Cloning of Dirac fermions in graphene superlattices

Deterministic fabrication of graphene hexagonal boron nitride moiré superlattices

The electronic properties of moiré heterostructures depend sensitively on the relative orientation between layers of the stack. For example, near-magic-angle twisted bilayer graphene (TBG) commonly shows superconductivity, yet a TBG sample with one of the graphene layers rotationally aligned to a hexagonal Boron Nitride (hBN) cladding layer provided experimental observation of orbital ferromagnetism. To create samples with aligned graphene/hBN, researchers often align edges of exfoliated flakes that appear straight in optical micrographs. However, graphene or hBN can cleave along either zig-zag or armchair lattice directions, introducing a [Formula: see text] ambiguity in the relative orientation of two flakes. By characterizing the crystal lattice orientation of exfoliated flakes prior to stacking using Raman and second-harmonic generation for graphene and hBN, respectively, we unambiguously align monolayer graphene to hBN at a near-[Formula: see text], not [Formula: see text], relative twist angle. We confirm this alignment by torsional force microscopy of the graphene/hBN moiré on an open-face stack, and then by cryogenic transport measurements, after full encapsulation with a second, nonaligned hBN layer. This work demonstrates a key step toward systematically exploring the effects of the relative twist angle between dissimilar materials within moiré heterostructures.

Efficient Charge Transfer in Graphene/CrOCl Heterostructures by van der Waals Interfacial Coupling

Due to the large volume of exposed atoms and electrons at the surface of two-dimensional materials, interfacial charge coupling has been proven as an efficient strategy to engineer the electronic structures of two-dimensional materials assembled in van der Waals heterostructures. Recently, heterostructures formed by graphene stacked with CrOCl have demonstrated intriguing quantum states, including a distorted quantum Hall phase in the monolayer graphene and the unconventional correlated insulator in the bilayer graphene. Yet, the understanding of the interlayer charge coupling in the heterostructure remains challenging. Here, we demonstrate clear evidences of efficient hole doping in the interfacial-coupled graphene/CrOCl heterostructure by detailed Raman spectroscopy and electrical transport measurements. The observation of significant blue shifts and stiffness of graphene Raman modes quantitatively determines the concentration of hole injection of about 1.2 × 1013 cm-2 from CrOCl to graphene, which is highly consistent with the enhanced conductivity of graphene. First-principles calculations based on density functional theory reveal that due to the large work function difference and the electronegativity of Cl atoms in CrOCl, the electrons are efficiently transferred from graphene to CrOCl, leading to hole doping in graphene. Our findings provide clues for understanding the exotic physical properties of graphene/CrOCl heterostructures, paving the way for further engineering of quantum electronic states by efficient interfacial charge coupling in van der Waals heterostructures.

Modulation of Electrostatic Potential in 2D Crystal Engineered by an Array of Alternating Polar Molecules

The moiré potential in rotationally misfit two-dimensional (2D) heterostructures has been used to build artificial exciton and electron lattices, which have become platforms for realizing exotic electronic phases. Here, we demonstrate a different approach to create a superlattice potential in 2D crystals by using the near field of an array of polar molecules. A bilayer of titanyl phthalocyanine (TiOPc), consisting of alternating out-of-plane dipoles, is deposited on monolayer MoS2. Time-resolved two-photon photoemission spectroscopy reveals a pair of interlayer exciton states with an energy difference of ∼0.1 eV, which is consistent with the electrostatic potential modulation induced by the TiOPc bilayer as determined by density functional theory calculations. Because the symmetry and the period of this potential superlattice can be changed readily by using molecules of different shapes and sizes, molecule/2D heterostructures can be promising platforms for designing artificial exciton and electron lattices.

Giant Second Harmonic Generation in Supertwisted WS2 Spirals Grown in Step-Edge Particle-Induced Non-Euclidean Surfaces

In moiré crystals resulting from the stacking of twisted two-dimensional (2D) layered materials, a subtle adjustment in the twist angle surprisingly gives rise to a wide range of correlated optical and electrical properties. Herein, we report the synthesis of supertwisted WS2 spirals and the observation of giant second harmonic generation (SHG) in these spirals. Supertwisted WS2 spirals featuring different twist angles are synthesized on a Euclidean or step-edge particle-induced non-Euclidean surface using carefully designed water-assisted chemical vapor deposition. We observed an oscillatory dependence of SHG intensity on layer number, attributed to atomically phase-matched nonlinear dipoles within layers of supertwisted spiral crystals where inversion symmetry is restored. Through an investigation into the twist angle evolution of SHG intensity, we discovered that the stacking model between layers plays a crucial role in determining the nonlinearity, and the SHG signals in supertwisted spirals exhibit enhancements by a factor of 2 to 136 when compared with the SHG of the single-layer structure. These findings provide helpful perspectives on the rational growth of 2D twisted structures and the implementation of twist angle adjustable endowing them great potential for exploring strong coupling correlation physics and applications in the field of twistronics.

Dispersion-Selective Band Engineering in an Artificial Kagome Superlattice

The relentless pursuit of band structure engineering continues to be a fundamental aspect in solid-state research. Here, we meticulously construct an artificial kagome potential to generate and control multiple Dirac bands of graphene. This unique high-order potential harbors natural multiperiodic components, enabling the reconstruction of band structures through different potential contributions. As a result, the band components, each characterized by distinct dispersions, shift in energy at different velocities in response to the variation of artificial potential. Thereby, we observe a significant spectral weight redistribution of the multiple Dirac peaks. Furthermore, the magnetic field can effectively weaken the superlattice effect and reactivate the intrinsic Dirac band. Overall, we achieve actively dispersion-selective band engineering, a functionality that would substantially increase the freedom in band design.

