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Interactions among charge carriers in graphene can lead to the spontaneous breaking of multiple degeneracies. When increasing the number of graphene layers following rhombohedral stacking, the dominant role of Coulomb interactions becomes pronounced due to the significant reduction in kinetic energy. In this study, we employ phonon–polariton-assisted near-field infrared imaging to determine the stacking orders of tetralayer graphene devices. Through quantum transport measurements, we observe a range of spontaneous broken-symmetry states and their transitions, which can be finely tuned by carrier density nand electric displacement field D. Specifically, we observe a layer-antiferromagnetic insulator at n= D= 0 with a gap of approximately 15 meV. Increasing Dallows for a continuous phase transition from a layer-antiferromagnetic insulator to a layer-polarized insulator. By simultaneously tuning nand D, we observe isospin-polarized metals, including spin–valley-polarized and spin-polarized metals. These transitions are associated with changes in the Fermi surface topology and are consistent with the Stoner criteria. Our findings highlight the efficient fabrication of specially stacked multilayer graphene devices and demonstrate that crystalline multilayer graphene is an ideal platform for investigating a wide range of broken symmetries driven by Coulomb interactions.

The dominance of Coulomb interactions over the kinetic energy of electrons in flat moiré bands of magic-angle twisted bilayer graphene (TBG) gives rise to a variety of correlated phases, including correlated insulators1–3, superconductivity2,4,5, orbital ferromagnetism2,6, Chern insulators7–10and nematicity11. Most of these phases occur when the carrier density is at or near an integer number of carriers per moiré unit cell. However, the demonstration of ordered states at fractional moiré band fillings at zero applied magnetic field is more challenging. Here we report the observation of states near half-integer band fillings 0.5 and ±3.5 at near-zero magnetic field in TBG proximitized by tungsten diselenide. Furthermore, at a band filling near −0.5, a symmetry-broken Chern insulator emerges at high magnetic field that is compatible with the band structure calculations within a translational symmetry-broken supercell with twice the area of the original TBG moiré cell. Our results are consistent with a spin or charge density wave ground state in TBG in the zero-magnetic-field limit.

We predict that layer antiferromagnetic bilayers formed from van der Waals (vdW) materials with weak interlayer versus intralayer exchange coupling have strong magnetoelectric response that can be detected in dual-gated devices where internal displacement fields and carrier densities can be varied independently. We illustrate this strong temperature-dependent magnetoelectric response in bilayer CrI3at charge neutrality by calculating the gate voltage-dependent total magnetization through Monte Carlo simulations and mean-field solutions of the anisotropic Heisenberg model informed from density functional theory and experimental data and present a simple model for electrical control of magnetism by electrostatic doping.

Bilayer graphene has been predicted to host a moiré miniband with flat dispersion if the layers are stacked at specific twist angles known as the ’magic angles’1,2. Recently, twisted bilayer graphene (tBLG) with a magic angle twist was reported to exhibit a correlated insulating state and superconductivity3,4, where the presence of the flat miniband in the system is thought to be essential for the emergence of these ordered phases in the transport measurements. Although tunnelling spectroscopy5–9and electronic compressibility measurements10in tBLG have found a van Hove singularity that is consistent with the presence of the flat miniband, a direct observation of the flat dispersion in the momentum space of such a moiré miniband in tBLG is still lacking. Here, we report the visualization of this flat moiré miniband by using angle-resolved photoemission spectroscopy with nanoscale resolution. The high spatial resolution of this technique enabled the measurement of the local electronic structure of the tBLG. The measurements demonstrate the existence of the flat moiré band near the charge neutrality for tBLG close to the magic angle at room temperature.

Moiré superlattices have become a fertile playground for topological Chern insulators, where the displacement field can tune the quantum geometry and Chern number of the topological band. However, in experiments, displacement field engineering of spontaneous symmetry-breaking Chern bands has not been demonstrated. Here in a rhombohedral trilayer graphene moiré superlattice, we use a thermodynamic probe and transport measurement to monitor the Chern number evolution as a function of the displacement field. At a quarter filling of the moiré band, a novel Chern number of three is unveiled to compete with the well-established number of two upon turning on the electric field and survives when the displacement field is sufficiently strong. The transition can be reconciled by a nematic instability on the Fermi surface due to the pseudomagnetic vector field potentials associated with moiré strain patterns. Our work opens more opportunities to active control of Chern numbers in van der Waals moiré systems.

Understanding the mechanism of high-transition-temperature (high-Tc) superconductivity is a central problem in condensed matter physics. It is often speculated that high-Tcsuperconductivity arises in a doped Mott insulator1as described by the Hubbard model2–4. An exact solution of the Hubbard model, however, is extremely challenging owing to the strong electron–electron correlation in Mott insulators. Therefore, it is highly desirable to study a tunable Hubbard system, in which systematic investigations of the unconventional superconductivity and its evolution with the Hubbard parameters can deepen our understanding of the Hubbard model. Here we report signatures of tunable superconductivity in an ABC-trilayer graphene (TLG) and hexagonal boron nitride (hBN) moiré superlattice. Unlike in ‘magic angle’ twisted bilayer graphene, theoretical calculations show that under a vertical displacement field, the ABC-TLG/hBN heterostructure features an isolated flat valence miniband associated with a Hubbard model on a triangular superlattice5,6where the bandwidth can be tuned continuously with the vertical displacement field. Upon applying such a displacement field we find experimentally that the ABC-TLG/hBN superlattice displays Mott insulating states below 20 kelvin at one-quarter and one-half fillings of the states, corresponding to one and two holes per unit cell, respectively. Upon further cooling, signatures of superconductivity (‘domes’) emerge below 1 kelvin for the electron- and hole-doped sides of the one-quarter-filling Mott state. The electronic behaviour in the ABC-TLG/hBN superlattice is expected to depend sensitively on the interplay between the electron–electron interaction and the miniband bandwidth. By varying the vertical displacement field, we demonstrate transitions from the candidate superconductor to Mott insulator and metallic phases. Our study shows that ABC-TLG/hBN heterostructures offer attractive model systems in which to explore rich correlated behaviour emerging in the tunable triangular Hubbard model. By varying the vertical displacement field in a trilayer graphene and hexagonal boron nitride moiré superlattice, transitions can be observed from the superconducting phase to Mott insulator and metallic phases.

