Large-area, periodic, and tunable intrinsic pseudo-magnetic fields in low-angle twisted bilayer graphene

Elastic Screening of Pseudogauge Fields in Graphene

Lattice deformations in graphene couple to the low-energy electronic degrees of freedom as effective scalar and gauge fields. Using molecular dynamics simulations, we show that the optical component of the displacement field, i.e., the relative motion of different sublattices, contributes at equal order as the acoustic component and effectively screens the pseudogauge fields. In particular, we consider twisted bilayer graphene and corrugated monolayer graphene. In both cases, optical lattice displacements significantly reduce the overall magnitude of the pseudomagnetic fields. For corrugated graphene, optical contributions also reshape the pseudomagnetic field and significantly modify the electronic bands near charge neutrality. Previous studies based on continuum elasticity, which ignores this effect, have therefore systematically overestimated the strength of the strain-induced pseudomagnetic field. Our results have important consequences for the interpretation of experiments and design of straintronic applications.

Twist-angle dependent pseudo-magnetic fields in monolayer CrCl2/graphene heterostructures

The generation of pseudo-magnetic fields in strained graphene leads to quantized Landau levels in the absence of an external magnetic field, providing the potential to achieve a zero-magnetic-field analogue of the quantum Hall effect. Here, we report the realization of a pseudo-magnetic field in epitaxial graphene by building a monolayer CrCl2/graphene heterointerface. The CrCl2 crystal structure exhibits spontaneous breaking of three-fold rotational symmetry, yielding an anisotropic displacement field at the interface. Using scanning tunneling spectroscopy, we have discovered a sequence of pseudo-Landau levels associated with massless Dirac fermions. A control experiment performed on the CrCl2/NbSe2 interface confirms the origin as the pseudo-magnetic field in the graphene layer that strongly interacts with CrCl2. More interestingly, the strength of the pseudo-magnetic fields can be tuned by the twist angle between the monolayer CrCl2 and graphene, with a variation of up to threefold, depending on the twist angle of 0° to 30°. This work presents a rare 2D heterojunction for exploring PMF-related physics, such as the valley Hall effect, with the advantage of easy and flexible implementation.

A new approach in generating stable crack propagation at twisted bilayer graphene/hBN heterostructures

Thermodynamic theory suggests that the obvious mechanical behavior caused by temperature and interlayer angle will affect the physical properties of materials, such as mechanical properties and transportation behavior, and it is different from the behavior in three-dimensional bulk materials. We observe an abnormal physical effect of bilayer graphene/hexagonal boron nitride (G/BN)-carbon nanotube (CNT) heterostructures, with a normalized out-of-plane deformation and normalized bond angle percentage to almost several times higher those of pristine G/BN heterostructures (without CNT) at 700-800 K. Our combined finite element theory and molecular dynamics simulations confirmed that the combination of CNT and interlayer angle diverted and bridged the propagating crack and provided a stable crack propagation path and crack tip opening displacement, resulting in the stress fields to be controlled around the CNT at high temperature. It offers an ideal design for two-dimensional (2D) materials that can maintain exceptional mechanical properties in flexible device applications.

A Deterministic Method to Construct a Common Supercell Between Two Similar Crystalline Surfaces

Here, a deterministic algorithm is proposed, that is capable of constructing a common supercell between two similar crystalline surfaces without scanning all possible cases. Using the complex plane, the 2D lattice is defined as the 2D complex vector. Then, the relationship between two surfaces becomes the eigenvector-eigenvalue relation where an operator corresponds to a transformation matrix. It is shown that this transformation matrix can be directly determined from the lattice parameters and rotation angle of the two given crystalline surfaces with O(log Nmax) time complexity, where Nmax is the maximum index of repetition matrix elements. This process is much faster than the conventional brute force approach (O ( N max 4 ) $O(N_{\mathrm{max}}^4)$ ). By implementing the method in Python code, experimental 2D heterostructures and their moiré patterns and additionally find new moiré patterns that have not yet been reported are successfully generated. According to the density functional theory (DFT) calculations, some of the new moiré patterns are expected to be as stable as experimentally-observed moiré patterns. Taken together, it is believed that the method can be widely applied as a useful tool for designing new heterostructures with interesting properties.

