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.

Effective Manipulation of a Colossal Second-Order Transverse Response in an Electric-Field-Tunable Graphene Moiré System.

The second-order nonlinear transport illuminates a frequency-doubling response emerging in quantum materials with a broken inversion symmetry. The two principal driving mechanisms, the Berry curvature dipole and the skew scattering, reflect various information including ground-state symmetries, band dispersions, and topology of electronic wave functions. However, effective manipulation of them in a single system has been lacking, hindering the pursuit of strong responses. Here, we report on the effective manipulation of the two mechanisms in a single graphene moiré superlattice, AB-BA stacked twisted double bilayer graphene. Most saliently, by virtue of the high tunability of moiré band structures and scattering rates, a record-high second-order transverse conductivity ∼ 510 µm S V-1 is observed, which is orders of magnitude higher than any reported values in the literature. Our findings establish the potential of electrically tunable graphene moiré systems for nonlinear transport manipulations and applications.

Chemical Potential Characterization of Symmetry-Breaking Phases in a Rhombohedral Trilayer Graphene.

Rhombohedral trilayer graphene has recently emerged as a natural flat-band platform for studying interaction-driven symmetry-breaking phases. The displacement field (D) can further flatten the band to enhance the density of states, thereby controlling the electronic correlation that tips the energy balance between spin and valley degrees of freedom. To characterize the energy competition, chemical potential measurement─a direct thermodynamic probe of Fermi surfaces─is highly demanding to be conducted under a constant D. In this work, we characterize D-dependent isospin flavor polarization, where electronic states with isospin degeneracies of one and two can be identified. We also developed a method to measure the chemical potential at a fixed D, allowing for the extraction of energy variation during phase transitions. Furthermore, symmetry breaking could also be invoked in Landau levels, manifesting as quantum Hall ferromagnetism. Our work opens more opportunities for the thermodynamic characterization of displacement-field tuned van der Waals heterostructures.

Giant Second-Order Nonlinear Hall Effect in Twisted Bilayer Graphene.

In the second-order response regime, the Hall voltage can be nonzero without time-reversal symmetry breaking but inversion symmetry breaking. Multiple mechanisms contribute to the nonlinear Hall effect. The disorder-related contributions can enter the NLHE in the leading role, but experimental investigations are scarce, especially the exploration of the contributions from different disorder sources. Here, we report a giant nonlinear response in twisted bilayer graphene, dominated by disorder-induced skew scattering. The magnitude and direction of the second-order nonlinearity can be effectively tuned by the gate voltage. A peak value of the second-order Hall conductivity reaching 8.76 µm SV^{-1} is observed close to the full filling of the moiré band, four order larger than the intrinsic contribution detected in WTe_{2}. The scaling shows that the giant second-order nonlinear Hall effect in twisted bilayer graphene stems from the collaboration of the static (impurities) and dynamic (phonons) disorders. It is mainly determined by the impurity skew scattering at 1.7 K. The phonon skew scattering, however, has a much larger coupling coefficient, and becomes comparable to the impurity contribution as the temperature rises. Our observations provide a comprehensive experimental understanding of the disorder-related mechanisms in the nonlinear Hall effect.

Quantum Hall phase in graphene engineered by interfacial charge coupling.

The quantum Hall effect can be substantially affected by interfacial coupling between the host two-dimensional electron gases and the substrate, and has been predicted to give rise to exotic topological states. Yet the understanding of the underlying physics and the controllable engineering of this interaction remains challenging. Here we demonstrate the observation of an unusual quantum Hall effect, which differs markedly from that of the known picture, in graphene samples in contact with an antiferromagnetic insulator CrOCl equipped with dual gates. Two distinct quantum Hall phases are developed, with the Landau levels in monolayer graphene remaining intact at the conventional phase, but largely distorted for the interfacial-coupling phase. The latter quantum Hall phase is even present close to the absence of a magnetic field, with the consequential Landau quantization following a parabolic relation between the displacement field and the magnetic field. This characteristic prevails up to 100 K in a wide effective doping range from 0 to 1013 cm-2.

Giant ferroelectric polarization in a bilayer graphene heterostructure.

At the interface of van der Waals heterostructures, the crystal symmetry and the electronic structure can be reconstructed, giving rise to physical properties superior to or absent in parent materials. Here by studying a Bernal bilayer graphene moiré superlattice encapsulated by 30°-twisted boron nitride flakes, we report an unprecedented ferroelectric polarization with the areal charge density up to 1013 cm-2, which is far beyond the capacity of a moiré band. The translated polarization ~5 pC m-1 is among the highest interfacial ferroelectrics engineered by artificially stacking van der Waals crystals. The gate-specific ferroelectricity and co-occurring anomalous screening are further visualized via Landau levels, and remain robust for Fermi surfaces outside moiré bands, confirming their independence on correlated electrons. We also find that the gate-specific resistance hysteresis loops could be turned off by the other gate, providing an additional control knob. Furthermore, the ferroelectric switching can be applied to intrinsic properties such as topological valley current. Overall, the gate-specific ferroelectricity with strongly enhanced charge polarization may encourage more explorations to optimize and enrich this novel class of ferroelectricity, and promote device applications for ferroelectric switching of various quantum phenomena.

