Deterministic fabrication of graphene hexagonal boron nitride moiré superlattices.

The electronic properties of moiré heterostructures depend sensitively on the relative orientation between layers of the stack. For example, near-magic-angle twisted bilayer graphene (TBG) commonly shows superconductivity, yet a TBG sample with one of the graphene layers rotationally aligned to a hexagonal Boron Nitride (hBN) cladding layer provided experimental observation of orbital ferromagnetism. To create samples with aligned graphene/hBN, researchers often align edges of exfoliated flakes that appear straight in optical micrographs. However, graphene or hBN can cleave along either zig-zag or armchair lattice directions, introducing a [Formula: see text] ambiguity in the relative orientation of two flakes. By characterizing the crystal lattice orientation of exfoliated flakes prior to stacking using Raman and second-harmonic generation for graphene and hBN, respectively, we unambiguously align monolayer graphene to hBN at a near-[Formula: see text], not [Formula: see text], relative twist angle. We confirm this alignment by torsional force microscopy of the graphene/hBN moiré on an open-face stack, and then by cryogenic transport measurements, after full encapsulation with a second, nonaligned hBN layer. This work demonstrates a key step toward systematically exploring the effects of the relative twist angle between dissimilar materials within moiré heterostructures.

Maximally localized Wannier functions, interaction models, and fractional quantum anomalous Hall effect in twisted bilayer MoTe2.

We investigate the moiré band structures and the strong correlation effects in twisted bilayer MoTe[Formula: see text] for a wide range of twist angles, employing a combination of various techniques. Using large-scale first-principles calculations, we pinpoint realistic continuum modeling parameters, subsequently deriving the maximally localized Wannier functions for the top three moiré bands. Simplifying our model with reasonable assumptions, we obtain a minimal two-band model, encompassing Coulomb repulsion, correlated hopping, and spin exchange. Our minimal interaction models pave the way for further exploration of the rich many-body physics in twisted MoTe[Formula: see text]. Furthermore, we explore the phase diagrams of the system through Hartree-Fock approximation and exact diagonalization (ED). Our two-band ED analysis underscores significant band-mixing effects in this system, which enlarge the optimal twist angle for fractional quantum anomalous Hall states.

Manipulation of Moiré Superlattice in Twisted Monolayer-multilayer Graphene by Moving Nanobubbles.

In the heterostructure of two-dimensional (2D) materials, many novel physics phenomena are strongly dependent on the Moiré superlattice. How to achieve the continuous manipulation of the Moiré superlattice in the same sample is very important to study the evolution of various physical properties. Here, in minimally twisted monolayer-multilayer graphene, we found that bubble-induced strain has a huge impact on the Moiré superlattice. By employing the AFM tip to dynamically and continuously move the nanobubble, we realized the modulation of the Moiré superlattice, like the evolution of regular triangular domains into long strip domain structures with single or double domain walls. We also achieved controllable modulation of the Moiré superlattice by moving multiple nanobubbles and establishing the coupling of nanobubbles. Our work presents a flexible method for continuous and controllable manipulation of Moiré superlattices, which will be widely used to study novel physical properties in 2D heterostructures.

Emergence of Optical Anisotropy in Moiré Superlattice via Heterointerface Engineering.

The interaction between light and moiré superlattices presents a platform for exploring unique light-matter phenomena. Tailoring these optical properties holds immense potential for advancing the utilization of moiré superlattices in photonics, optoelectronics, and valleytronics. However, the control of the optical polarization state in moiré superlattices, particularly in the presence of moiré effects, remains elusive. Here, we unveil the emergence of optical anisotropy in moiré superlattices by constructing twisted WSe2/WSe2/SiP heterostructures. We report a linear polarization degree of ∼70% for moiré excitons, attributed to the spatially nonuniform charge distribution, corroborated by first-principles calculations. Furthermore, we demonstrate the modulation of this linear polarization state via the application of a magnetic field, resulting in polarization angle rotation and a magnetic-field-dependent linear polarization degree, influenced by valley coherence and moiré potential effects. Our findings demonstrate an efficient strategy for tuning the optical polarization state of moiré superlattices using heterointerface engineering.

Nonlinear Landau Fan Diagram for Graphene Electrons Exposed to a Moiré Potential.

Due to Landau quantization, the conductance of two-dimensional electrons exposed to a perpendicular magnetic field exhibits oscillations that generate a fan of linear trajectories when plotted in the parameter space spanned by density and field. This fan looks identical, irrespective of the dispersion and field dependence of the Landau level energy. This is no surprise because the position of conductance minima depends solely on the level degeneracy that is linear in flux. The fractal energy spectrum that emerges within each Landau band when electrons are also exposed to a two-dimensional superlattice potential produces numerous additional oscillations, but they also create just linear fans for identical reasons. Here, we report conductance oscillations of graphene electrons exposed to a moiré potential that defy this general rule and form nonlinear trajectories in the density-field plane. We attribute this anomalous behavior to the simultaneous occupation of multiple minibands and magnetic breakdown-induced open orbits.

