Dynamically tunable moiré exciton Rydberg states in a monolayer semiconductor on twisted bilayer graphene.

Moiré excitons are emergent optical excitations in two-dimensional semiconductors with moiré superlattice potentials. Although these excitations have been observed on several platforms, a system with dynamically tunable moiré potential to tailor their properties is yet to be realized. Here we present a continuously tunable moiré potential in monolayer WSe2, enabled by its proximity to twisted bilayer graphene (TBG) near the magic angle. By tuning local charge density via gating, TBG provides a spatially varying and dynamically tunable dielectric superlattice for modulation of monolayer WSe2 exciton wave functions. We observed emergent moiré exciton Rydberg branches with increased energy splitting following doping of TBG due to exciton wave function hybridization between bright and dark Rydberg states. In addition, emergent Rydberg states can probe strongly correlated states in TBG at the magic angle. Our study provides a new platform for engineering moiré excitons and optical accessibility to electronic states with small correlation gaps in TBG.

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.

Graphene-Based Analog of Single-Slit Electron Diffraction.

This work reports the experimental demonstration of single-slit diffraction exhibited by electrons propagating in encapsulated graphene with an effective de Broglie wavelength corresponding to their attributes as massless Dirac fermions. Nanometer-scale device designs were implemented to fabricate a single-slit followed by five detector paths. Predictive calculations were also utilized to readily understand the observations reported. These calculations required the modeling of wave propagation in ideal case scenarios of the reported device designs to more accurately describe the observed single-slit phenomenon. This experiment was performed at room temperature and 190 K, where data from the latter highlighted the exaggerated asymmetry between electrons and holes, recently ascribed to slightly different Fermi velocities near the K point. This observation and device concept may be used for building diffraction switches with versatile applicability.

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.

Gate-Tunable Proximity Effects in Graphene on Layered Magnetic Insulators.

The extreme versatility of van der Waals materials originates from their ability to exhibit new electronic properties when assembled in close proximity to dissimilar crystals. For example, although graphene is inherently nonmagnetic, recent work has reported a magnetic proximity effect in graphene interfaced with magnetic substrates, potentially enabling a pathway toward achieving a high-temperature quantum anomalous Hall effect. Here, we investigate heterostructures of graphene and chromium trihalide magnetic insulators (CrI3, CrBr3, and CrCl3). Surprisingly, we are unable to detect a magnetic exchange field in the graphene but instead discover proximity effects featuring unprecedented gate tunability. The graphene becomes highly hole-doped due to charge transfer from the neighboring magnetic insulator and further exhibits a variety of atypical gate-dependent transport features. The charge transfer can additionally be altered upon switching the magnetic states of the nearest CrI3 layers. Our results provide a roadmap for exploiting proximity effects arising in graphene coupled to magnetic insulators.

Unusual magnetotransport in twisted bilayer graphene.

SignificanceWhen two sheets of graphene are twisted to the magic angle of 1.1∘, the resulting flat moiré bands can host exotic correlated electronic states such as superconductivity and ferromagnetism. Here, we show transport properties of a twisted bilayer graphene device at 1.38∘, far enough above the magic angle that we do not expect exotic correlated states. Instead, we see several unusual behaviors in the device's resistivity upon tuning both charge carrier density and perpendicular magnetic field. We can reproduce these behaviors with a surprisingly simple model based on Hofstadter's butterfly. These results shed light on the underlying properties of twisted bilayer graphene.

Unraveling Strain Gradient Induced Electromechanical Coupling in Twisted Double Bilayer Graphene Moiré Superlattices.

Moiré superlattices of 2D materials with a small twist angle are thought to exhibit appreciable flexoelectric effect, though unambiguous confirmation of their flexoelectricity is challenging due to artifacts associated with commonly used piezoresponse force microscopy (PFM). For example, unexpectedly small phase contrast (≈8°) between opposite flexoelectric polarizations is reported in twisted bilayer graphene (tBG), though theoretically predicted value is 180°. Here a methodology is developed to extract intrinsic moiré flexoelectricity using twisted double bilayer graphene (tDBG) as a model system, probed by lateral PFM. For small twist angle samples, it is found that a vectorial decomposition is essential to recover the small intrinsic flexoelectric response at domain walls from a large background signal. The obtained threefold symmetry of commensurate domains with significant flexoelectric response at domain walls is fully consistent with the theoretical calculations. Incommensurate domains in tDBG with relatively large twist angles can also be observed by this technique. A general strategy is provided here for unraveling intrinsic flexoelectricity in van der Waals moiré superlattices while providing insights into engineered symmetry breaking in centrosymmetric materials.

