Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene.

In Bernal-stacked bilayer graphene (BBG), the Landau levels give rise to an intimate connection between valley and layer degrees of freedom. Adding a moiré superlattice potential enriches the BBG physics with the formation of topological minibands - potentially leading to tunable exotic quantum transport. Here, we present magnetotransport measurements of a high-quality bilayer graphene-hexagonal boron nitride (hBN) heterostructure. The zero-degree alignment generates a strong moiré superlattice potential for the electrons in BBG and the resulting Landau fan diagram of longitudinal and Hall resistance displays a Hofstadter butterfly pattern with a high level of detail. We demonstrate that the intricate relationship between valley and layer degrees of freedom controls the topology of moiré-induced bands, significantly influencing the energetics of interacting quantum phases in the BBG superlattice. We further observe signatures of field-induced correlated insulators, helical edge states and clear quantizations of interaction-driven topological quantum phases, such as symmetry broken Chern insulators.

Observation of dichotomic field-tunable electronic structure in twisted monolayer-bilayer graphene.

Twisted bilayer graphene (tBLG) provides a fascinating platform for engineering flat bands and inducing correlated phenomena. By designing the stacking architecture of graphene layers, twisted multilayer graphene can exhibit different symmetries with rich tunability. For example, in twisted monolayer-bilayer graphene (tMBG) which breaks the C2z symmetry, transport measurements reveal an asymmetric phase diagram under an out-of-plane electric field, exhibiting correlated insulating state and ferromagnetic state respectively when reversing the field direction. Revealing how the electronic structure evolves with electric field is critical for providing a better understanding of such asymmetric field-tunable properties. Here we report the experimental observation of field-tunable dichotomic electronic structure of tMBG by nanospot angle-resolved photoemission spectroscopy (NanoARPES) with operando gating. Interestingly, selective enhancement of the relative spectral weight contributions from monolayer and bilayer graphene is observed when switching the polarity of the bias voltage. Combining experimental results with theoretical calculations, the origin of such field-tunable electronic structure, resembling either tBLG or twisted double-bilayer graphene (tDBG), is attributed to the selectively enhanced contribution from different stacking graphene layers with a strong electron-hole asymmetry. Our work provides electronic structure insights for understanding the rich field-tunable physics of tMBG.

Engineering the Band Topology in a Rhombohedral Trilayer Graphene Moiré Superlattice.

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.

Spontaneous broken-symmetry insulator and metals in tetralayer rhombohedral graphene.

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 n and electric displacement field D. Specifically, we observe a layer-antiferromagnetic insulator at n = D = 0 with a gap of approximately 15 meV. Increasing D allows for a continuous phase transition from a layer-antiferromagnetic insulator to a layer-polarized insulator. By simultaneously tuning n and 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.

Spin-orbit coupling-enhanced valley ordering of malleable bands in twisted bilayer graphene on WSe2.

Recent experiments in magic-angle twisted bilayer graphene have revealed a wealth of novel electronic phases as a result of interaction-driven spin-valley flavour polarisation. In this work, we investigate correlated phases due to the combined effect of spin-orbit coupling-enhanced valley polarisation and the large density of states below half filling of the moiré band in twisted bilayer graphene coupled to tungsten diselenide. We observe an anomalous Hall effect, accompanied by a series of Lifshitz transitions that are highly tunable with carrier density and magnetic field. The magnetisation shows an abrupt change of sign near half-filling, confirming its orbital nature. While the Hall resistance is not quantised at zero magnetic fields-indicating a ground state with partial valley polarisation-perfect quantisation and complete valley polarisation are observed at finite fields. Our results illustrate that singularities in the flat bands in the presence of spin-orbit coupling can stabilise ordered phases even at non-integer moiré band fillings.

Layer-Dependent Interaction Effects in the Electronic Structure of Twisted Bilayer Graphene Devices.

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 K points 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.

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.

Magnetoelectric Response of Antiferromagnetic CrI3 Bilayers.

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 CrI3 at 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.

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.

Ultrahigh-resolution scanning microwave impedance microscopy of moiré lattices and superstructures.

Two-dimensional heterostructures composed of layers with slightly different lattice vectors exhibit new periodic structure known as moiré lattices, which, in turn, can support novel correlated and topological phenomena. Moreover, moiré superstructures can emerge from multiple misaligned moiré lattices or inhomogeneous strain distributions, offering additional degrees of freedom in tailoring electronic structure. High-resolution imaging of the moiré lattices and superstructures is critical for understanding the emerging physics. Here, we report the imaging of moiré lattices and superstructures in graphene-based samples under ambient conditions using an ultrahigh-resolution implementation of scanning microwave impedance microscopy. Although the probe tip has a gross radius of ~100 nm, spatial resolution better than 5 nm is achieved, which allows direct visualization of the structural details in moiré lattices and the composite super-moiré. We also demonstrate artificial synthesis of novel superstructures, including the Kagome moiré arising from the interplay between different layers.

Bulk valley transport and Berry curvature spreading at the edge of flat bands.