Emergent phases in graphene flat bands

Electronic correlations in two-dimensional materials play a crucial role in stabilising emergent phases of matter. The realisation of correlation-driven phenomena in graphene has remained a longstanding goal, primarily due to the absence of strong electron-electron interactions within its low-energy bands. In this context, magic-angle twisted bilayer graphene has recently emerged as a novel platform featuring correlated phases favoured by the low-energy flat bands of the underlying moiré superlattice. Notably, the observation of correlated insulators and superconductivity, and the interplay between these phases have garnered significant attention. A wealth of correlated phases with unprecedented tunability was discovered subsequently, including orbital ferromagnetism, Chern insulators, strange metallicity, density waves, and nematicity. However, a comprehensive understanding of these closely competing phases remains elusive. The ability to controllably twist and stack multiple graphene layers has enabled the creation of a whole new family of moiré superlattices with myriad properties. Here, we review the progress and development achieved so far, encompassing the rich phase diagrams offered by these graphene-based moiré systems. Additionally, we discuss multiple phases recently observed in non-moiré multilayer graphene systems. Finally, we outline future opportunities and challenges for the exploration of hidden phases in this new generation of moiré materials.

Directional Localization from a Magnetic Field in Moiré Systems

Moiré materials provide a highly tunable platform in which novel electronic phenomena can emerge. We study strained moiré materials in a uniform magnetic field and predict highly anisotropic electrical conductivity that switches easy axis as magnetic field or strain is varied. The dramatic anisotropy reflects one-dimensional localization (directional localization) of the electron wave functions along a crystal axis due to quantum interference effects. This can be understood in an effective one-dimensional quasiperiodic Aubry-André-Harper-like model, or in a complementary semiclassical picture. This phenomenon should be observable in strained moiré materials at realistic fields and low strain disorder, as well as unstrained systems with anisotropic Fermi surfaces.

Dynamic Acoustic Beamshaping with Coupling-Immune Moiré Metasurfaces

Moiré effects arising from mutually twisted metasurfaces have showcased remarkable wave manipulation capabilities, unveiling tantalizing emerging phenomena such as acoustic moiré flat bands and topological phase transitions. However, the pursuit of strong near-field coupling in layers has necessitated acoustic moiré metasurfaces to be tightly stacked at narrow distances in the subwavelength range. Here, moiré effects beyond near-field interlayer coupling in acoustics are reported and the concept of coupling-immune moiré metasurfaces is proposed. Remote acoustic moiré effects decoupled from the interlayer distance are theoretically, numerically, and experimentally demonstrated. Tunable out-of-plane acoustic beam scanning is successfully achieved by dynamically controlling twist angles. The engineered coupling-immune properties are further extended to multilayered acoustic moiré metasurfaces and manipulation of acoustic vortices. Good robustness against external disturbances is also observed for the fabricated coupling-immune acoustic moiré metasurfaces. The presented work unlocks the potential of twisted moiré devices for out-of-plane acoustic beam shaping, enabling practical applications in remote dynamic detection, and multiplexed underwater acoustic communication.

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

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

Emergent Correlated Phases in Rhombohedral Trilayer Graphene Induced by Proximity Spin-Orbit and Exchange Coupling

The impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagram of rhombohedral trilayer graphene (RTG) is investigated theoretically. By employing ab initio-fitted effective models of RTG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr_{2}Ge_{2}Te_{6} (exchange proximity effect), we incorporate the Coulomb interactions within the random-phase approximation to explore potential correlated phases at different displacement fields and doping. We find a rich spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a spin-valley-coherent phase due to the presence of valley-Zeeman coupling. Similarly, proximity exchange removes the phase degeneracies by biasing the spin direction, enabling a magnetocorrelation effect-strong sensitivity of the correlated phases to the relative magnetization orientations (parallel or antiparallel) of the encapsulating ferromagnetic layers.

Gold-Template-Assisted Mechanical Exfoliation of Large-Area 2D Layers Enables Efficient and Precise Construction of Moiré Superlattices

Moiré superlattices, consisting of rotationally aligned 2D atomically thin layers, provide a highly novel platform for the study of correlated quantum phenomena. However, reliable and efficient construction of moiré superlattices is challenging because of difficulties to accurately angle-align small exfoliated 2D layers and the need to shun wet-transfer processes. Here, efficient and precise construction of various moiré superlattices is demonstrated by picking up and stacking large-area 2D mono- or few-layer crystals with predetermined crystal axes, made possible by a gold-template-assisted mechanical exfoliation method. The exfoliated 2D layers are semiconductors, superconductors, or magnets and their high quality is confirmed by photoluminescence and Raman spectra and by electrical transport measurements of fabricated field-effect transistors and Hall devices. Twisted homobilayers with angle-twisting accuracy of ≈0.3°, twisted heterobilayers with sub-degree angle-alignment accuracy, and multilayer superlattices are precisely constructed and characterized by their moiré patterns, interlayer excitons, and second harmonic generation. The present study paves the way for exploring emergent phenomena in moiré superlattices.