Chern Insulator States with Tunable Chern Numbers in a Graphene Moiré Superlattice.

Moiré superlattices, constituted by two-dimensional materials, demonstrate a variety of strongly correlated and topological phenomena including correlated insulators, superconductivity, and integer/fractional Chern insulators. In the realm of topological nontrivial Chern insulators within specific moiré superlattices, previous studies usually observe a single Chern number at a given filling factor in a device. Here we present the observation of gate-tunable Chern numbers within the Chern insulator state of an ABC-stacked trilayer graphene/hexagonal boron nitride moiré superlattice device. Near quarter filling, the moiré superlattice exhibits spontaneous valley polarization and distinct ferromagnetism associated with the Chern insulator states over a range of the displacement field. Surprisingly we find a transition of the Chern number from C = 3 to 4 as the displacement field is increased. Our observation of gate-tunable correlated Chern insulators suggests new ways to control and manipulate topological states in a moiré superlattice device.

Spatial Filtering of Interlayer Exciton Ground State in WSe2/MoS2 Heterobilayer.

Long-life interlayer excitons (IXs) in transition metal dichalcogenide (TMD) heterostructure are promising for realizing excitonic condensates at high temperatures. Critical to this objective is to separate the IX ground state (the lowest energy of IX state) emission from other states' emissions. Filtering the IX ground state is also essential in uncovering the dynamics of correlated excitonic states, such as the excitonic Mott insulator. Here, we show that the IX ground state in the WSe2/MoS2 heterobilayer can be separated from other states by its spatial profile. The emissions from different moiré IX modes are identified by their different energies and spatial distributions, which fits well with the rate-diffusion model for cascading emission. Our results show spatial filtering of the ground state mode and enrich the toolbox to realize correlated states at elevated temperatures.

Experimental Demonstration of High-Efficiency Harmonic Generation in Photonic Moiré Superlattice Microcavities.

Integrated photonic microcavities have demonstrated powerful enhancement of nonlinear effects, but they face a challenge in achieving critical coupling for sufficient use of incident pump power. In this work, we first experimentally demonstrate that highly efficient third-harmonic generation (THG) and detectable second-harmonic generation (SHG) can be produced from high-Q photonic moiré superlattice microcavities, where a critical coupling condition can be achieved via selecting a magic angle. Furthermore, at the magic angle of 13.17°, critical coupling is satisfied, resulting in a normalized THG conversion efficiency of 136%/W2 at a relatively low peak pump power of 6.8 MW/cm2, which is 3 orders of magnitude higher than the best results reported previously. Our work shows the power of photonic moiré superlattices in enhancing nonlinear optical performances through flexible and feasible engineering resonant modes, which can be applied in integrated frequency conversion and generation of quantum light sources.

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.

Emergent Inhomogeneity and Nonlocality in a Graphene Field-Effect Transistor on a Near-Parallel Moiré Superlattice of Transition Metal Dichalcogenides.

At near-parallel orientation, twisted bilayers of transition metal dichalcogenides exhibit interlayer charge transfer-driven out-of-plane ferroelectricity. Here, we report detailed electrical transport in a dual-gated graphene field-effect transistor placed on a 2.1° twisted bilayer WSe2. We observe hysteretic transfer characteristics and an emergent charge inhomogeneity with multiple local Dirac points evolving with an increasing electric displacement field (D). Concomitantly, we also observe a strong nonlocal voltage signal at D ∼ 0 V/nm that decreases rapidly with increasing D. A linear scaling of the nonlocal signal with longitudinal resistance suggests edge mode transport, which we attribute to the breaking of valley symmetry of graphene due to the spatially fluctuating electric field from the underlying polarized moiré domains. A quantitative analysis suggests the emergence of finite-size domains in graphene that modulate the charge and the valley currents simultaneously. This work underlines the impact of interfacial ferroelectricity that can trigger a new generation of devices.

Kagome Quantum Oscillations in Graphene Superlattices.

Electronic spectra of solids subjected to a magnetic field are often discussed in terms of Landau levels and Hofstadter-butterfly-style Brown-Zak minibands manifested by magneto-oscillations in two-dimensional electron systems. Here, we present the semiclassical precursors of these quantum magneto-oscillations which appear in graphene superlattices at low magnetic field near the Lifshitz transitions and persist at elevated temperatures. These oscillations originate from Aharonov-Bohm interference of electron waves following open trajectories that belong to a kagome-shaped network of paths characteristic for Lifshitz transitions in the moire superlattice minibands of twistronic graphenes.