Competing correlated states and abundant orbital magnetism in twisted monolayer-bilayer graphene.

Flat band moiré superlattices have recently emerged as unique platforms for investigating the interplay between strong electronic correlations, nontrivial band topology, and multiple isospin 'flavor' symmetries. Twisted monolayer-bilayer graphene (tMBG) is an especially rich system owing to its low crystal symmetry and the tunability of its bandwidth and topology with an external electric field. Here, we find that orbital magnetism is abundant within the correlated phase diagram of tMBG, giving rise to the anomalous Hall effect in correlated metallic states nearby most odd integer fillings of the flat conduction band, as well as correlated Chern insulator states stabilized in an external magnetic field. The behavior of the states at zero field appears to be inconsistent with simple spin and valley polarization for the specific range of twist angles we investigate, and instead may plausibly result from an intervalley coherent (IVC) state with an order parameter that breaks time reversal symmetry. The application of a magnetic field further tunes the competition between correlated states, in some cases driving first-order topological phase transitions. Our results underscore the rich interplay between closely competing correlated ground states in tMBG, with possible implications for probing exotic IVC ordering.

Hierarchical nanosheets built from superatomic clusters: properties, exfoliation and single-crystal-to-single-crystal intercalation.

Tuning the properties of atomic crystals in the two-dimensional (2D) limit is synthetically challenging, but critical to unlock their potential in fundamental research and nanotechnology alike. 2D crystals assembled using superatomic blocks could provide a route to encrypt desirable functionality, yet strategies to link the inorganic blocks together in predetermined dimensionality or symmetry are scarce. Here, we describe the synthesis of anisotropic van der Waals crystalline frameworks using the designer superatomic nanocluster Co3(py)3Co6Se8L6 (py = pyridine, L = Ph2PN(Tol)), and ditopic linkers. Post-synthetically, the 3D crystals can be mechanically exfoliated into ultrathin flakes (8 to 60 nm), or intercalated with the redox-active guest tetracyanoethylene in a single-crystal-to-single-crystal transformation. Extensive characterization, including by single crystal X-ray diffraction, reveals how intrinsic features of the nanocluster, such as its structure, chirality, redox-activity and magnetic profile, predetermine key properties of the emerging 2D structures. Within the nanosheets, the strict and unusual stereoselectivity of the nanocluster's Co edges for the low symmetry (α,α,ß) isomer gives rise to in-plane structural anisotropy, while the helically chiral nanoclusters self-organize into alternating Δ- and Λ-homochiral rows. The nanocluster's high-spin Co edges, and its rich redox profile make the nanosheets both magnetically and electrochemically active, as revealed by solid state magnetic and cyclic voltammetry studies. The length and flexibility of the ditopic linker was varied, and found to have a secondary effect on the structure and stacking of the nanosheets within the 3D crystals. With these results we introduce a deterministic and versatile synthetic entry to programmable functionality and symmetry in 2D superatomic crystals.

Switching 2D magnetic states via pressure tuning of layer stacking.

The physical properties of two-dimensional van der Waals crystals can be sensitive to interlayer coupling. For two-dimensional magnets1-3, theory suggests that interlayer exchange coupling is strongly dependent on layer separation while the stacking arrangement can even change the sign of the interlayer magnetic exchange, thus drastically modifying the ground state4-10. Here, we demonstrate pressure tuning of magnetic order in the two-dimensional magnet CrI3. We probe the magnetic states using tunnelling8,11-13 and scanning magnetic circular dichroism microscopy measurements2. We find that interlayer magnetic coupling can be more than doubled by hydrostatic pressure. In bilayer CrI3, pressure induces a transition from layered antiferromagnetic to ferromagnetic phase. In trilayer CrI3, pressure can create coexisting domains of three phases, one ferromagnetic and two antiferromagnetic. The observed changes in magnetic order can be explained by changes in the stacking arrangement. Such coupling between stacking order and magnetism provides ample opportunities for designer magnetic phases and functionalities.

