Graphene bilayer with a twist: electronic structure

Gate-Defined Single-Electron Transistors in Twisted Bilayer Graphene

Twisted bilayer graphene (tBLG) near the magic angle is a unique platform where the combination of topology and strong correlations gives rise to exotic electronic phases. These phases are gate-tunable and related to the presence of flat electronic bands, isolated by single-particle band gaps. This enables gate-controlled charge confinements, essential for the operation of single-electron transistors (SETs), and allows one to explore the interplay of confinement, electron interactions, band renormalization, and the moiré superlattice, potentially revealing key paradigms of strong correlations. Here, we present gate-defined SETs in tBLG with well-tunable Coulomb blockade resonances. These SETs allow us to study magnetic field-induced quantum oscillations in the density of states of the source-drain reservoirs, providing insight into gate-tunable Fermi surfaces of tBLG. Comparison with tight-binding calculations highlights the importance of displacement-field-induced band renormalization crucial for future advanced gate-tunable quantum devices and circuits in tBLG including, e.g., quantum dots and Josephson junction arrays.

Intrinsic One-Dimensional Moiré Superlattice in Large-Angle Twisted Bilayer WTe2

Moiré effects in two-dimensional (2D) twisted van der Waals structures are attracting great interest owing to the emergence of intriguing physical properties. Despite growing interests, moiré effects with large twist angles remain unexplored because the increase of twist angle is thought to quickly suppress the size of moiré patterns. In this study, we focused on large-angle twisted tungsten ditelluride and discovered two orthogonal one-dimensional (1D) moiré patterns at twist angles around 62° and 58° using transmission electron microscopy. Their diffraction patterns exhibited pair formation features supporting the one-dimensionality of these moiré patterns. We also succeeded in revealing the origin of large-angle moiré patterns as well as the intrinsic nature of 1D moiré patterns. The observed moiré patterns are purely 1D in the sense that the long-range periodicity exists only along one direction, being a promising platform to study 1D phenomena. Our results propose a universal concept for studying large-angle twisted structures.

Interface-Enhanced and Self-Guided Growth of 2D Interlayer Heterostructure Wafers with Vertically Aligned Van Der Waals Layers

2D heterostructures have garnered significant interest in the scientific community owing to their exceptional carrier transport properties and tunable band alignment. The fabrication of these heterostructures on a wafer scale is crucial for advancing industrial applications but remains particularly challenging for metals with low sulfidation activity, such as Hf. Herein, the one-pot method is developed for fabricating wafer-scale HfSe2/WSe2 interlayer heterostructures with vertically aligned van der Waals layers via interface-enhanced selenization and self-guided growth. By depositing a W layer (high sulfidation activity) over a Hf layer, followed by a one-pot selenization process, the chemical combination between Hf and Se atoms is enhanced through interfacial Se diffusion and confined lattice reaction. Moreover, the WSe2 layers grow perpendicular to the substrate and further guide the crystallization of the bottom HfSe2 layers. The resulting heterostructures, characterized by covalent bonds, demonstrate significant charge transfer, enhanced piezoelectricity, notable rectification effects, and Si-compatible transistor integration. This interface-enhanced selenization and self-guided growth pathway may provide valuable insights into the fabrication of covalently connected interlayer heterostructures involving metals with low sulfidation activity, as well as the development of high-density integrated circuits.

Crystallography of quasiperiodic moiré patterns in homophase twisted bilayers

This paper discusses the geometric properties and symmetries of general moiré patterns generated by homophase bilayers twisted by rotation 2δ. These patterns are generically quasiperiodic of rank 4 and result from the interferences between two basic periodicities incommensurate to each other, defined by the sites in the layers that are kept invariant through the symmetry operations of the structure. These invariant sites are distributed on the nodes of a set of lattices called Φ-lattices - where Φ runs on the rotation operations of the symmetry group of the monolayers - which are the centers of rotation 2δ + Φ transforming a lattice node of the first layer into a node of the second. It is demonstrated that when a coincidence lattice exists, it is the intersection of all the Φ-lattices of the structure.

