circuits, with potential to accelerate progress in electronics, photonics, and sensing.

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.

Observation of Time-Reversal Invariant Helical Edge-Modes in Bilayer Graphene/WSe2 Heterostructure

Topological insulators, along with Chern insulators and quantum Hall insulator phases, are considered as paradigms for symmetry protected topological phases of matter. This article reports the experimental realization of the time-reversal invariant helical edge-modes in bilayer graphene/monolayer WSe₂-based heterostructures-a phase generally considered as a precursor to the field of generic topological insulators. Our observation of this elusive phase depended crucially on our ability to create mesoscopic devices comprising both a moiré superlattice potential and strong spin-orbit coupling; this resulted in materials whose electronic band structure could be tuned from trivial to topological by an external displacement field. We find that the topological phase is characterized by a bulk bandgap and by helical edge-modes with electrical conductance quantized exactly to 2e²/h in zero external magnetic field. We put the helical edge-modes on firm ground through supporting experiments, including the verification of predictions of the Landauer-Büttiker model for quantum transport in multiterminal mesoscopic devices. Our nonlocal transport properties measurements show that the helical edge-modes are dissipationless and equilibrate at the contact probes. We achieved the tunability of the different topological phases with electric and magnetic fields, which allowed us to achieve topological phase transitions between trivial and multiple, distinct topological phases. We also present results of a theoretical study of a realistic model which, in addition to replicating our experimental results, explains the origin of the topological insulating bulk and helical edge-modes. Our experimental and theoretical results establish a viable route to realizing the time-reversal invariant Z2 topological phase of matter.

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.

Investigations of Electron-Electron and Interlayer Electron-Phonon Coupling in van der Waals hBN/WSe2/hBN Heterostructures by Photoluminescence Excitation Experiments

Monolayers of transition metal dichalcogenides (TMDs) with their unique physical properties are very promising for future applications in novel electronic devices. In TMDs monolayers, strong and opposite spin splittings of the energy gaps at the K points allow for exciting carriers with various combinations of valley and spin indices using circularly polarized light, which can further be used in spintronics and valleytronics. The physical properties of van der Waals heterostructures composed of TMDs monolayers and hexagonal boron nitride (hBN) layers significantly depend on different kinds of interactions. Here, we report on observing both a strong increase in the emission intensity as well as a preservation of the helicity of the excitation light in the emission from hBN/WSe₂/hBN heterostructures related to interlayer electron-phonon coupling. In combined low-temperature (T = 7 K) reflectivity contrast and photoluminescence excitation experiments, we find that the increase in the emission intensity is attributed to a double resonance, where the laser excitation and the combined Raman mode A'₁ (WSe₂) + ZO (hBN) are in resonance with the excited (2s) and ground (1s) states of the A exciton in a WSe₂ monolayer. In reference to the 2s state, our interpretation is in contrast with previous reports, in which this state has been attributed to the hybrid exciton state existing only in the hBN-encapsulated WSe₂ monolayer. Moreover, we observe that the electron-phonon coupling also enhances the helicity preservation of the exciting light in the emission of all observed excitonic complexes. The highest helicity preservation of more than 60% is obtained in the emission of the neutral biexciton and negatively charged exciton (trion) in its triplet state. Additionally, to the best of our knowledge, the strongly intensified emission of the neutral biexciton XX⁰ at double resonance condition is observed for the first time.

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.

Fabrication of BP2T functionalized graphene via non-covalent π–π stacking interactions for enhanced ammonia detection

Graphene has stimulated great enthusiasm in a variety of fields, while its chemically inert surface still remains challenging for functionalization towards various applications. Herein, we report an approach to fabricate non-covalently functionalized graphene by employing π–π stacking interactions, which has potentialities for enhanced ammonia detection. 5,5′-Di(4-biphenylyl)-2,2′-bithiophene (BP2T) molecules are used in our work for the non-covalent functionalization through strong π–π interactions of aromatic structures with graphene, and systematic investigations by employing various spectroscopic and microscopic characterization methods confirm the successful non-covalent attachment of the BP2T on the top of graphene. From our gas sensing experiments, the BP2T functionalized graphene is promising for ammonia sensing with a 3-fold higher sensitivity comparing to that of the pristine graphene, which is mainly attributed to the enhanced binding energy between the ammonia and BP2T molecules derived by employing the Langmuir isotherm model. This work provides essential evidence of the π–π stacking interactions between graphene and aromatic molecules, and the reported approach also has the potential to be widely employed in a variety of graphene functionalizations for chemical detection.

Non-covalent functionalization of graphene has been achieved by employing π–π stacking interactions, and it is promising for ammonia detection with greatly enhanced sensitivity.

Substrate-Dependent Band Structures in Trilayer Graphene/h-BN Heterostructures

The tight-binding model has been spectacularly successful in elucidating the electronic and optical properties of a vast number of materials. Within the tight-binding model, the hopping parameters that determine much of the band structure are often taken as constants. Here, using ABA-stacked trilayer graphene as the model system, we show that, contrary to conventional wisdom, the hopping parameters and therefore band structures are not constants, but are systematically variable depending on their relative alignment angle between h-BN. Moreover, the addition or removal of the h-BN substrate results in an inversion of the K and K^{'} valley in trilayer graphene's lowest Landau level. Our work illustrates the oft-ignored and rather surprising impact of the substrates on band structures of 2D materials.

Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices

We study quantum phase transitions in graphene superlattices in external magnetic fields, where a framework is presented to classify multiflavor Dirac fermion critical points describing hopping-tuned topological phase transitions of integer and fractional Hofstadter-Chern insulators. We argue and provide numerical support for the existence of transitions that can be explained by a nontrivial interplay of Chern bands and van Hove singularities near charge neutrality. This work provides a route to critical phenomena beyond conventional quantum Hall plateau transitions.

Hofstadter Topology: Noncrystalline Topological Materials at High Flux

The Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding ∼10^{4}  T magnetic fields to a trivial band structure. In this Letter, we show that when a magnetic field is added to an initially topological band structure, a wealth of possible phases emerges. Remarkably, we find topological phases that cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with a nonzero Chern number or mirror Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with a nontrivial Kane-Mele invariant can be classified as a 3D topological insulator (TI) or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of twofold rotation and time reversal and show that there exists a higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group that exists at rational values of the flux. The advent of Moiré lattices renders our work relevant experimentally. Due to the enlarged Moiré unit cell, it is possible for laboratory-strength fields to reach one flux per plaquette and allow access to our proposed Hofstadter topological phase.

2D Materials and Heterostructures at Extreme Pressure

2D materials possess wide-tuning properties ranging from semiconducting and metallization to superconducting, etc., which are determined by their structure, empowering them to be appealing in optoelectronic and photovoltaic applications. Pressure is an effective and clean tool that allows modifications of the electronic structure, crystal structure, morphologies, and compositions of 2D materials through van der Waals (vdW) interaction engineering. This enables an insightful understanding of the variable vdW interaction induced structural changes, structure-property relations as well as contributes to the versatile implications of 2D materials. Here, the recent progress of high-pressure research toward 2D materials and heterostructures, involving graphene, boron nitride, transition metal dichalcogenides, 2D perovskites, black phosphorene, MXene, and covalent-organic frameworks, using diamond anvil cell is summarized. A detailed analysis of pressurized structure, phonon dynamics, superconducting, metallization, doping together with optical property is performed. Further, the pressure-induced optimized properties and potential applications as well as the vision of engineering the vdW interactions in heterostructures are highlighted. Finally, conclusions and outlook are presented on the way forward.

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.

Configurable phonon polaritons in twisted α-MoO3

Moiré engineering is being intensively investigated as a method to tune the electronic, magnetic and optical properties of twisted van der Waals materials. Advances in moiré engineering stem from the formation of peculiar moiré superlattices at small, specific twist angles. Here we report configurable nanoscale light-matter waves-phonon polaritons-by twisting stacked α-phase molybdenum trioxide (α-MoO₃) slabs over a broad range of twist angles from 0° to 90°. Our combined experimental and theoretical results reveal a variety of polariton wavefront geometries and topological transitions as a function of the twist angle. In contrast to the origin of the modified electronic band structure in moiré superlattices, the polariton twisting configuration is attributed to the electromagnetic interaction of highly anisotropic hyperbolic polaritons in stacked α-MoO₃ slabs. These results indicate twisted α-MoO₃ to be a promising platform for nanophotonic devices with tunable functionalities.

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.

Electric polarization related Dirac half-metallicity in Mn-trihalide Janus monolayers

A two-dimensional Dirac half-metal system, in which the 100% spin polarization and massless Dirac fermions can coexist, will show more advantages on the efficient spin injection and high spin mobility in spintronic devices. Moreover, it is attractive to achieve out-of-plane electric polarization in addition to the Dirac half-metal behavior, because this will open a new horizon in the field of multifunctional devices. In this work, a systematic study is made of Janus monolayers of Mn2X3Y3 (X, Y = Cl, Br and I, X ≠ Y) with asymmetric out-of-plane structural configurations, based on first-principles calculations. We demonstrate that monolayer Mn2X3Y3 freestanding films will remain stable experimentally by using the stability analysis. All the Janus monolayers show a ferromagnetic ground state and maintain their original DHM behavior. However, due to the large electric polarization, the hybridization intensities of Mn and the halogen atoms on both sides of Mn2Cl3I3 are very different, resulting in an obvious distortion of the spin-polarized Dirac cone. The distorted Dirac cone is repaired by the compression, indicating that strain can improve the orbital distortion induced by the electric polarization. All Mn2X3Y3 monolayer have in-plane magnetization anisotropy, which is mainly contributed by heavy halogen elements (Br and I), and the polarized substitution and biaxial strain will not change the easy magnetization orientation of the system. Thus, the electrically polarized Dirac half-metal system has potential for application in multifunctional spintronic devices.