Topological Flat Bands in Graphene Super-Moiré Lattices

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

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

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

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

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

Stacking engineering in layered homostructures: transitioning from 2D to 3D architectures

Artificial materials, characterized by their distinctive properties and customized functionalities, occupy a central role in a wide range of applications including electronics, spintronics, optoelectronics, catalysis, and energy storage. The emergence of atomically thin two-dimensional (2D) materials has driven the creation of artificial heterostructures, harnessing the potential of combining various 2D building blocks with complementary properties through the art of stacking engineering. The promising outcomes achieved for heterostructures have spurred an inquisitive exploration of homostructures, where identical 2D layers are precisely stacked. This perspective primarily focuses on the field of stacking engineering within layered homostructures, where precise control over translational or rotational degrees of freedom between vertically stacked planes or layers is paramount. In particular, we provide an overview of recent advancements in the stacking engineering applied to 2D homostructures. Additionally, we will shed light on research endeavors venturing into three-dimensional (3D) structures, which allow us to proactively address the limitations associated with artificial 2D homostructures. We anticipate that the breakthroughs in stacking engineering in 3D materials will provide valuable insights into the mechanisms governing stacking effects. Such advancements have the potential to unlock the full capability of artificial layered homostructures, propelling the future development of materials, physics, and device applications.

Twisted van der Waals Quantum Materials: Fundamentals, Tunability, and Applications

Twisted van der Waals (vdW) quantum materials have emerged as a rapidly developing field of two-dimensional (2D) semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single photon emission, nonlinear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moiré patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This paper offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moiré superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes, lasers, and photodetectors. It highlights the unique ability of moiré superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moiré superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.

Controlling Umklapp Scattering in a Bilayer Graphene Moiré Superlattice

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

Transport Anisotropy in One-Dimensional Graphene Superlattice in the High Kronig-Penney Potential Limit

One-dimensional graphene superlattice subjected to strong Kronig-Penney (KP) potential is promising for achieving the electron-lensing effect, while previous studies utilizing the modulated dielectric gates can only yield a moderate, spatially dispersed potential profile. Here, we realize high KP potential modulation of graphene via nanoscale ferroelectric domain gating. Graphene transistors are fabricated on PbZr_{0.2}Ti_{0.8}O_{3} back gates patterned with periodic, 100-200 nm wide stripe domains. Because of band reconstruction, the h-BN top gating induces satellite Dirac points in samples with current along the superlattice vector s[over ^], a feature absent in samples with current perpendicular to s[over ^]. The satellite Dirac point position scales with the superlattice period (L) as ∝L^{β}, with β=-1.18±0.06. These results can be well explained by the high KP potential scenario, with the Fermi velocity perpendicular to s[over ^] quenched to about 1% of that for pristine graphene. Our study presents a promising material platform for realizing electron supercollimation and investigating flat band phenomena.

Towards large scale integration of MoS2/graphene heterostructure with ALD-grown MoS2

In the pursuit of ultrathin and highly sensitive photodetectors, a promising approach involves leveraging the combination of light-sensitive two-dimensional (2D) semiconducting transition-metal dichalcogenides, such as MoS2and the high electrical conductivity of graphene. Over the past decade, exfoliated 2D materials and electron-beam lithography have been used extensively to demonstrate feasibility on single devices. But for these devices to be used in the real-world systems, it is necessary to demonstrate good device performance similar to lab-based devices with repeatability of the results from device to device and a path to large scale manufacturing. To work in this way, a fabrication process of MoS2/graphene vertical heterostructures with a wafer-scale integration in a CMOS compatible foundry environment is evaluated here. Large-scale atomic layer deposition on 8 inch silicon wafers is used for the growth of MoS2layers which are then transferred on a 4 inch graphene-based wafer. The MoS2/graphene phototransistors are fabricated collectively, achieving a minimum channel length of 10μm. The results measured on dozen of devices demonstrate a photoresponsivity of 50 A W-1and a remarkable sensitivity as low as 10 nW at 660 nm. These results not only compete with lab-based photodetectors made of chemical vapor deposition grown MoS2layers transferred on graphene, but also pave the way for the large-scale integration of these emerging 2D heterostructures in optoelectronic devices and sensors.

Engineering correlated insulators in bilayer graphene with a remote Coulomb superlattice

Electron superlattices allow the engineering of correlated and topological quantum phenomena. The recent emergence of moiré superlattices in two-dimensional heterostructures has led to exciting discoveries related to quantum phenomena. However, the requirement for the moiré pattern poses stringent limitations, and its potential cannot be switched on and off. Here, we demonstrate remote engineering and on/off switching of correlated states in bilayer graphene. Employing a remote Coulomb superlattice realized by localized electrons in twisted bilayer WS2, we impose a Coulomb superlattice in the bilayer graphene with period and strength determined by the twisted bilayer WS2. When the remote superlattice is turned off, the two-dimensional electron gas in the bilayer graphene is described by a Fermi liquid. When it is turned on, correlated insulating states at both integer and fractional filling factors emerge. This approach enables in situ control of correlated quantum phenomena in two-dimensional materials hosting a two-dimensional electron gas.

Graphene/Hexagonal Boron Nitride Heterostructures for O2 Activation and CO Oxidation: Metal-Free Catalysts by Design

Pristine graphene and h-BN monolayers are chemically inert to oxygen and thus exhibit very limited catalytic activity toward O2 activation. Herein, we show that graphene/h-BN heterostructures exhibit a surprising O2 activation capability. We theoretically designed ten graphene/h-BN heterostructures with three types of interfaces and investigated their catalytic activities toward O2 activation and CO-oxidation. In general, O2 can be molecularly chemisorbed and activated on electron-rich graphene/h-BN heterostructures. Electron-deficient graphene/h-BN heterostructures can lead to dissociative O2 adsorption with relatively low dissociation energy barriers (<0.4 eV). For CO-oxidation, the computed energy barrier can be as low as 0.67 eV. The high catalytic activities toward O2 stem from either electron-deficient heterostructures' accumulated electrons or electron richness and low work function for the electron-rich heterostructures. Although the catalytic activities of graphene/h-BN heterostructures depend strongly on the interface type, they are insensitive to the patterns of BN-substitutes, hence benefiting applicability of a wide range of heterostructures.