Understanding Twist-Angle-Dependent Carrier Lifetimes in MoSSe Bilayer

Two-dimensional (2D) materials with tunable interlayer interactions hold immense potential for optoelectronic and photocatalytic applications. Understanding the dependence of carrier dynamics on twist angle in Janus bilayers is essential, as it directly impacts device efficiency. This study employs time-dependent density functional theory (TD-DFT) and nonadiabatic molecular dynamics (NAMD) to investigate twist-angle-dependent carrier dynamics in Janus MoSSe bilayers with type-II band alignment. Simulations reveal ultrafast charge transfer times of approximately 70 and 500 fs, largely independent of the twist angle due to multiple intermediate states. In contrast, the electron-hole recombination times depend strongly on twist angles, extending up to 133 ns for twisted configurations (21.8° and 38.2°) compared to 57 ns in high-symmetry bilayers (0.0° and 60.0°). Structural randomness in twisted bilayers weakens interlayer interactions, reducing nonadiabatic coupling and coherence time, which collectively prolong carrier lifetimes. These findings offer valuable guidance for designing 2D materials for high-efficiency photovoltaics and long-durable photocatalysts.

Mechanical Properties and Fracture Mechanisms of Nanocomposites of Metal and Graphene with Overlapping Edges

The fracture mechanism and mechanical response of Ni/graphene nanocomposites under nanoindentation are investigated by molecular dynamics simulations. We analyze the effect of the overlapping area on the microstructural transition, HCP atomic fraction, dislocation density, load-displacement relationship, and stress distribution. It was found that the maximum indentation depth of embedded graphene has a nonlinear dependence relation with the overlapping area, and it becomes smaller at the overlapping width comparable to the indenter diameter. The graphene layer is able to hinder the expansion of the dislocation into the interior of the Ni matrix in the initial stage. The densities of HCP atoms and dislocations in the composite gradually increase with increasing indentation depth. The stress concentration tends to cause nucleation of dislocations below the indentation surface. When the graphene is ruptured, the elastic recovery to some extent occurs in the deformed substrate. This work sheds light on modifying the mechanical properties of metal/graphene composites by tuning the overlapping boundary of graphene.

Electric Field-Tunable Superconductivity with Competing Orders in Twisted Bilayer Graphene near the Magic Angle

Superconductivity (SC) in twisted bilayer graphene (tBLG) has been explored by varying carrier concentrations, twist angles, and screening strength, with the aim of uncovering its origin and possible connections to strong electronic correlations in narrow bands and various resulting broken symmetries. However, the link between the tBLG band structure and the onset of SC and other orders largely remains unclear. In this study, we address this crucial gap by examining in situ band structure tuning of a near magic-angle (θ ≈ 0.95°) tBLG device with a displacement field (D) and reveal competition between SC and other broken symmetries. At zero D, the device exhibits superconducting signatures without the resistance peak at half-filling, a characteristic signature with a strong electronic correlation. As D increases, the SC is suppressed, accompanied by the appearance of a resistance peak at half-filling. Hall density measurements reveal that at zero D, SC arises around the van Hove singularity (vHs) from an isospin or spin-valley unpolarized band. At higher D, the suppression of SC coincides with broken isospin symmetry near half-filling with lifted degeneracy (gd ∼ 2). Additionally, as the SC phase becomes weaker with D, vHs shifts to higher fillings, highlighting the modification of the underlying band structure with the applied electric field. These findings, with recent theoretical study on SC in tBLG, highlight the competition, rather than being connected concomitantly, between SC and other orders promoted by broken symmetries.

Elastic Screening of Pseudogauge Fields in Graphene

Lattice deformations in graphene couple to the low-energy electronic degrees of freedom as effective scalar and gauge fields. Using molecular dynamics simulations, we show that the optical component of the displacement field, i.e., the relative motion of different sublattices, contributes at equal order as the acoustic component and effectively screens the pseudogauge fields. In particular, we consider twisted bilayer graphene and corrugated monolayer graphene. In both cases, optical lattice displacements significantly reduce the overall magnitude of the pseudomagnetic fields. For corrugated graphene, optical contributions also reshape the pseudomagnetic field and significantly modify the electronic bands near charge neutrality. Previous studies based on continuum elasticity, which ignores this effect, have therefore systematically overestimated the strength of the strain-induced pseudomagnetic field. Our results have important consequences for the interpretation of experiments and design of straintronic applications.