The Mott insulator is a central concept in strongly correlated physics and manifests when the repulsive Coulomb interaction between electrons dominates over their kinetic energy1,2. Doping additional carriers into a Mott insulator can give rise to other correlated phenomena such as unusual magnetism and even high-temperature superconductivity2,3. A tunable Mott insulator, where the competition between the Coulomb interaction and the kinetic energy can be varied in situ, can provide an invaluable model system for the study of Mott physics. Here we report the possible realization of such a tunable Mott insulator in a trilayer graphene heterostructure with a moiré superlattice. The combination of the cubic energy dispersion in ABC-stacked trilayer graphene4–8and the narrow electronic minibands induced by the moiré potential9–15leads to the observation of insulating states at the predicted band fillings for the Mott insulator. Moreover, the insulating states in the heterostructure can be tuned: the bandgap can be modulated by a vertical electrical field, and at the same time the electron doping can be modified by a gate to fill the band from one insulating state to another. This opens up exciting opportunities to explore strongly correlated phenomena in two-dimensional moiré superlattice heterostructures.

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

Heterostructures can be assembled from atomically thin materials by combining a wide range of available van der Waals crystals, providing exciting possibilities for designer electronics1. 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 layers2. 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.

Near the magic angle, strong correlations drive many intriguing phases in twisted bilayer graphene (tBG) including unconventional superconductivity and chern insulation. Whether correlations can tune symmetry breaking phases in tBG at intermediate (≳ 2°) twist angles remains an open fundamental question. Here, using ARPES, we study the effects of many-body interactions and displacement field on the band structure of tBG devices at an intermediate (3°) twist angle. We observe a layer- and doping-dependent renormalization of bands at the Kpoints that is qualitatively consistent with moiré models of the Hartree–Fock interaction. We provide evidence of correlation-enhanced inversion symmetry-breaking, manifested by gaps at the Dirac points that are tunable with doping. These results suggest that electronic interactions play a significant role in the physics of tBG even at intermediate twist angles and present a new pathway toward engineering band structure and symmetry-breaking phases in moiré heterostructures.

Graphene/hexagonal boron nitride (h-BN) has emerged as a model van der Waals heterostructure as the superlattice potential, which is induced by lattice mismatch and crystal orientation, gives rise to various novel quantum phenomena, such as the self-similar Hofstadter butterfly states. Although the newly generated second-generation Dirac cones (SDCs) are believed to be crucial for understanding such intriguing phenomena, fundamental knowledge of SDCs, such as locations and dispersion, and the effect of inversion symmetry breaking on the gap opening, still remains highly debated due to the lack of direct experimental results. Here we report direct experimental results on the dispersion of SDCs in 0°-aligned graphene/h-BN heterostructures using angle-resolved photoemission spectroscopy. Our data unambiguously reveal SDCs at the corners of the superlattice Brillouin zone, and at only one of the two superlattice valleys. Moreover, gaps of approximately 100 meV and approximately 160 meV are observed at the SDCs and the original graphene Dirac cone, respectively. Our work highlights the important role of a strong inversion-symmetry-breaking perturbation potential in the physics of graphene/h-BN, and fills critical knowledge gaps in the band structure engineering of Dirac fermions by a superlattice potential.

Polycrystalline growth of molybdenum disulfide (MoS2) using chemical vapor deposition (CVD) methods is subject to the formation of grain boundaries (GBs), which have a large effect on the electrical and optical properties of MoS2-based optoelectronic devices. The identification of grains and GBs of CVD-grown monolayer MoS2has traditionally required atomic resolution microscopy or nonlinear optical imaging techniques. Here, we present a simple spectroscopic method for visualizing GBs of polycrystalline monolayer MoS2using stacked bilayers and mapping their indirect photoluminescence (PL) peak positions and Raman peak intensities. We were able to distinguish a GB between two MoS2grains with tilt angles as small as 6° in their grain orientations and, based on the inspection of several GBs, found a simple empirical rule to predict the location of the GBs. In addition, the large number of twist angle domains traced through our facile spectroscopic mapping technique allowed us to identify a continuous evolution of the coupled structural and optical properties of bilayer MoS2in the vicinity of the 0° and 60° commensuration angles which were explained by elastic deformation model of the MoS2membranes.

We use a self-consistent Hartree-Fock approximation with realistic Coulomb interactions for π-band electrons to explore the possibility of broken symmetry states in weakly disordered ABC-stacked trilayer graphene. The competition between gapped and gapless broken symmetry states and normal states is studied by comparing total energies. We find that gapped states are favored and that, unlike the bilayer case, gapless nematic broken symmetry states are not metastable. Among the gapped states, the layer antiferromagnetic state is favored over anomalous and spin Hall states. [ABSTRACT FROM AUTHOR]