Kagome Quantum Oscillations in Graphene Superlattices

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

Exfoliable Transition Metal Chalcogenide Semiconductor NbSe2I2

As the field of exfoliated van der Waals electronics grows to include complex heterostructures, the variety of available in-plane symmetries and geometries becomes increasingly valuable. In this work, we present an efficient chemical vapor transport synthesis of NbSe2I2 with the triclinic space group P1̅. This material contains Nb-Nb dimers and an in-plane crystallographic angle γ = 61.3°. We show that NbSe2I2 can be exfoliated down to few-layer and monolayer structures and use Raman spectroscopy to test the preservation of the crystal structure of exfoliated thin films. The crystal structure was verified by single-crystal and powder X-ray diffraction methods. Density functional theory calculations show triclinic NbSe2I2 to be a semiconductor with a band gap of around 1 eV, with similar band structure features for bulk and monolayer crystals. The physical properties of NbSe2I2 have been characterized by transport, thermal, optical, and magnetic measurements, demonstrating triclinic NbSe2I2 to be a diamagnetic semiconductor that does not exhibit any phase transformation below room temperature.

De Haas-van Alphen spectroscopy and magnetic breakdown in moiré graphene

Quantum oscillations originating from the quantization of electron cyclotron orbits provide sensitive diagnostics of electron bands and interactions. We report on nanoscale imaging of the thermodynamic magnetization oscillations caused by the de Haas-van Alphen effect in moiré graphene. Scanning by means of superconducting quantum interference device (SQUID)-on-tip in Bernal bilayer graphene crystal axis-aligned to hexagonal boron nitride reveals large magnetization oscillations with amplitudes reaching 500 Bohr magneton per electron in weak magnetic fields, unexpectedly low frequencies, and high sensitivity to superlattice filling fraction. The oscillations allow us to reconstruct the complex band structure, revealing narrow moiré bands with multiple overlapping Fermi surfaces separated by unusually small momentum gaps. We identified sets of oscillations that violate the textbook Onsager Fermi surface sum rule, signaling formation of broad-band particle-hole superposition states induced by coherent magnetic breakdown.

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.

Reconfigurable moiré nanolaser arrays with phase synchronization

Miniaturized lasers play a central role in the infrastructure of modern information society. The breakthrough in laser miniaturization beyond the wavelength scale has opened up new opportunities for a wide range of applications1-4, as well as for investigating light-matter interactions in extreme-optical-field localization and lasing-mode engineering5-19. An ultimate objective of microscale laser research is to develop reconfigurable coherent nanolaser arrays that can simultaneously enhance information capacity and functionality. However, the absence of a suitable physical mechanism for reconfiguring nanolaser cavities hinders the demonstration of nanolasers in either a single cavity or a fixed array. Here we propose and demonstrate moiré nanolaser arrays based on optical flatbands in twisted photonic graphene lattices, in which coherent nanolasing is realized from a single nanocavity to reconfigurable arrays of nanocavities. We observe synchronized nanolaser arrays exhibiting high spatial and spectral coherence, across a range of distinct patterns, including P, K and U shapes and the Chinese characters '' and '' ('China' in Chinese). Moreover, we obtain nanolaser arrays that emit with spatially varying relative phases, allowing us to manipulate emission directions. Our work lays the foundation for the development of reconfigurable active devices that have potential applications in communication, LiDAR (light detection and ranging), optical computing and imaging.

Symmetry-Broken Chern Insulators in Twisted Double Bilayer Graphene

Twisted double bilayer graphene (tDBG) has emerged as a rich platform for studying strongly correlated and topological states, as its flat bands can be continuously tuned by both a perpendicular displacement field and a twist angle. Here, we construct a phase diagram representing the correlated and topological states as a function of these parameters, based on measurements of over a dozen tDBG devices encompassing two distinct stacking configurations. We find a hierarchy of symmetry-broken states that emerge sequentially as the twist angle approaches an apparent optimal value of θ ≈ 1.34°. Nearby this angle, we discover a symmetry-broken Chern insulator (SBCI) state associated with a band filling of 7/2 as well as an incipient SBCI state associated with 11/3 filling. We further observe an anomalous Hall effect at zero field in all samples supporting SBCI states, indicating spontaneous time-reversal symmetry breaking and possible moiré unit cell enlargement at zero magnetic field.

A Novel Quasi-Planar Two-dimensional Carbon Sulfide with Negative Poisson's Ratio and Dirac Fermions

In the present study, a novel and unconventional two-dimensional (2D) material with Dirac electronic features has been designed using sulflower with the help of density functional theory methods and first principles calculations. This 2D material comprises of hetero atoms (C, S) and belongs to the tetragonal lattice with P4 /nmm space group. Scrutiny of the results show that the 2D nanosheet exhibits a nanoporous wave-like geometrical structure. Quantum molecular dynamics simulations and phonon mode analysis emphasize the dynamical and thermal stability. The novel 2D nanosheet is an auxetic material with an anisotropy in the in-plane mechanical properties. Both composition and geometrical features are completely different from the conditions necessary for the formation of Dirac cones in graphene. However, the presence of semi-metallic nature, linear band dispersion relation, massive fermions and massless Dirac fermions are observed in the novel 2D nanosheet. The massless Dirac fermions exhibit highly isotropic Fermi velocities (vf =0.68×106  m/s) along all crystallographic directions. The zero-band gap semi metallic features of the novel 2D nanosheet are perturbative to the electric field and external strain.