Twisting nanoporous graphene on graphene: electronic decoupling and chiral currents

Nanoporous graphene (NPG), laterally bonded carbon nanoribbons, is a promising platform for controlling coherent electron propagation in the nanoscale. However, for its successful device integration NPG should ideally be on a substrate that preserves or enhances its anisotropic transport properties. Here, using an atomistic tight-binding model combined with nonequilibrium Green's functions, we study NPG on graphene and show that their electronic coupling is modulated as a function of the interlayer twist angle. At small twist angles (θ ≲ 10°), strong hybridization leads to substantial interlayer transmission and Talbot-like interference in the current flow on both layers. Besides, injected currents exhibit chiral features due to the twist-induced mirror-symmetry-breaking. Upon increasing the twist angle, the coupling is weakened and the monolayer electronic properties are restored. Furthermore, we predict spectroscopic signatures that allow to probe the twist-dependent interlayer coupling via scanning tunneling microscopy.

Analytical Model for Atomic Relaxation in Twisted Moiré Materials

By virtue of being atomically thin, the electronic properties of heterostructures built from two-dimensional materials are strongly influenced by atomic relaxation. The atomic layers behave as flexible membranes rather than rigid crystals. Here we develop an analytical theory of lattice relaxation in twisted moiré materials. We obtain analytical results for the lattice displacements and corresponding pseudo gauge fields, as a function of twist angle. We benchmark our results for twisted bilayer graphene and twisted WSe_{2} bilayers using large-scale molecular dynamics simulations. Our single-parameter theory is valid in graphene bilayers for twist angles θ≳0.7°, and in twisted WSe_{2} for θ≳1.6°. We also investigate how relaxation alters the electronic structure in twisted bilayer graphene, providing a simple extension to the continuum model to account for lattice relaxation.

Topological Moiré Polaritons

The combination of an in-plane honeycomb potential and of a photonic spin-orbit coupling (SOC) emulates a photonic or polaritonic analog of bilayer graphene. We show that modulating the SOC magnitude allows us to change the overall lattice periodicity, emulating any type of moiré-arranged bilayer graphene with unique all-optical access to the moiré band topology. We show that breaking the time-reversal symmetry by an effective exciton-polariton Zeeman splitting opens a large topological gap in the array of moiré flat bands. This gap contains one-way topological edge states whose constant group velocity makes an increasingly sharp contrast with the flattening moiré bands.

Twisted Bilayer MoS2 under Electric Fields: A System with Tunable Symmetry

Gate voltages take full advantage of 2D systems, making it possible to explore novel states of matter by controlling their electron concentration or applying perpendicular electric fields. Here, we study the electronic properties of small-angle twisted bilayer MoS2 under a strong electric field. We show that transport across one of its constituent layers can be effectively regarded as a two-dimensional electron gas under a nanoscale potential. We find that the band structure of such a system is reconstructed following two fundamentally different symmetries depending on the orientation of the external electric field, namely, hexagonal or honeycomb. By studying this system under magnetic fields, we demonstrate that this duality not only translates into two different transport responses but also results in having two different Hofstadter's spectra. Our work opens up a new route for the creation of controllable artificial superlattices in van der Waals heterostructures.

Infrared Spectroscopy for Diagnosing Superlattice Minibands in Twisted Bilayer Graphene near the Magic Angle

Twisted bilayer graphene (TBG) represents a highly tunable, strongly correlated electron system. However, understanding the single-particle band structure alone has been challenging due to a lack of spectroscopic measurements over a broad energy range. Here, we probe the band structure of TBG around the magic angle using infrared spectroscopy and reveal spectral features that originate from interband transitions. In combination with quantum transport, we connect spectral features over a broad energy range (10-700 meV) and track their evolution with the twist angle. We compare our data with calculations of the band structures obtained via the continuum model and find good agreement only when considering a variation of interlayer/intralayer tunneling parameters with the twist angle. Our analysis suggests that the magic angle also shifts due to lattice relaxation and is better defined for a wide angular range of 0.9-1.1°. Additionally, our measurements offer an optical fingerprint of the magic angle for screening heterostructures before nanofabrication.