Real-Space Topology-Engineering of Skyrmionic Spin Textures in a van der Waals Ferromagnet Fe3GaTe2

Realizing magnetic skyrmions in two-dimensional (2D) van der Waals (vdW) ferromagnets offers unparalleled prospects for future spintronic applications. The room-temperature ferromagnet Fe3GaTe2 provides an ideal platform for tailoring these magnetic solitons. Here, skyrmions of distinct topological charges are artificially introduced and engineered by using magnetic force microscopy (MFM). The skyrmion lattice is realized by a specific field-cooling process and can be further erased and painted via delicate manipulation of the tip stray field. The skyrmion lattice with opposite topological charges (S = ±1) can be tailored at the target regions to form topological skyrmion junctions (TSJs) with specific configurations. The delicate interplay of TSJs and spin-polarized device current were finally investigated via the in situ transport measurements, alongside the topological stability of TSJs. Our results demonstrate that Fe3GaTe2 not only serves as a potential building block for skyrmion-based spintronic devices, but also presents prospects for Fe3GaTe2-based heterostructures with the engineered topological spin textures.

Manipulating 2D Materials through Strain Engineering

This review explores the growing interest in 2D layered materials, such as graphene, h-BN, transition metal dichalcogenides (TMDs), and black phosphorus (BP), with a specific focus on recent advances in strain engineering. Both experimental and theoretical results are delved into, highlighting the potential of strain to modulate physical properties, thereby enhancing device performance. Various strain engineering methods are summarized, and the impact of strain on the electrical, optical, magnetic, thermal, and valleytronic properties of 2D materials is thoroughly examined. Finally, the review concludes by addressing potential applications and challenges in utilizing strain engineering for functional devices, offering valuable insights for further research and applications in optoelectronics, thermionics, and spintronics.

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.

Evolution of the flat band and the role of lattice relaxations in twisted bilayer graphene

Magic-angle twisted bilayer graphene exhibits correlated phenomena such as superconductivity and Mott insulating states related to the weakly dispersing flat band near the Fermi energy. Such a flat band is expected to be sensitive to both the moiré period and lattice relaxations. Thus, clarifying the evolution of the electronic structure with the twist angle is critical for understanding the physics of magic-angle twisted bilayer graphene. Here we combine nano-spot angle-resolved photoemission spectroscopy and atomic force microscopy to resolve the fine electronic structure of the flat band and remote bands, as well as their evolution with twist angle from 1.07° to 2.60°. Near the magic angle, the dispersion is characterized by a flat band near the Fermi energy with a strongly reduced band width. Moreover, we observe a spectral weight transfer between remote bands at higher binding energy, which allows to extract the modulated interlayer spacing near the magic angle. Our work provides direct spectroscopic information on flat band physics and highlights the important role of lattice relaxations.

Coulomb blockade and Coulomb staircases in CoBi nanoislands on SrTiO3(001)

We successfully fabricated two-dimensional metallic CoBi nanoislands on SrTiO3(001) substrate by molecular beam epitaxy, and systematically investigated their electronic structures by scanning tunneling microscopy and spectroscopyin situat 4.2 K. Coulomb blockade and Coulomb staircases with discrete and well-separated levels are observed for the individual nanoisland, which is attributed to single-electron tunneling via two tunnel junction barriers. They are in excellent agreement with the simulations based on orthodox theory. Furthermore, we demonstrated that the Coulomb blockade becomes weaker with increasing temperature and almost disappears at ∼22 K in our variable temperature experiment, and its full-width at half-maximum of dI/dVpeaks with temperature is ∼6 mV. Our results provide a new platform for designing single-electron transistors that have potential applications in future microelectronics.