Kinetic magnetism in triangular moiré materials

Magnetic properties of materials ranging from conventional ferromagnetic metals to strongly correlated materials such as cuprates originate from Coulomb exchange interactions. The existence of alternate mechanisms for magnetism that could naturally facilitate electrical control has been discussed theoretically1-7, but an experimental demonstration8 in an extended system has been missing. Here we investigate MoSe2/WS2 van der Waals heterostructures in the vicinity of Mott insulator states of electrons forming a frustrated triangular lattice and observe direct evidence of magnetic correlations originating from a kinetic mechanism. By directly measuring electronic magnetization through the strength of the polarization-selective attractive polaron resonance9,10, we find that when the Mott state is electron-doped, the system exhibits ferromagnetic correlations in agreement with the Nagaoka mechanism.

Emerging Characteristics and Properties of Moiré Materials

In recent years, scientists have conducted extensive research on Moiré materials and have discovered some compelling properties. The Moiré superlattice allows superconductivity through flat-band and strong correlation effects. The presence of flat bands causes the Moiré material to exhibit topological properties as well. Modulating electronic interactions with magnetic fields in Moiré materials enables the fractional quantum Hall effect. In addition, Moiré materials have ferromagnetic and antiferromagnetic properties. By tuning the interlayer coupling and spin interactions of the Moiré superlattice, different magnetic properties can be achieved. Finally, this review also discusses the applications of Moiré materials in the fields of photocurrent, superconductivity, and thermoelectricity. Overall, Moiré superlattices provide a new dimension in the development of two-dimensional materials.

Edge Contacts to Atomically Precise Graphene Nanoribbons

Bottom-up-synthesized graphene nanoribbons (GNRs) are an emerging class of designer quantum materials that possess superior properties, including atomically controlled uniformity and chemically tunable electronic properties. GNR-based devices are promising candidates for next-generation electronic, spintronic, and thermoelectric applications. However, due to their extremely small size, making electrical contact with GNRs remains a major challenge. Currently, the most commonly used methods are top metallic electrodes and bottom graphene electrodes, but for both, the contact resistance is expected to scale with overlap area. Here, we develop metallic edge contacts to contact nine-atom-wide armchair GNRs (9-AGNRs) after encapsulation in hexagonal boron-nitride (h-BN), resulting in ultrashort contact lengths. We find that charge transport in our devices occurs via two different mechanisms: at low temperatures (9 K), charges flow through single GNRs, resulting in quantum dot (QD) behavior with well-defined Coulomb diamonds (CDs), with addition energies in the range of 16 to 400 meV. For temperatures above 100 K, a combination of temperature-activated hopping and polaron-assisted tunneling takes over, with charges being able to flow through a network of 9-AGNRs across distances significantly exceeding the length of individual GNRs. At room temperature, our short-channel field-effect transistor devices exhibit on/off ratios as high as 3 × 105 with on-state current up to 50 nA at 0.2 V. Moreover, we find that the contact performance of our edge-contact devices is comparable to that of top/bottom contact geometries but with a significantly reduced footprint. Overall, our work demonstrates that 9-AGNRs can be contacted at their ends in ultra-short-channel FET devices while being encapsulated in h-BN.

Ballistic transport spectroscopy of spin-orbit-coupled bands in monolayer graphene on WSe2

Van der Waals interactions with transition metal dichalcogenides were shown to induce strong spin-orbit coupling (SOC) in graphene, offering great promises to combine large experimental flexibility of graphene with unique tuning capabilities of the SOC. Here, we probe SOC-driven band splitting and electron dynamics in graphene on WSe2 by measuring ballistic transverse magnetic focusing. We found a clear splitting in the first focusing peak whose evolution in charge density and magnetic field is well reproduced by calculations using the SOC strength of ~ 13 meV, and no splitting in the second peak that indicates stronger Rashba SOC. Possible suppression of electron-electron scatterings was found in temperature dependence measurement. Further, we found that Shubnikov-de Haas oscillations exhibit a weaker band splitting, suggesting that it probes different electron dynamics, calling for a new theory. Our study demonstrates an interesting possibility to exploit ballistic electron motion pronounced in graphene for emerging spin-orbitronics.

Probing the Twist-Controlled Interlayer Coupling in Artificially Stacked Transition Metal Dichalcogenide Bilayers by Second-Harmonic Generation

Interlayer coupling plays a critical role in the electronic band structures and optoelectronic properties of van der Waals (vdW) materials and heterostructures. Here, we utilize optical second-harmonic generation (SHG) measurements to probe the twist-controlled interlayer coupling in artificially stacked WSe2/WSe2 homobilayers and WSe2/WS2 and WSe2/MoS2 heterobilayers with a postannealing procedure. In the large angle twisted WSe2/WSe2 and WSe2/WS2, the angular dependence of the SHG intensity follows the interference relations up to angles above 10°. For lower angles, the SHG is significantly suppressed. Furthermore, for the twisted WSe2/MoS2 the SHG intensity largely deviates from the coherent superposition model and shows consistent quenching for all the stacking angles. The suppressed SHG in twisted transition metal dichalcogenide (TMDC) bilayers is predominantly attributed to the interlayer coupling between the two adjacent monolayers. The evolution of the interlayer Raman mode in WSe2 demonstrates that the interlayer coupling in the twisted WSe2/WSe2 and WSe2/WS2 is highly angle-dependent. Alternatively, the interlayer coupling generally exists in the twisted WSe2/MoS2, regardless of the different angles. The interlayer coupling is further confirmed by the quenching and red-shift of the photoluminescence of WSe2 in the twisted TMDC bilayers. Combined with density functional theory calculations, we reveal that the stacking-angle-modulated interlayer coupling originates from the variation of the interlayer spacing and the binding energy in the twisted TMDC bilayers.