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

In van der Waals (vdW) heterostructures consisting of atomically thin crystals layered on top of one another, lattice mismatch and rotation between the layers can result in long-wavelength moiré superlattices. These moiré patterns can drive notable band structure reconstruction of the composite material, leading to a wide range of emergent phenomena including superconductivity1-3, magnetism4, fractional Chern insulating states5 and moiré excitons6-9. Here, we investigate devices consisting of monolayer graphene encapsulated between two crystals of boron nitride (BN), in which the rotational alignment of all three components is controlled. We find that bandgaps in the graphene arising from perfect rotational alignment with both BN layers can be modified considerably depending on whether the relative orientation of the two BN layers is 0° or 60°, suggesting a tunable transition between the absence or presence of inversion symmetry in the heterostructure. Small deviations (<1°) from perfect alignment of all three layers leads to coexisting long-wavelength moiré potentials, resulting in a highly reconstructed graphene band structure featuring multiple secondary Dirac points. Our results demonstrate that the interplay between multiple moiré patterns can be utilized to controllably modify the symmetry and electronic properties of the composite heterostructure.

Maximized electron interactions at the magic angle in twisted bilayer graphene.

The electronic properties of heterostructures of atomically thin van der Waals crystals can be modified substantially by moiré superlattice potentials from an interlayer twist between crystals1,2. Moiré tuning of the band structure has led to the recent discovery of superconductivity3,4 and correlated insulating phases5 in twisted bilayer graphene (TBG) near the 'magic angle' of twist of about 1.1 degrees, with a phase diagram reminiscent of high-transition-temperature superconductors. Here we directly map the atomic-scale structural and electronic properties of TBG near the magic angle using scanning tunnelling microscopy and spectroscopy. We observe two distinct van Hove singularities (VHSs) in the local density of states around the magic angle, with an energy separation of 57 millielectronvolts that drops to 40 millielectronvolts with high electron/hole doping. Unexpectedly, the VHS energy separation continues to decrease with decreasing twist angle, with a lowest value of 7 to 13 millielectronvolts at a magic angle of 0.79 degrees. More crucial to the correlated behaviour of this material, we find that at the magic angle, the ratio of the Coulomb interaction to the bandwidth of each individual VHS (U/t) is maximized, which is optimal for electronic Cooper pairing mechanisms. When doped near the half-moiré-band filling, a correlation-induced gap splits the conduction VHS with a maximum size of 6.5 millielectronvolts at 1.15 degrees, dropping to 4 millielectronvolts at 0.79 degrees. We capture the doping-dependent and angle-dependent spectroscopy results using a Hartree-Fock model, which allows us to extract the on-site and nearest-neighbour Coulomb interactions. This analysis yields a U/t of order unity indicating that magic-angle TBG is moderately correlated. In addition, scanning tunnelling spectroscopy maps reveal an energy- and doping-dependent three-fold rotational-symmetry breaking of the local density of states in TBG, with the strongest symmetry breaking near the Fermi level and further enhanced when doped to the correlated gap regime. This indicates the presence of a strong electronic nematic susceptibility or even nematic order in TBG in regions of the phase diagram where superconductivity is observed.

Tuning superconductivity in twisted bilayer graphene.

Materials with flat electronic bands often exhibit exotic quantum phenomena owing to strong correlations. An isolated low-energy flat band can be induced in bilayer graphene by simply rotating the layers by 1.1°, resulting in the appearance of gate-tunable superconducting and correlated insulating phases. In this study, we demonstrate that in addition to the twist angle, the interlayer coupling can be varied to precisely tune these phases. We induce superconductivity at a twist angle larger than 1.1°-in which correlated phases are otherwise absent-by varying the interlayer spacing with hydrostatic pressure. Our low-disorder devices reveal details about the superconducting phase diagram and its relationship to the nearby insulator. Our results demonstrate twisted bilayer graphene to be a distinctively tunable platform for exploring correlated states.

Dynamic band-structure tuning of graphene moiré superlattices with pressure.