Anomalous Cyclotron Motion in Graphene Superlattice Cavities

We consider graphene superlattice miniband fermions probed by electronic interferometry in magnetotransport experiments. By decoding the observed Fabry-Pérot interference patterns together with our corresponding quantum transport simulations, we find that the Dirac quasiparticles originating from the superlattice minibands do not undergo conventional cyclotron motion but follow more subtle trajectories. In particular, dynamics at low magnetic fields is characterized by peculiar, straight trajectory segments. Our results provide new insights into superlattice miniband fermions and open up novel possibilities to use periodic potentials in electron optics experiments.

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.

Non-invasive detection of glucose via a solution-gated graphene transistor

Owing to its high sensitivity, a solution-gated graphene transistor has rapidly emerged as a cutting edge technology in electrochemical sensing. In this work, composites of gold nanoparticles and reduced graphene oxide were synthesized on a glassy carbon electrode by using the electrodeposition method. A modified glassy carbon electrode was used as the gate electrode and assembled into the solution-gated graphene transistor device along with the graphene channel for a non-invasive glucose detection. The sensing mechanism was based on the change in current in the channel of the device caused by the addition of glucose, of which electro-oxidation on the surface of the gold nanoparticles and reduced graphene oxide led to a change in equivalent gate voltage, and consequently, affected the channel carrier concentration. The self-amplification effect of transistors was utilized in our sensors, which resulted in a detection limit that was 10 times lower than those of conventional electrochemical sensors. Compared to traditional enzymatic transistor sensors, the novel solution-gated graphene transistor nonenzymatic sensors based on gold nanoparticles and reduced graphene oxide demonstrated significant sensing advantages, such as a simple structure, wide linear range from 10 μM to 400 μM and 400 μM to 31 mM, and low detection limit down to 4 μM. The chemicals coexisting in human sweat e.g. sodium chloride, urea, and lactic acid imposed no distinct interference for the glucose detection. Therefore, we achieved a non-invasive detection of glucose in the artificial sweat samples with satisfactory sensing results. This work demonstrates an effective route for non-invasive glucose testing in practical clinical diagnosis by using nonenzymatic, solution-gated graphene transistor devices.

Gate-Tunable Two-Dimensional Superlattices in Graphene

We report an efficient technique to induce gate-tunable two-dimensional superlattices in graphene by the combined action of a back gate and a few-layer graphene patterned bottom gate complementary to existing methods. The patterned gates in our approach can be easily fabricated and implemented in van der Waals stacking procedures, allowing flexible use of superlattices with arbitrary geometry. In transport measurements on a superlattice with a lattice constant a = 40 nm, well-pronounced satellite Dirac points and signatures of the Hofstadter butterfly including a nonmonotonic quantum Hall response are observed. Furthermore, the experimental results are accurately reproduced in transport simulations and show good agreement with features in the calculated band structure. Overall, we present a comprehensive picture of graphene-based superlattices, featuring a broad range of miniband effects, both in experiment and in theoretical modeling. The presented technique is suitable for studying more advanced geometries which are not accessible by other methods.

Highly Ordered Boron Nitride/Epigraphene Epitaxial Films on Silicon Carbide by Lateral Epitaxial Deposition

The realization of high-performance nanoelectronics requires control of materials at the nanoscale. Methods to produce high quality epitaxial graphene (EG) nanostructures on silicon carbide are known. The next step is to grow van der Waals semiconductors on top of EG nanostructures. Hexagonal boron nitride (h-BN) is a wide bandgap semiconductor with a honeycomb lattice structure that matches that of graphene, making it ideally suited for graphene-based nanoelectronics. Here, we describe the preparation and characterization of multilayer h-BN grown epitaxially on EG using a migration-enhanced metalorganic vapor phase epitaxy process. As a result of the lateral epitaxial deposition (LED) mechanism, the grown h-BN/EG heterostructures have highly ordered epitaxial interfaces, as desired in order to preserve the transport properties of pristine graphene. Atomic scale structural and energetic details of the observed row-by-row growth mechanism of the two-dimensional (2D) epitaxial h-BN film are analyzed through first-principles simulations, demonstrating one-dimensional nucleation-free-energy-barrierless growth. This industrially relevant LED process can be applied to a wide variety of van der Waals materials.

Emergence of orbital angular moment at van Hove singularity in graphene/h-BN moiré superlattice

Bloch electrons lacking inversion symmetry exhibit orbital magnetic moments owing to the rotation around their center of mass; this moment induces a valley splitting in a magnetic field. For the graphene/h-BN moiré superlattice, inversion symmetry is broken by the h-BN. The superlattice potential generates a series of Dirac points (DPs) and van Hove singularities (vHSs) within an experimentally accessible low energy state, providing a platform to study orbital moments with respect to band structure. In this work, theoretical calculations and magnetothermoelectric measurements are combined to reveal the emergence of an orbital magnetic moment at vHSs in graphene/h-BN moiré superlattices. The thermoelectric signal for the vHS at the low energy side of the hole-side secondary DP exhibited significant magnetic field-induced valley splitting with an effective g-factor of approximately 130; splitting for other vHSs was negligible. This was attributed to the emergence of an orbital magnetic moment at the second vHS at the hole-side.

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.