Controlling Umklapp Scattering in a Bilayer Graphene Moiré Superlattice.

We present experimental findings on electron-electron scattering in two-dimensional moiré heterostructures with a tunable Fermi wave vector, reciprocal lattice vector, and band gap. We achieve this in high-mobility aligned heterostructures of bilayer graphene (BLG) and hBN. Around the half-full point, the primary contribution to the resistance of these devices arises from Umklapp electron-electron (Uee) scattering, making the resistance of graphene/hBN moiré devices significantly larger than that of non-aligned devices (where Uee is forbidden). We find that the strength of Uee scattering follows a universal scaling with Fermi energy and is nonmonotonically dependent on the superlattice period. The Uee scattering can be tuned with the electric field and is affected by layer polarization of BLG. It has a strong particle-hole asymmetry; the resistance when the chemical potential is in the conduction band is significantly lower than when it is in the valence band, making the electron-doped regime more practical for potential applications.

Nature of Long-Lived Moiré Interlayer Excitons in Electrically Tunable MoS2/MoSe2 Heterobilayers.

Interlayer excitons in transition-metal dichalcogenide heterobilayers combine high binding energy and valley-contrasting physics with a long optical lifetime and strong dipolar character. Their permanent electric dipole enables electric-field control of the emission energy, lifetime, and location. Device material and geometry impact the nature of the interlayer excitons via their real- and momentum-space configurations. Here, we show that interlayer excitons in MoS2/MoSe2 heterobilayers are formed by charge carriers residing at the Brillouin zone edges, with negligible interlayer hybridization. We find that the moiré superlattice leads to the reversal of the valley-dependent optical selection rules, yielding a positively valued g-factor and cross-polarized photoluminescence. Time-resolved photoluminescence measurements reveal that the interlayer exciton population retains the optically induced valley polarization throughout its microsecond-long lifetime. The combination of a long optical lifetime and valley polarization retention makes MoS2/MoSe2 heterobilayers a promising platform for studying fundamental bosonic interactions and developing excitonic circuits for optical information processing.

Coexistence of Ferroelectricity and Ferromagnetism in Atomically Thin Two-Dimensional Cr2S3/WS2 Vertical Heterostructures.

Two-dimensional (2D) heterostructures with ferromagnetism and ferroelectricity provide a promising avenue to miniaturize the device size, increase computational power, and reduce energy consumption. However, the direct synthesis of such eye-catching heterostructures has yet to be realized up to now. Here, we design a two-step chemical vapor deposition strategy to growth of Cr2S3/WS2 vertical heterostructures with atomically sharp and clean interfaces on sapphire. The interlayer charge transfer and periodic moiré superlattice result in the emergence of room-temperature ferroelectricity in atomically thin Cr2S3/WS2 vertical heterostructures. In parallel, long-range ferromagnetic order is discovered in 2D Cr2S3 via the magneto-optical Kerr effect technique with the Curie temperature approaching 170 K. The charge distribution variation induced by the moiré superlattice changes the ferromagnetic coupling strength and enhances the Curie temperature. The coexistence of ferroelectricity and ferromagnetism in 2D Cr2S3/WS2 vertical heterostructures provides a cornerstone for the further design of logic-in-memory devices to build new computing architectures.

Supersymmetry dictated topology in periodic gauge fields and realization in strained and twisted 2D materials.

Supersymmetry (SUSY) of a Hamiltonian dictates double degeneracy between a pair of superpartners (SPs) transformed by supercharge, except at zero energy where modes remain unpaired in many cases. Here we explore a SUSY of complete isospectrum between SPs-with paired zero modes-realized by 2D electrons in zero-flux periodic gauge fields, which can describe twisted or periodically strained 2D materials. We find their low-energy sector containing zero (or threshold) modes must be topologically non-trivial, by proving that Chern numbers of the two SPs have a finite difference dictated by the number of zero modes and energy dispersion in their vicinity. In 30° twisted bilayer (double bilayer) transition metal dichalcogenides subject to periodic strain, we find one SP is topologically trivial in its lowest miniband, while the twin SP of identical dispersion has a Chern number of 1 (2), in stark contrast to time-reversal partners that have to be simultaneously trivial or nontrivial. For systems whose physical Hamiltonian corresponds to the square root of a SUSY Hamiltonian, such as twisted or strained bilayer graphene, we reveal that topological properties of the two SUSY SPs are transferred respectively to the conduction and valence bands, including the contrasted topology in the low-energy sector and identical topology in the high-energy sector. This offers a unified perspective for understanding topological properties in many flat-band systems described by such square-root models. Both types of SUSY systems provide unique opportunities for exploring correlated and topological phases of matter.