Strain Engineering of Twisted Bilayer Graphene: The Rise of Strain-Twistronics

The layer-by-layer stacked van der Waals structures (termed vdW hetero/homostructures) offer a new paradigm for materials design-their physical properties can be tuned by the vertical stacking sequence as well as by adding a mechanical twist, stretch, and hydrostatic pressure to the atomic structure. In particular, simple twisting and stacking of two layers of graphene can form a uniform and ordered Moiré superlattice, which can effectively modulate the electrons of graphene layers and lead to the discovery of unconventional superconductivity and strong correlations. However, the twist angle of twisted bilayer graphene (tBLG) is almost unchangeable once the interlayer stacking is determined, while applying mechanical elastic strain provides an alternative way to deeply regulate the electronic structure by controlling the lattice spacing and symmetry. In this review, diverse experimental advances are introduced in straining tBLG by in-plane and out-of-plane modes, followed by the characterizations and calculations toward quantitatively tuning the strain-engineered electronic structures. It is further discussed that the structural relaxation in strained Moiré superlattice and its influence on electronic structures. Finally, the conclusion entails prospects for opportunities of strained twisted 2D materials, discussions on existing challenges, and an outlook on the intriguing emerging field, namely "strain-twistronics".

Mechanical Control of Quantum Transport in Graphene

2D materials (2DMs) are fundamentally electro-mechanical systems. Their environment unavoidably strains them and modifies their quantum transport properties. For instance, a simple uniaxial strain can completely turn off the conductance of ballistic graphene or switch on/off the superconducting phase of magic-angle bilayer graphene. This article reports measurements of quantum transport in strained graphene transistors which agree quantitatively with models based on mechanically-induced gauge potentials. A scalar potential is mechanically induced in situ to modify graphene's work function by up to 25 meV. Mechanically generated vector potentials suppress the ballistic conductance of graphene by up to 30% and control its quantum interferences. The data are measured with a custom experimental platform able to precisely tune both the mechanics and electrostatics of suspended graphene transistors at low-temperature over a broad range of strain (up to 2.6%). This work opens many opportunities to harness quantitative strain effects in 2DM quantum transport and technologies.

Surface potential-adjusted surface states in 3D topological photonic crystals

Surface potential in a topological matter could unprecedentedly localize the waves. However, this surface potential is yet to be exploited in topological photonic systems. Here, we demonstrate that photonic surface states can be induced and controlled by the surface potential in a dielectric double gyroid (DG) photonic crystal. The basis translation in a unit cell enables tuning of the surface potential, which in turn regulates the degree of wave localization. The gradual modulation of DG photonic crystals enables the generation of a pseudomagnetic field. Overall, this study shows the interplay between surface potential and pseudomagnetic field regarding the surface states. The physical consequences outlined herein not only widen the scope of surface states in 3D photonic crystals but also highlight the importance of surface treatments in a photonic system.

Imaging quantum oscillations and millitesla pseudomagnetic fields in graphene

The exceptional control of the electronic energy bands in atomically thin quantum materials has led to the discovery of several emergent phenomena1. However, at present there is no versatile method for mapping the local band structure in advanced two-dimensional materials devices in which the active layer is commonly embedded in the insulating layers and metallic gates. Using a scanning superconducting quantum interference device, here we image the de Haas-van Alphen quantum oscillations in a model system, the Bernal-stacked trilayer graphene with dual gates, which shows several highly tunable bands2-4. By resolving thermodynamic quantum oscillations spanning more than 100 Landau levels in low magnetic fields, we reconstruct the band structure and its evolution with the displacement field with excellent precision and nanoscale spatial resolution. Moreover, by developing Landau-level interferometry, we show shear-strain-induced pseudomagnetic fields and map their spatial dependence. In contrast to artificially induced large strain, which leads to pseudomagnetic fields of hundreds of tesla5-7, we detect naturally occurring pseudomagnetic fields as low as 1 mT corresponding to graphene twisting by 1 millidegree, two orders of magnitude lower than the typical angle disorder in twisted bilayer graphene8-11. This ability to resolve the local band structure and strain at the nanoscale level enables the characterization and use of tunable band engineering in practical van der Waals devices.