Stacking transfer of wafer-scale graphene-based van der Waals superlattices

High-quality graphene-based van der Waals superlattices are crucial for investigating physical properties and developing functional devices. However, achieving homogeneous wafer-scale graphene-based superlattices with controlled twist angles is challenging. Here, we present a flat-to-flat transfer method for fabricating wafer-scale graphene and graphene-based superlattices. The aqueous solution between graphene and substrate is removed by a two-step spinning-assisted dehydration procedure with the optimal wetting angle. Proton-assisted treatment is further used to clean graphene surfaces and interfaces, which also decouples graphene and neutralizes the doping levels. Twist angles between different layers are accurately controlled by adjusting the macroscopic stacking angle through their wafer flats. Transferred films exhibit minimal defects, homogeneous morphology, and uniform electrical properties over wafer scale. Even at room temperature, robust quantum Hall effects are observed in graphene films with centimetre-scale linewidth. Our stacking transfer method can facilitate the fabrication of graphene-based van der Waals superlattices and accelerate functional device applications.

Inducing Single Spin-Polarized Flat Bands in Monolayer Graphene

Due to the fundamental and technological implications in driving the appearance of non-trivial, exotic topological spin textures and emerging symmetry-broken phases, flat electronic bands in 2D materials, including graphene, are nowadays a relevant topic in the field of spintronics. Here, via europium doping, single spin-polarized bands are generated in monolayer graphene supported by the Co(0001) surface. The doping is controlled by Eu positioning, allowing for the formation of aK ¯ $\bar{\mathrm{K}}$ -valley localized single spin-polarized low-dispersive parabolic band close to the Fermi energy when Eu is on top, and of a π* flat band with single spin character when Eu is intercalated underneath graphene. In the latter case, Eu also induces a bandgap opening at the Dirac point while the Eu 4f states act as a spin filter, splitting the π band into two spin-polarized branches. The generation of flat bands with single spin character, as revealed by the spin- and angle-resolved photoemission spectroscopy (ARPES) experiments, complemented by density functional theory (DFT) calculations, opens up new pathways toward the realization of spintronic devices exploiting such novel exotic electronic and magnetic states.

Stack growth of wafer-scale van der Waals superconductor heterostructures

Two-dimensional (2D) van der Waals (vdW) heterostructures have attracted considerable attention in recent years1-5. The most widely used method of fabrication is to stack mechanically exfoliated micrometre-sized flakes6-18, but this process is not scalable for practical applications. Despite thousands of 2D materials being created, using various stacking combinations1-3,19-21, hardly any large 2D superconductors can be stacked intact into vdW heterostructures, greatly restricting the applications for such devices. Here we report a high-to-low temperature strategy for controllably growing stacks of multiple-layered vdW superconductor heterostructure (vdWSH) films at a wafer scale. The number of layers of 2D superconductors in the vdWSHs can be precisely controlled, and we have successfully grown 27 double-block, 15 triple-block, 5 four-block and 3 five-block vdWSH films (where one block represents one 2D material). Morphological, spectroscopic and atomic-scale structural analyses reveal the presence of parallel, clean and atomically sharp vdW interfaces on a large scale, with very little contamination between neighbouring layers. The intact vdW interfaces allow us to achieve proximity-induced superconductivity and superconducting Josephson junctions on a centimetre scale. Our process for making multiple-layered vdWSHs can easily be generalized to other situations involving 2D materials, potentially accelerating the design of next-generation functional devices and applications22-24.

Magnetic Field-Stabilized Wigner Crystal States in a Graphene Moiré Superlattice

ABC-stacked trilayer graphene on boron nitride (ABC-TLG/hBN) moiré superlattices provides a tunable platform for exploring Wigner crystal states in which the electron correlation can be controlled by electric and magnetic fields. Here we report the observation of magnetic field-stabilized Wigner crystal states in a ABC-TLG/hBN. We show that correlated insulating states emerge at multiple fractional and integer fillings corresponding to ν = 1/3, 2/3, 1, 4/3, 5/3, and 2 electrons per moiré lattice site under a magnetic field. These correlated insulating states can be attributed to generalized Mott states for the integer fillings and generalized Wigner crystal states for the fractional fillings. The generalized Wigner crystal states are stabilized by a vertical magnetic field and are strongest at one magnetic flux quantum per three moiré superlattices. The ν = 2 insulating state persists up to 30 T, which can be described by a Mott-Hofstadter transition at a high magnetic field.

Flatband polaritonic router in twisted bilayer van der Waals materials

In recent years, van der Waals (vdW) polaritons excited by the hybrid of matter and photons have shown great promise for applications in nanoimaging, biosensing, and on-chip light guiding. In particular, polaritons with a flatband dispersion allow for mode canalization and diffractionless propagation, which showcase advantages for on-chip technologies requiring long-range transportation of optical information. Here, we propose a flatband polaritonic router based on twisted α-MoO₃ bilayers, which allows for on-chip routing of highly confined and low-loss phonon polaritons (PhPs) along multichannel propagating paths under different circular polarized dipole excitations. Our work combines flatband physics and optical spin- orbit coupling, with potential applications in nanoscale light propagation, on-chip optical switching, and communication.