Imaging topological and correlated insulating states in twisted monolayer-bilayer graphene.

Flat bands in Van der Waals heterostructure provide an ideal platform for unveiling emergent quantum electronic phases. One celebrated example is twisted monolayer-bilayer graphene, in which the effects of electronic correlation have been observed. Here, we report the observation via scanning tunnelling microscopy and spectroscopy of correlated insulating states in twisted monolayer-bilayer graphene, leading to the formation of an electron crystal phase. At integer fillings, the strong Coulomb interaction redistributes flat-band electrons within one moiré unit cell, producing an insulating state with vanishing density of states at the Fermi level. Moreover, our approach enables the direct visualization of an ordered lattice of topological torus-shaped states, generated by the interaction between the electron crystal and the non-trivial band topology of twisted monolayer-bilayer graphene. Our results illustrate an efficient strategy for entwining topological physics with strong electron correlation in twisted van der Waals structures.

Correlated states in doubly-aligned hBN/graphene/hBN heterostructures.

Interfacial moiré superlattices in van der Waals vertical assemblies effectively reconstruct the crystal symmetry, leading to opportunities for investigating exotic quantum states. Notably, a two-dimensional nanosheet has top and bottom open surfaces, allowing the specific case of doubly aligned super-moiré lattice to serve as a toy model for studying the tunable lattice symmetry and the complexity of related electronic structures. Here, we show that by doubly aligning a graphene monolayer to both top and bottom encapsulating hexagonal boron nitride (h-BN), multiple conductivity minima are observed away from the main Dirac point, which are sensitively tunable with respect to the small twist angles. Moreover, our experimental evidences together with theoretical calculations suggest correlated insulating states at integer fillings of -5, -6, -7 electrons per moiré unit cell, possibly due to inter-valley coherence. Our results provide a way to construct intriguing correlations in 2D electronic systems in the weak interaction regime.

Evidence of flat bands and correlated states in buckled graphene superlattices.

Two-dimensional atomic crystals can radically change their properties in response to external influences, such as substrate orientation or strain, forming materials with novel electronic structure1-5. An example is the creation of weakly dispersive, 'flat' bands in bilayer graphene for certain 'magic' angles of twist between the orientations of the two layers6. The quenched kinetic energy in these flat bands promotes electron-electron interactions and facilitates the emergence of strongly correlated phases, such as superconductivity and correlated insulators. However, the very accurate fine-tuning required to obtain the magic angle in twisted-bilayer graphene poses challenges to fabrication and scalability. Here we present an alternative route to creating flat bands that does not involve fine-tuning. Using scanning tunnelling microscopy and spectroscopy, together with numerical simulations, we demonstrate that graphene monolayers placed on an atomically flat substrate can be forced to undergo a buckling transition7-9, resulting in a periodically modulated pseudo-magnetic field10-14, which in turn creates a 'post-graphene' material with flat electronic bands. When we introduce the Fermi level into these flat bands using electrostatic doping, we observe a pseudogap-like depletion in the density of states, which signals the emergence of a correlated state15-17. This buckling of two-dimensional crystals offers a strategy for creating other superlattice systems and, in particular, for exploring interaction phenomena characteristic of flat bands.

Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene.

Bilayer graphene can be modified by rotating (twisting) one layer with respect to the other. The interlayer twist gives rise to a moiré superlattice that affects the electronic motion and alters the band structure1-4. Near a 'magic angle' of twist2,4, where the emergence of a flat band causes the charge carriers to slow down3, correlated electronic phases including Mott-like insulators and superconductors were recently discovered5-8 by using electronic transport. These measurements revealed an intriguing similarity between magic-angle twisted bilayer graphene and high-temperature superconductors, which spurred intensive research into the underlying physical mechanism9-14. Essential clues to this puzzle, such as the symmetry and spatial distribution of the spectral function, can be accessed through scanning tunnelling spectroscopy. Here we use scanning tunnelling microscopy and spectroscopy to visualize the local density of states and charge distribution in magic-angle twisted bilayer graphene. Doping the sample to partially fill the flat band, we observe a pseudogap phase accompanied by a global stripe charge order that breaks the rotational symmetry of the moiré superlattice. Both the pseudogap and the stripe charge order disappear when the band is either empty or full. The close resemblance to similar observations in high-temperature superconductors15-21 provides new evidence of a deeper link underlying the phenomenology of these systems.

Inducing Kondo screening of vacancy magnetic moments in graphene with gating and local curvature.