Observation of Rydberg moiré excitons

Rydberg excitons, the solid-state counterparts of Rydberg atoms, have sparked considerable interest with regard to the harnessing of their quantum application potentials, but realizing their spatial confinement and manipulation poses a major challenge. Lately, the rise of two-dimensional moiré superlattices with highly tunable periodic potentials provides a possible pathway. Here, we experimentally demonstrate this capability through the spectroscopic evidence of Rydberg moiré excitons (X_RM), which are moiré-trapped Rydberg excitons in monolayer semiconductor tungsten diselenide adjacent to twisted bilayer graphene. In the strong coupling regime, the X_RM manifest as multiple energy splittings, pronounced red shift, and narrowed linewidth in the reflectance spectra, highlighting their charge-transfer character wherein electron-hole separation is enforced by strongly asymmetric interlayer Coulomb interactions. Our findings establish the excitonic Rydberg states as candidates for exploitation in quantum technologies.

Theory of quantized photonic spin Hall effect in strained graphene under a sub-Tesla external magnetic field

The quantized photonic spin Hall effect (PSHE) in the strained graphene-substrate system is predicted under a sub-Tesla external magnetic field, which is two orders of magnitude smaller than required to produce the quantized effect in the conventional graphene-substrate system. It is found that in-plane and transverse spin-dependent splittings in the PSHE, exhibit different quantized behaviors and are closely related to the reflection coefficients. Unlike the quantized PSHE in the conventional graphene-substrate system formed by the splitting of real Landau levels, the quantized PSHE in the strained graphene-substrate system is attributed to the splitting of pseudo-Landau levels caused by the pseudo-magnetic field and the lifting of valley degeneracy of the n ≠ 0 pseudo-Landau levels induced by the sub-Tesla external magnetic field. At the same time, the pseudo-Brewster angles of the system are also quantized with the change of Fermi energy. The sub-Tesla external magnetic field and the PSHE appear as quantized peak values near these angles. The giant quantized PSHE is expected to be used for direct optical measurements of the quantized conductivities and pseudo-Landau levels in the monolayer strained graphene.

Realizing One-Dimensional Electronic States in Graphene via Coupled Zeroth Pseudo-Landau Levels

Strain-induced pseudomagnetic fields can mimic real magnetic fields to generate a zero-magnetic-field analog of the Landau levels (LLs), i.e., the pseudo-Landau levels (PLLs), in graphene. The distinct nature of the PLLs enables one to realize novel electronic states beyond what is feasible with real LLs. Here, we show that it is possible to realize exotic electronic states through the coupling of zeroth PLLs in strained graphene. In our experiment, nanoscale strained structures embedded with PLLs are generated along a one-dimensional (1D) channel of suspended graphene monolayer. Our results demonstrate that the zeroth PLLs of the strained structures are coupled together, exhibiting a serpentine pattern that snakes back and forth along the 1D suspended graphene monolayer. These results are verified theoretically by large-scale tight-binding calculations of the strained samples. Our result provides a new approach to realizing novel quantum states and to engineering the electronic properties of graphene by using localized PLLs as building blocks.

Recent advances in two-dimensional ferromagnetism: strain-, doping-, structural- and electric field-engineering toward spintronic applications

Since the first report on truly two-dimensional (2D) magnetic materials in 2017, a wide variety of merging 2D magnetic materials with unusual physical characteristics have been discovered and thus provide an effective platform for exploring the associated novel 2D spintronic devices, which have been made significant progress in both theoretical and experimental studies. Herein, we make a comprehensive review on the recent scientific endeavors and advances on the various engineering strategies on 2D ferromagnets, such as strain-, doping-, structural- and electric field-engineering, toward practical spintronic applications, including spin tunneling junctions, spin field-effect transistors and spin logic gate, etc. In the last, we discuss on current challenges and future opportunities in this field, which may provide useful guidelines for scientists who are exploring the fundamental physical properties and practical spintronic devices of low-dimensional magnets.