Mixing of moiré-surface and bulk states in graphite

Van der Waals assembly enables the design of electronic states in two-dimensional (2D) materials, often by superimposing a long-wavelength periodic potential on a crystal lattice using moiré superlattices1-9. This twistronics approach has resulted in numerous previously undescribed physics, including strong correlations and superconductivity in twisted bilayer graphene10-12, resonant excitons, charge ordering and Wigner crystallization in transition-metal chalcogenide moiré structures13-18 and Hofstadter's butterfly spectra and Brown-Zak quantum oscillations in graphene superlattices19-22. Moreover, twistronics has been used to modify near-surface states at the interface between van der Waals crystals23,24. Here we show that electronic states in three-dimensional (3D) crystals such as graphite can be tuned by a superlattice potential occurring at the interface with another crystal-namely, crystallographically aligned hexagonal boron nitride. This alignment results in several Lifshitz transitions and Brown-Zak oscillations arising from near-surface states, whereas, in high magnetic fields, fractal states of Hofstadter's butterfly draw deep into the bulk of graphite. Our work shows a way in which 3D spectra can be controlled using the approach of 2D twistronics.

Mixed-dimensional moiré systems of twisted graphitic thin films

Moiré patterns formed by stacking atomically thin van der Waals crystals with a relative twist angle can give rise to notable new physical properties1,2. The study of moiré materials has so far been limited to structures comprising no more than a few van der Waals sheets, because a moiré pattern localized to a single two-dimensional interface is generally assumed to be incapable of appreciably modifying the properties of a bulk three-dimensional crystal. Here, we perform transport measurements of dual-gated devices constructed by slightly rotating a monolayer graphene sheet atop a thin bulk graphite crystal. We find that the moiré potential transforms the electronic properties of the entire bulk graphitic thin film. At zero and in small magnetic fields, transport is mediated by a combination of gate-tuneable moiré and graphite surface states, as well as coexisting semimetallic bulk states that do not respond to gating. At high field, the moiré potential hybridizes with the graphitic bulk states due to the unique properties of the two lowest Landau bands of graphite. These Landau bands facilitate the formation of a single quasi-two-dimensional hybrid structure in which the moiré and bulk graphite states are inextricably mixed. Our results establish twisted graphene-graphite as the first in a new class of mixed-dimensional moiré materials.

Controlled alignment of supermoiré lattice in double-aligned graphene heterostructures

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

Multiple and spectrally robust photonic magic angles in reconfigurable α-MoO3 trilayers

The emergence of a topological transition of the polaritonic dispersion in twisted bilayers of anisotropic van der Waals materials at a given twist angle-the photonic magic angle-results in the diffractionless propagation of polaritons with deep-subwavelength resolution. This type of propagation, generally referred to as canalization, holds promise for the control of light at the nanoscale. However, the existence of a single photonic magic angle hinders such control since the canalization direction in twisted bilayers is unique and fixed for each incident frequency. Here we overcome this limitation by demonstrating multiple spectrally robust photonic magic angles in reconfigurable twisted α-phase molybdenum trioxide (α-MoO₃) trilayers. We show that canalization of polaritons can be programmed at will along any desired in-plane direction in a single device with broad spectral ranges. These findings open the door for nanophotonics applications where on-demand control is crucial, such as thermal management, nanoimaging or entanglement of quantum emitters.

Ultraflexible two-dimensional Janus heterostructure superlattice: a novel intrinsic wrinkled structure

The recently reported two-dimensional Janus transition metal dichalcogenide materials present promising applications such as in transistors, photocatalysts, and thermoelectric nanodevices. In this work, using molecular dynamics simulations, the self-assembled in-plane MoSSe/WSSe heterostructure superlattice is predicted with a natural sinusoidal structure constructed by an asymmetric interface. Such a sinusoidal structure shows extraordinary mechanical behavior where the fracture strain can be enhanced up to 4.7 times than that of the symmetrical interface. Besides, the deformational structure of all these MoSSe/WSSe heterostructure superlattice are in accordance with the Fourier function curve; the fracture strength and fracture strain also demonstrate pronounced size dependence. Our investigations proposed an ultrastretchable assembled heterostructure superlattice and provided a desirable strategy to tune the mechanical properties of such an in-plane two-dimensional heterostructure.

Topological and Stacked Flat Bands in Bilayer Graphene with a Superlattice Potential

We show that bilayer graphene in the presence of a 2D superlattice potential provides a highly tunable setup that can realize a variety of flat band phenomena. We focus on two regimes: (i) topological flat bands with nonzero Chern numbers, C, including bands with higher Chern numbers |C|>1 and (ii) an unprecedented phase consisting of a stack of nearly perfect flat bands with C=0. For realistic values of the potential and superlattice periodicity, this stack can span nearly 100 meV, encompassing nearly all of the low-energy spectrum. We further show that in the topological regime, the topological flat band has a favorable band geometry for realizing a fractional Chern insulator (FCI) and use exact diagonalization to show that the FCI is in fact the ground state at 1/3 filling. Our results provide a realistic guide for future experiments to realize a new platform for flat band phenomena.

High-Order Fractal Quantum Oscillations in Graphene/BN Superlattices in the Extreme Doping Limit

Recent studies of van der Waals (vdW) heterostructures and superlattices have shown intriguing quantum phenomena, but these have been largely explored only in the moderate carrier density regime. Here, we report the probe of high-temperature fractal Brown-Zak (BZ) quantum oscillations through magnetotransport in the extreme doping regimes by applying a newly developed electron beam doping technique. This technique gives access to both ultrahigh electron and hole densities beyond the dielectric breakdown limit in graphene/BN superlattices, enabling the observation of nonmonotonic carrier-density dependence of fractal BZ states and up to fourth-order fractal BZ features despite strong electron-hole asymmetry. Theoretical tight-binding simulations qualitatively reproduce all observed fractal BZ features and attribute the nonmonotonic dependence to the weakening of superlattice effects at high carrier densities.