In-plane anisotropic two-dimensional materials for twistronics.

In-plane anisotropic two-dimensional (2D) materials exhibit in-plane orientation-dependent properties. The anisotropic unit cell causes these materials to show lower symmetry but more diverse physical properties than in-plane isotropic 2D materials. In addition, the artificial stacking of in-plane anisotropic 2D materials can generate new phenomena that cannot be achieved in in-plane isotropic 2D materials. In this perspective we provide an overview of representative in-plane anisotropic 2D materials and their properties, such as black phosphorus, group IV monochalcogenides, group VI transition metal dichalcogenides with 1T' and Tdphases, and rhenium dichalcogenides. In addition, we discuss recent theoretical and experimental investigations of twistronics using in-plane anisotropic 2D materials. Both in-plane anisotropic 2D materials and their twistronics hold considerable potential for advancing the field of 2D materials, particularly in the context of orientation-dependent optoelectronic devices.

Spin-textured Chern bands in AB-stacked transition metal dichalcogenide bilayers.

While transition-metal dichalcogenide (TMD)-based moiré materials have been shown to host various correlated electronic phenomena, topological states have not been experimentally observed until now [T. Li et al., Quantum anomalous Hall effect from intertwined moiré bands. arXiv [Preprint] (2021). https://arxiv.org/abs/2107.01796 (Accessed 5 July 2021)]. In this work, using first-principle calculations and continuum modeling, we reveal the displacement field-induced topological moiré bands in AB-stacked TMD heterobilayer [Formula: see text]/[Formula: see text] Valley-contrasting Chern bands with nontrivial spin texture are formed from interlayer hybridization between [Formula: see text] and [Formula: see text] bands of nominally opposite spins. Our study establishes a recipe for creating topological bands in AB-stacked TMD bilayers in general, which provides a highly tunable platform for realizing quantum-spin Hall and interaction-induced quantum anomalous Hall effects.

Interplay of Trapped Species and Absence of Electron Capture in Moiré Heterobilayers.

Moiré heterobilayers host interlayer excitons in a natural, periodic array of trapping potentials. Recent work has elucidated the structure of the trapped interlayer excitons and the nature of photoluminescence (PL) from trapped and itinerant charged complexes such as interlayer trions in these structures. In this paper, our results serve to add to the understanding of the nature of PL emission and explain its characteristic blueshift with increasing carrier density, along with demonstrating a significant difference between the interlayer exciton-trion conversion efficiency as compared to both localized and itinerant intralayer species in conventional monolayers. Our results show the absence of optical generation of trions in these materials, which we suggest arises from the highly localized, near subnanometer confinement of trapped species in these Moiré potentials.

Switching the Moiré Lattice Models in the Twisted Bilayer WSe2 by Strain or Pressure.

Moiré superlattices of twisted van der Waals heterostructures provide a promising and tunable platform for simulating correlated two-dimensional physical models. In twisted bilayer transition-metal dichalcogenides with twist angles close to 0°, the Γ and K valley moiré bands are described by the honeycomb and the triangular effective lattice models, respectively, with distinct physics. Using large-scale first-principles calculations, we show that in-plane biaxial strain and out-of-plane pressure provide effective knobs for switching the moiré lattice models that emerged at the band edges in twisted bilayer WSe2 by shifting the energy positions of the Γ and K valley minibands. The shifting mechanism originates from the differences in the orbital characters of the Γ and K valley states and their responses to strain and pressure. The critical strain and pressure for switching the Γ/K valleys are 2.11% and 2.175 GPa, respectively.

Magnetic Field-Stabilized Wigner Crystal States in a Graphene Moiré Superlattice.

ABC-stacked trilayer graphene on boron nitride (ABC-TLG/hBN) moiré superlattices provides a tunable platform for exploring Wigner crystal states in which the electron correlation can be controlled by electric and magnetic fields. Here we report the observation of magnetic field-stabilized Wigner crystal states in a ABC-TLG/hBN. We show that correlated insulating states emerge at multiple fractional and integer fillings corresponding to ν = 1/3, 2/3, 1, 4/3, 5/3, and 2 electrons per moiré lattice site under a magnetic field. These correlated insulating states can be attributed to generalized Mott states for the integer fillings and generalized Wigner crystal states for the fractional fillings. The generalized Wigner crystal states are stabilized by a vertical magnetic field and are strongest at one magnetic flux quantum per three moiré superlattices. The ν = 2 insulating state persists up to 30 T, which can be described by a Mott-Hofstadter transition at a high magnetic field.