Reproducibility in the fabrication and physics of moiré materials

Overlaying two atomic layers with a slight lattice mismatch or at a small rotation angle creates a moiré superlattice, which has properties that are markedly modified from (and at times entirely absent in) the 'parent' materials. Such moiré materials have progressed the study and engineering of strongly correlated phenomena and topological systems in reduced dimensions. The fundamental understanding of the electronic phases, such as superconductivity, requires a precise control of the challenging fabrication process, involving the rotational alignment of two atomically thin layers with an angular precision below 0.1 degrees. Here we review the essential properties of moiré materials and discuss their fabrication and physics from a reproducibility perspective.

Extracting the Strain Matrix and Twist Angle from the Moiré Superlattice in van der Waals Heterostructures

When two atomic layers are brought into contact at a relative twist angle, a large-scale pattern, called a moiré superlattice, emerges due to the (angular or lattice) mismatch between the layers. This has profound consequences in terms of the Hamiltonian of the system but was also considered in several publications as a means to extract the local strain tensor. While extracting the twist angle based on knowledge of the periodicity of the moiré is trivial in the case of a regular moiré pattern, in many examples in the literature, that is not the case. In particular, extracting the strain tensor and twist angle maps from a spatially varying moiré pattern is not straightforward. This article aims to provide a practical tool to extract the strain tensor and twist angle from an experimentally observable pattern. It further addresses the limitation of any such approach in the absence of additional experimental information beyond the moiré superlattice pattern.

Valley-Polarized Quantum Anomalous Hall State in Moiré MoTe_{2}/WSe_{2} Heterobilayers

Moiré heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moiré bands in heterobilayer TMDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling ν=2 (two holes per moiré unit cell) and a valley-polarized quantum anomalous Hall state at filling ν=1 were observed in AB stacked moiré MoTe_{2}/WSe_{2} heterobilayers. However, how the topologically nontrivial states emerge is not known. In this Letter, we propose that the pseudomagnetic fields induced by lattice relaxation in moiré MoTe_{2}/WSe_{2} heterobilayers could naturally give rise to moiré bands with finite Chern numbers. We show that a time-reversal invariant quantum valley Hall insulator is formed at full filling ν=2, when two moiré bands with opposite Chern numbers are filled. At half filling ν=1, the Coulomb interaction lifts the valley degeneracy and results in a valley-polarized quantum anomalous Hall state, as observed in the experiment. Our theory identifies a new way to achieve topologically nontrivial states in heterobilayer TMD materials.

Developing Graphene-Based Moiré Heterostructures for Twistronics

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

Coupling and Decoupling of Bilayer Graphene Monitored by Electron Energy Loss Spectroscopy

We studied the interlayer coupling and decoupling of bilayer graphene (BLG) using spatially resolved electron energy loss spectroscopy with a monochromated electron source. We correlated the twist-angle-dependent energy band hybridization with Moiré superlattices and the corresponding optical absorption peaks. The optical absorption peak originates from the excitonic transition between the hybridized van Hove singularities (vHSs), which shifts systematically with the twist angle. We then proved that the BLG decouples when a monolayer of metal chloride is intercalated in its van der Waals gap and results in the elimination of the vHS peak.

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.

