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.

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.

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.

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.

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.

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.

Tunability of 1/f Noise at Multiple Dirac Cones in hBN Encapsulated Graphene Devices.

The emergence of multiple Dirac cones in hexagonal boron nitride (hBN)-graphene heterostructures is particularly attractive because it offers potentially better landscape for higher and versatile transport properties than the primary Dirac cone. However, the transport coefficients of the cloned Dirac cones is yet not fully characterized and many open questions, including the evolution of charge dynamics and impurity scattering responsible for them, have remained unexplored. Noise measurements, having the potential to address these questions, have not been performed to date in dual-gated hBN-graphene-hBN devices. Here, we present the low-frequency 1/f noise measurements at multiple Dirac cones in hBN encapsulated single and bilayer graphene in dual-gated geometry. Our results reveal that the low-frequency noise in graphene can be tuned by more than two-orders of magnitude by changing carrier concentration as well as by modifying the band structure in bilayer graphene. We find that the noise is surprisingly suppressed at the cloned Dirac cone compared to the primary Dirac cone in single layer graphene device, while it is strongly enhanced for the bilayer graphene with band gap opening. The results are explained with the calculation of dielectric function using tight-binding model. Our results also indicate that the 1/f noise indeed follows the Hooge's empirical formula in hBN-protected devices in dual-gated geometry. We also present for the first time the noise data in bipolar regime of a graphene device.

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.

Van der Waals force: a dominant factor for reactivity of graphene.

Reactivity control of graphene is an important issue because chemical functionalization can modulate graphene's unique mechanical, optical, and electronic properties. Using systematic optical studies, we demonstrate that van der Waals interaction is the dominant factor for the chemical reactivity of graphene on two-dimensional (2D) heterostructures. A significant enhancement in the chemical stability of graphene is achieved by replacing the common SiO2 substrate with 2D crystals such as an additional graphene layer, WS2, MoS2, or h-BN. Our theoretical and experimental results show that its origin is a strong van der Waals interaction between the graphene layer and the 2D substrate. This results in a high resistive force on graphene toward geometric lattice deformation. We also demonstrate that the chemical reactivity of graphene can be controlled by the relative lattice orientation with respect to the substrates and thus can be used for a wide range of applications including hydrogen storage.

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.

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.

Transport properties of graphene nanoroads in boron nitride sheets.

We demonstrate that the one-dimensional (1D) transport channels that appear in the gap when graphene nanoroads are embedded in boron nitride (BN) sheets are more robust when they are inserted at AB/BA grain boundaries. Our conclusions are based on ab initio electronic structure calculations for a variety of different crystal orientations and bonding arrangements at the BN/C interfaces. This property is related to the valley Hall conductivity present in the BN band structure and to the topologically protected kink states that appear in continuum Dirac models with position-dependent masses.

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.

Electronic highways in bilayer graphene.

Bilayer graphene with an interlayer potential difference has an energy gap and, when the potential difference varies spatially, topologically protected one-dimensional states localized along the difference's zero lines. When disorder is absent, electronic travel directions along zero-line trajectories are fixed by valley Hall properties. Using the Landauer-Büttiker formula and the nonequilibrium Green's function technique, we demonstrate numerically that collisions between electrons traveling in opposite directions, due to either disorder or changes in path direction, are strongly suppressed. We find that extremely long mean free paths of the order of hundreds of micrometers can be expected in relatively clean samples. This finding suggests the possibility of designing low power nanoscale electronic devices in which transport paths are controlled by gates which alter the interlayer potential landscape.

Spontaneous quantum Hall states in chirally stacked few-layer graphene systems.

Chirally stacked N-layer graphene systems with N≥2 exhibit a variety of distinct broken symmetry states in which charge density contributions from different spins and valleys are spontaneously transferred between layers. We explain how these states are distinguished by their charge, spin, and valley Hall conductivities, by their orbital magnetizations, and by their edge state properties. We argue that valley Hall states have [N/2] edge channels per spin valley.

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.

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.