2D materials based superlattices have emerged as a promising platform to modulate band structure and its symmetries. In particular, moiré periodicity in twisted graphene systems produces flat Chern bands. The recent observation of anomalous Hall effect (AHE) and orbital magnetism in twisted bilayer graphene has been associated with spontaneous symmetry breaking of such Chern bands. However, the valley Hall state as a precursor of AHE state, when time-reversal symmetry is still protected, has not been observed. Our work probes this precursor state using the valley Hall effect. We show that broken inversion symmetry in twisted double bilayer graphene (TDBG) facilitates the generation of bulk valley current by reporting experimental evidence of nonlocal transport in a nearly flat band system. Despite the spread of Berry curvature hotspots and reduced quasiparticle velocities of the carriers in these flat bands, we observe large nonlocal voltage several micrometers away from the charge current path - this persists when the Fermi energy lies inside a gap with large Berry curvature. The high sensitivity of the nonlocal voltage to gate tunable carrier density and gap modulating perpendicular electric field makes TDBG an attractive platform for valley-twistronics based on flat bands.

Carrier Depletion near the Grain Boundary of a SiC Bicrystal.

Silicon carbide (SiC) bicrystals were prepared by diffusion bonding, and their grain boundary was observed using scanning transmission electron microscopy. The n-type electrical conductivity of a SiC single crystal was confirmed by scanning nonlinear dielectric microscopy (SNDM). Dopant profiling of the sample by SNDM showed that the interface acted as an electrical insulator with a ~2-µm-thick carrier depletion layer. The carrier depletion layer contained a higher number of oxygen impurities than the bulk crystals due to the incorporation of oxygen from the native oxide film during diffusion bonding. Density functional theory calculations of the density of states as a function of the bandgap also supported these findings. The existence of a carrier depletion layer was also confirmed in a p-type polycrystalline SiC ceramic. These results suggest that the electrical conductivity of SiC ceramics was mostly affected by carrier depletion near the grain boundary rather than the grain boundary itself.

Signatures of tunable superconductivity in a trilayer graphene moiré superlattice.

Understanding the mechanism of high-transition-temperature (high-Tc) superconductivity is a central problem in condensed matter physics. It is often speculated that high-Tc superconductivity arises in a doped Mott insulator1 as 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 superlattice5,6 where 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.

Gate-Tunable Topological Flat Bands in Trilayer Graphene Boron-Nitride Moiré Superlattices.

We investigate the electronic structure of the flat bands induced by moiré superlattices and electric fields in nearly aligned ABC trilayer graphene (TLG) boron-nitride (BN) interfaces where Coulomb effects can lead to correlated gapped phases. Our calculations indicate that valley-spin resolved isolated superlattice flat bands that carry a finite Chern number C=3 proportional to the layer number can appear near charge neutrality for appropriate perpendicular electric fields and twist angles. When the degeneracy of the bands is lifted by Coulomb interactions, these topological bands can lead to anomalous quantum Hall phases that embody orbital and spin magnetism. Narrow bandwidths of ∼10 meV achievable for a continuous range of twist angles θ≲0.6° with moderate interlayer potential differences of ∼50 meV make the TLG-BN systems a promising platform for the study of electric-field tunable Coulomb-interaction-driven spontaneous Hall phases.

Accurate Gap Determination in Monolayer and Bilayer Graphene/ h-BN Moiré Superlattices.

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.

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.

Emergence of Tertiary Dirac Points in Graphene Moiré Superlattices.

The electronic structure of a crystalline solid is largely determined by its lattice structure. Recent advances in van der Waals solids, artificial crystals with controlled stacking of two-dimensional (2D) atomic films, have enabled the creation of materials with novel electronic structures. In particular, stacking graphene on hexagonal boron nitride (hBN) introduces a moiré superlattice that fundamentally modifies graphene's band structure and gives rise to secondary Dirac points (SDPs). Here we find that the formation of a moiré superlattice in graphene on hBN yields new, unexpected consequences: a set of tertiary Dirac points (TDPs) emerge, which give rise to additional sets of Landau levels when the sample is subjected to an external magnetic field. Our observations hint at the formation of a hidden Kekulé superstructure on top of the moiré superlattice under appropriate carrier doping and magnetic fields.

Graphene bubbles and their role in graphene quantum transport.

Graphene bubbles are often formed when graphene and other layered two-dimensional materials are vertically stacked as van der Waals heterostructures. Here, we investigate how graphene bubbles and their related disorder impact the quantum transport behavior of graphene in the absence and presence of external magnetic fields. By combining experimental observations and numerical simulations, we find that the disorder induced by the graphene bubbles is mainly from p-type dopants and the charge transport in pristine graphene can be severely influenced by the presence of bubbles via long- and short-range scattering even with a small bubble-coverage of 2% and below. Upon bubble density increase, we observe an overall decrease in carrier mobility, and the appearance of a second Dirac point on the electron carrier side. At high magnetic fields, the disorder from graphene bubbles primarily impacts the quantization of the lowest Landau level, resulting in quantum Hall features associated with a new Dirac cone at high charge carrier density.

Fractional Hofstadter States in Graphene on Hexagonal Boron Nitride.

In fractionally filled Landau levels there is only a small energy difference between broken translational symmetry electron-crystal states and exotic correlated quantum fluid states. We show that the spatially periodic substrate interaction associated with the long period moiré patterns present in graphene on nearly aligned hexagonal boron nitride tilts this close competition in favor of the former, explaining surprising recent experimental findings.