Emerging flat bands in large-angle twisted bi-layer graphene under pressure

Recent experiments on magic-angle twisted bi-layer graphene have attracted intensive attention due to exotic properties such as unconventional superconductivity and correlated insulation. These phenomena were often found at a magic angle less than 1.1°. However, the preparation of precisely controlled bi-layer graphene with a small magic angle is challenging. In this work, electronic properties of large-angle twisted bi-layer graphene (TBG) under pressure are investigated with density functional theory. We demonstrate that large-angle TBG can display flat bands nearby the Fermi level under pressure, which may also induce interesting properties such as superconductivity which have only been found in small-angle TBG at ambient pressure. The Fermi velocity is found to decrease monotonously with pressure for large twisted angles, e.g., 21.8°. Our work indicates that applying pressure provides opportunities for flat-band engineering in larger angle TBG and supports further exploration in related investigations.

Moiré Patterns in 2D Materials: A Review

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

Fabrication Strategies of Twisted Bilayer Graphenes and Their Unique Properties

Twisted bilayer graphene (tBLG) exhibits a host of innovative physical phenomena owing to the formation of moiré superlattice. Especially, the discovery of superconducting behavior has generated new interest in graphene. The growing studies of tBLG mainly focus on its physical properties, while the fabrication of high-quality tBLG is a prerequisite for achieving the desired properties due to the great dependence on the twist angle and the interfacial contact. Here, the cutting-edge preparation strategies and challenges of tBLG fabrication are reviewed. The advantages and disadvantages of chemical vapor deposition, epitaxial growth on silicon carbide, stacking monolayer graphene, and folding monolayer graphene methods for the fabrication of tBLG are analyzed in detail, providing a reference for further development of preparation methods. Moreover, the characterization methods of twist angle for the tBLG are presented. Then, the unique physicochemical properties and corresponding applications of tBLG, containing correlated insulating and superconducting states, ferromagnetic state, soliton, enhanced optical absorption, tunable bandgap, and lithium intercalation and diffusion, are described. Finally, the opportunities and challenges for fabricating high-quality and large-area tBLG are discussed, unique physical properties are displayed, and new applications inferred from its angle-dependent features are explored, thereby impelling the commercialization of tBLG from laboratory to market.

Enhanced third-harmonic generation by manipulating the twist angle of bilayer graphene

Twisted bilayer graphene (tBLG) has received substantial attention in various research fields due to its unconventional physical properties originating from Moiré superlattices. The electronic band structure in tBLG modified by interlayer interactions enables the emergence of low-energy van Hove singularities in the density of states, allowing the observation of intriguing features such as increased optical conductivity and photocurrent at visible or near-infrared wavelengths. Here, we show that the third-order optical nonlinearity can be considerably modified depending on the stacking angle in tBLG. The third-harmonic generation (THG) efficiency is found to significantly increase when the energy gap at the van Hove singularity matches the three-photon resonance of incident light. Further study on electrically tuneable optical nonlinearity reveals that the gate-controlled THG enhancement varies with the twist angle in tBLG, resulting in a THG enhanced up to 60 times compared to neutral monolayer graphene. Our results prove that the twist angle opens up a new way to control and increase the optical nonlinearity of tBLG, suggesting rotation-induced tuneable nonlinear optics in stacked two-dimensional material systems.

Tunable Lattice Reconstruction, Triangular Network of Chiral One-Dimensional States, and Bandwidth of Flat Bands in Magic Angle Twisted Bilayer Graphene

The interplay between interlayer van der Waals interaction and intralayer lattice distortion can lead to structural reconstruction in slightly twisted bilayer graphene (TBG) with the twist angle being smaller than a characteristic angle θ_{c}. Experimentally, the θ_{c} is demonstrated to be very close to the magic angle (θ≈1.08°). Here we address the transition between reconstructed and unreconstructed structures of the TBG across the magic angle by using scanning tunneling microscopy (STM). Our experiment demonstrates that both structures are stable in the TBG around the magic angle. By using a STM tip, we show that the two structures can be changed to each other and a triangular network of chiral one-dimensional states hosted by domain boundaries can be switched on and off. Consequently, the bandwidth of the flat band, which plays a vital role in the emergent strongly correlated states in the magic angle TBG, is tuned. This provides an extra control knob to manipulate the exotic electronic states of the TBG near the magic angle.