In normal metals the magnetic moment of impurity-spins disappears below a characteristic Kondo temperature which marks the formation of a cloud of conduction-band electrons that screen the local-moment. In contrast, moments embedded in insulators remain unscreened at all temperatures. What then is the fate of magnetic-moments in intermediate, pseudogap systems, such as graphene? Theory predicts that coupling to the conduction-band electrons will drive a quantum phase transition between a local-moment phase and a Kondo-screened phase. However, attempts to experimentally confirm this prediction and its intriguing consequences, such as electrostatically tunable magnetic-moments, have been elusive. Here we report the observation of Kondo-screening and the quantum phase-transition between screened and unscreened phases of vacancy magnetic moments in graphene. Using scanning tunneling spectroscopy and numerical renormalization-group calculations we show that this transition enables to control the screening of local moments by tuning the gate voltage and the local curvature of the graphene membrane.

Observing a scale anomaly and a universal quantum phase transition in graphene.

One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale-free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe 'Efimov physics'. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive 1/r Coulomb potential. The purpose of this article is to demonstrate the universality of this quantum phase transition and to present convincing experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realized in graphene.When the continuous scale symmetry of a quantum system is broken, anomalies occur which may lead to quantum phase transitions. Here, the authors provide evidence for such a quantum phase transition in the attractive Coulomb potential of vacancies in graphene, and further envision its universality for diverse physical systems.

Tuning a circular p-n junction in graphene from quantum confinement to optical guiding.

The photon-like propagation of the Dirac electrons in graphene, together with its record-high electronic mobility, can lead to applications based on ultrafast electronic response and low dissipation. However, the chiral nature of the charge carriers that is responsible for the high mobility also makes it difficult to control their motion and prevents electronic switching. Here, we show how to manipulate the charge carriers by using a circular p-n junction whose size can be continuously tuned from the nanometre to the micrometre scale. The junction size is controlled with a dual-gate device consisting of a planar back gate and a point-like top gate made by decorating a scanning tunnelling microscope tip with a gold nanowire. The nanometre-scale junction is defined by a deep potential well created by the tip-induced charge. It traps the Dirac electrons in quantum-confined states, which are the graphene equivalent of the atomic collapse states (ACSs) predicted to occur at supercritically charged nuclei. As the junction size increases, the transition to the optical regime is signalled by the emergence of whispering-gallery modes, similar to those observed at the perimeter of acoustic or optical resonators, and by the appearance of a Fabry-Pérot interference pattern for junctions close to a boundary.

Visualizing Strain-Induced Pseudomagnetic Fields in Graphene through an hBN Magnifying Glass.

Graphene's remarkable properties are inherent to its two-dimensional honeycomb lattice structure. Its low dimensionality, which makes it possible to rearrange the atoms by applying an external force, offers the intriguing prospect of mechanically controlling the electronic properties. In the presence of strain, graphene develops a pseudomagnetic field (PMF) that reconstructs the band structure into pseudo Landau levels (PLLs). However, a feasible route to realizing, characterizing and controlling PMFs is still lacking. Here we report on a method to generate and characterize PMFs in a graphene membrane supported on nanopillars. A direct measure of the local strain is achieved by using the magnifying effect of the moiré pattern formed against a hexagonal boron nitride substrate under scanning tunneling microscopy. We quantify the strain-induced PMF through the PLLs spectra observed in scanning tunneling spectroscopy. This work provides a pathway to strain induced engineering and electro-mechanical graphene-based devices.

Bandgap, mid-gap states, and gating effects in MoS2.

The discovery of graphene has put the spotlight on other layered materials including transition metal dichalcogenites (TMD) as building blocks for novel heterostructures assembled from stacked atomic layers. Molybdenum disulfide, MoS2, a semiconductor in the TMD family, with its remarkable thermal and chemical stability and high mobility, has emerged as a promising candidate for postsilicon applications such as switching, photonics, and flexible electronics. Because these rely on controlling the position of the Fermi energy (EF), it is crucial to understand its dependence on doping and gating. To elucidate these questions we carried out gated scanning tunneling microscopy (STM) and spectroscopy (STS) measurements and compared them with transport measurements in a field effect transistor (FET) device configuration. This made it possible to measure the bandgap and the position of EF in MoS2 and to track its evolution with gate voltage. For bulk samples, the measured bandgap (∼ 1.3 eV) is comparable to the value obtained by photoluminescence, and the position of EF (∼ 0.35 eV) below the conduction band, is consistent with N-doping reported in this material. We show that the N-doping in bulk samples can be attributed to S vacancies. In contrast, the significantly higher N-doping observed in thin MoS2 films deposited on SiO2 is dominated by charge traps at the sample-substrate interface.

Tunability of supramolecular Kagome lattices of magnetic phthalocyanines using graphene-based moire patterns as templates.

Self-assembly of various phthalocyanine (Pc) molecules and a derivative on an epitaxial graphene monolayer (MG) has been investigated by means of in situ ultrahigh vacuum scanning tunneling microscopy. The formation of regular Kagome lattices that duplicate the lattice of the moire pattern of MG was observed, demonstrating that MG can act as a wonderful template for the fabrication of unique nanoarchitectures with remarkable properties. Varying the central metal ion of the Pc molecule affords Kagome lattices with tunable molecular spins, providing ideal two-dimensional model systems for studying frustration physics.