A natural indirect-to-direct band gap transition in artificially fabricated MoS2 and MoSe2 flowers

Twisted bilayer (tB) transition metal dichalcogenide (TMD) structures formed from two pieces of a periodic pattern overlaid with a relative twist manifest novel electronic and optical properties and correlated electronic phenomena. Here, twisted flower-like MoS₂ and MoSe₂ bilayers were artificially fabricated by the chemical vapor deposition (CVD) method. Photoluminescence (PL) studies demonstrated that an energy band structural transition from the indirect gap to the direct gap happened in the region away from the flower center in tB MoS₂ (MoSe₂) flower patterns, accompanied by an enhanced PL intensity. The indirect-to-direct-gap transition in the tB-MoS₂ (MoSe₂) flower dominantly originated from a gradually enlarged interlayer spacing and thus, interlayer decoupling during the spiral growth of tB flower patterns. Meanwhile, the expanded interlayer spacing resulted in a decreased effective mass of the electrons. This means that the charged exciton (trion) population was reduced and the neutral exciton density was increased to obtain the upgraded PL intensity in the off-center region. Our experimental results were further evidenced by the density functional theory (DFT) calculations of the energy band structures and the effective masses of electrons and holes for the artificial tB-MoS₂ flower with different interlayer spacings. The single-layer behavior of tB flower-like homobilayers provided a viable route to finely manipulate the energy band gap and the corresponding exotic optical properties by locally tuning the stacked structures and to satisfy the real requirement in TMD-based optoelectronic devices.

Unconventional Flat Chern Bands and 2e Charges in Skyrmionic Moiré Superlattices

The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating |C| = 2 dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity match. Following the Wilczek argument, the statistics of the charge-carrying excitations in this case is bosonic, characterized by electronic charge Q = 2e, which is even in units of electron charge e. The skyrmion coupling strength triggering the topological phase transition is realistic, with its lower bound estimated as 4 meV. The Hofstadter butterfly spectrum results in an unexpected quantum Hall conductance sequence ±2e2h,±4e2h,... for TBG with the skyrmion order.

Nanoscale Periodic Trapping Sites for Interlayer Excitons Built by Deformable Molecular Crystal on 2D Crystal

The nanoscale moiré pattern formed at 2D transition-metal dichalcogenide crystal (TMDC) heterostructures provides periodic trapping sites for excitons, which is essential for realizing various exotic phases such as artificial exciton lattices, Bose-Einstein condensates, and exciton insulators. At organic molecule/TMDC heterostructures, similar periodic potentials can be formed via other degrees of freedom. Here, we utilize the structure deformability of a 2D molecular crystal as a degree of freedom to create a periodic nanoscale potential that can trap interlayer excitons (IXs). Specifically, two semiconducting molecules, PTCDI and PTCDA, which possess similar band gaps and ionization potentials but form different lattice structures on MoS₂, are investigated. The PTCDI lattice on MoS₂ is distorted geometrically, which lifts the degeneracy of the two molecules within the crystal's unit cell. The degeneracy lifting results in a spatial variation of the molecular orbital energy, with an amplitude and periodicity of ∼0.2 eV and ∼2 nm, respectively. On the other hand, no such energy variation is observed in PTCDA/MoS₂, where the PTCDA lattice is much less distorted. The periodic variation in molecular orbital energies provides effective trapping sites for IXs. For IXs formed at PTCDI/MoS₂, rapid spatial localization of the electron in the organic layer toward the interface is observed, which demonstrates the effectiveness of these interfacial IX traps.

Tuning the magnetoresistance properties of phosphorene with periodic magnetic modulation

Periodic superlattices constitute ideal structures to modulate the transport properties of two-dimensional materials. In this paper, we show that the tunneling magnetoresistance (TMR) in phosphorene can be tuned effectively through periodic magnetic modulation. Deltaic magnetic barriers are arranged periodically along the phosphorene armchair direction in parallel (PM) and anti-parallel magnetization (AM) fashion. The theoretical treatment is based on a low-energy effective Hamiltonian, the transfer matrix method and the Landauer-Büttiker formalism. We find that the periodic modulation gives rise to oscillating transport characteristics for both PM and AM configurations. More importantly, by adjusting the electrostatic potential appropriately we find Fermi energy regions for which the AM conductance is reduced significantly while the PM conductance keeps considerable values, resulting in an effective TMR that increases with the magnetic field strength. These findings could be useful in the design of magnetoresistive devices based on magnetic phosphorene superlattices.

Emergent second-harmonic generation in van der Waals heterostructure of bilayer MoS2 and monolayer graphene

Van der Waals (vdW) stacking of two-dimensional (2D) materials to create artificial structures has enabled remarkable discoveries and novel properties in fundamental physics. Here, we report that vdW stacking of centrosymmetric 2D materials, e.g., bilayer MoS₂ (2LM) and monolayer graphene (1LG), could support remarkable second-harmonic generation (SHG). The required centrosymmetry breaking for second-order hyperpolarizability arises from the interlayer charge transfer between 2LM and 1LG and the imbalanced charge distribution in 2LM, which are verified by first-principles calculations, Raman spectroscopy, and polarization-resolved SHG. The strength of SHG from 2LM/1LG is of the same order of magnitude as that from the monolayer MoS₂, which is well recognized with strong second-order nonlinearity. The emergent SHG reveals that the interlayer charge transfer can effectively modify the symmetry and nonlinear optical properties of 2D heterostructures. It also indicates the great opportunity of SHG spectroscopy for characterizing interlayer coupling in vdW heterostructures.