Heterostructures can be assembled from atomically thin materials by combining a wide range of available van der Waals crystals, providing exciting possibilities for designer electronics 1 . In many cases, beyond simply realizing new material combinations, interlayer interactions lead to emergent electronic properties that are fundamentally distinct from those of the constituent layers 2 . A critical parameter in these structures is the interlayer coupling strength, but this is often not easy to determine and is typically considered to be a fixed property of the system. Here we demonstrate that we can controllably tune the interlayer separation in van der Waals heterostructures using hydrostatic pressure, providing a dynamic way to modify their electronic properties. In devices in which graphene is encapsulated in boron nitride and aligned with one of the encapsulating layers, we observe that increasing pressure produces a superlinear increase in the moiré-superlattice-induced bandgap-nearly doubling within the studied range-together with an increase in the capacitive gate coupling to the active channel by as much as 25 per cent. Comparison to theoretical modelling highlights the role of atomic-scale structural deformations and how this can be altered with pressure. Our results demonstrate that combining hydrostatic pressure with controlled rotational order provides opportunities for dynamic band-structure engineering in van der Waals heterostructures.

Ambipolar Landau levels and strong band-selective carrier interactions in monolayer WSe2.

Monolayers (MLs) of transition-metal dichalcogenides (TMDs) exhibit unusual electrical behaviour under magnetic fields due to their intrinsic spin-orbit coupling and lack of inversion symmetry1-15. Although recent experiments have also identified the critical role of carrier interactions within these materials11,15, a complete mapping of the ambipolar Landau level (LL) sequence has remained elusive. Here we use single-electron transistors (SETs)16,17 to perform LL spectroscopy in ML WSe2, and provide a comprehensive picture of the electronic structure of a ML TMD for both electrons and holes. We find that the LLs differ notably between the two bands, and follow a unique sequence in the valence band (VB) that is dominated by strong Zeeman effects. The Zeeman splitting in the VB is several times higher than the cyclotron energy, far exceeding the predictions of a single-particle model and, moreover, tunes significantly with doping 15 . This implies exceptionally strong many-body interactions, and suggests that ML WSe2 can serve as a host for new correlated-electron phenomena.

Evolution of the electronic band structure of twisted bilayer graphene upon doping.

The electronic band structure of twisted bilayer graphene develops van Hove singularities whose energy depends on the twist angle between the two layers. Using Raman spectroscopy, we monitor the evolution of the electronic band structure upon doping using the G peak area which is enhanced when the laser photon energy is resonant with the energy separation of the van Hove singularities. Upon charge doping, the Raman G peak area initially increases for twist angles larger than a critical angle and decreases for smaller angles. To explain this behavior with twist angle, the energy separation of the van Hove singularities must decrease with increasing charge density demonstrating the ability to modify the electronic and optical properties of twisted bilayer graphene with doping.

Pressure-induced commensurate stacking of graphene on boron nitride.

Combining atomically-thin van der Waals materials into heterostructures provides a powerful path towards the creation of designer electronic devices. The interaction strength between neighbouring layers, most easily controlled through their interlayer separation, can have significant influence on the electronic properties of these composite materials. Here, we demonstrate unprecedented control over interlayer interactions by locally modifying the interlayer separation between graphene and boron nitride, which we achieve by applying pressure with a scanning tunnelling microscopy tip. For the special case of aligned or nearly-aligned graphene on boron nitride, the graphene lattice can stretch and compress locally to compensate for the slight lattice mismatch between the two materials. We find that modifying the interlayer separation directly tunes the lattice strain and induces commensurate stacking underneath the tip. Our results motivate future studies tailoring the electronic properties of van der Waals heterostructures by controlling the interlayer separation of the entire device using hydrostatic pressure.

van der Waals Heterostructures with High Accuracy Rotational Alignment.

We describe the realization of van der Waals (vdW) heterostructures with accurate rotational alignment of individual layer crystal axes. We illustrate the approach by demonstrating a Bernal-stacked bilayer graphene formed using successive transfers of monolayer graphene flakes. The Raman spectra of this artificial bilayer graphene possess a wide 2D band, which is best fit by four Lorentzians, consistent with Bernal stacking. Scanning tunneling microscopy reveals no moiré pattern on the artificial bilayer graphene, and tunneling spectroscopy as a function of gate voltage reveals a constant density of states, also in agreement with Bernal stacking. In addition, electron transport probed in dual-gated samples reveals a band gap opening as a function of transverse electric field. To illustrate the applicability of this technique to realize vdW heterostructuctures in which the functionality is critically dependent on rotational alignment, we demonstrate resonant tunneling double bilayer graphene heterostructures separated by hexagonal boron-nitride dielectric.