Strong Coupling between Moiré-Type Plasmons and Phonons in Suspended Monolayer Metallic Twisted Superlattices

We demonstrate both experimentally and analytically a strong coupling phenomenon between moiré-type plasmons and phonons within moiré superlattices. We study the dependence of moiré wave vector and the twist angle and numerically simulate and experimentally fabricate metallic moiré superlattices on a suspended thin film SiO2 substrate at different twist angles. The results suggest that the coupling strength initially increases and then decreases with increasing twist angles. When the twist angle is at 16.26°, we achieve a moiré-type plasmon-phonon strong coupling with a Rabi splitting strength approaching 45 meV. We further analyze the coupling system by utilizing the coupled-harmonic-oscillators theory and quantum mechanical theory. The calculations and numerical simulations further agree with the experimental results. The proposed strong coupling system has the potential to contribute substantially to electromagnetic field controlling and coupling.

Generation of Isolated Flat Bands with Tunable Numbers through Moiré Engineering

In contrast to the Dirac-cone materials in which the low-energy spectrum features a pseudospin-1/2 structure, Lieb and Dice lattices both host triply degenerate low-energy excitations. Here, we discuss moiré structures involving twisted bilayers of these lattices, which are shown to exhibit a tunable number of isolated flat bands near the Fermi level due to the bipartite nature of their structures. These flat bands remain isolated from the high-energy bands even in the presence of small higher-order terms and chiral-symmetry-breaking interlayer tunneling. At small twist angles, many isolated flat bands can be generated with a notable Berry curvature, which could provide a geometric contribution to the superfluid weight under a BCS-type pairing potential. Remarkably, the emergence of isolated flat bands is insensitive to the twist angle, so that fine-tuning of the twist angle in an experimental setup would not be required. Our study suggests a promising new and efficient avenue for exploring and engineering flat bands based on the twisted bilayer Lieb and Dice lattices.

Magnetic colloidal single particles and dumbbells on a tilted washboard moiré pattern in a precessing external field

We measure the dynamical behavior of colloidal singlets and dumbbells on an inclined magnetic moiré pattern, subject to a precessing external homogeneous magnetic field. At low external field strength single colloidal particles and dumbbells move everywhere on the pattern: at stronger external field strengths colloidal singlets and dumbbells are localized in generic locations. There are however nongeneric locations of flat channels that cross the moiré Wigner Seitz cell. In the flat channels we find gravitational driven translational and non-translational dynamic phase behavior of the colloidal singlets and dumbbells depending on the external field strength and the precession angle of the external homogeneous magnetic field.

The Cooper-Pair Distribution Function of Untwisted-Misaligned Bilayer Graphene

The Cooper-pair distribution function Dcp(ω,Tc) of Untwisted-Misaligned Bilayer Graphene (UMBLG) in the presence of an external electric field is calculated and analysed within the framework of first-principle calculations. A bilayer graphene structure is proposed using a structural geometric approximation, enabling the simulation of a structure rotated at a small angle, avoiding a supercell calculation. The Dcp(ω,Tc) function of UMBLG indicates the presence of the superconducting state for specific structural configurations, which is consistent with the superconductivity in Twisted Bilayer Graphene (TBLG) reported in the literature. The Dcp(ω,Tc) function of UMBLG suggests that Cooper-pairs are possible in the low-frequency vibration region. Furthermore, the structural geometric approximation allowed the evaluation of the effect of the electric field on the superconducting state of UMBLG and its superconducting critical temperature through the Ncp parameter.

Localizing Transitions via Interaction-Induced Flat Bands

This Letter presents a theory of interaction-induced band-flattening in strongly correlated electron systems. We begin by illustrating an inherent connection between flat bands and index theorems, and presenting a generic prescription for constructing flat bands by periodically repeating local Hamiltonians with topological zero modes. Specifically, we demonstrate that a Dirac particle in an external, spatially periodic magnetic field can be cast in this form. We derive a condition on the field to produce perfectly flat bands and provide an exact analytical solution for the flat band wave functions. Furthermore, we explore an interacting model of Dirac fermions in a spatially inhomogeneous field. We show that certain Hubbard-Stratonovich configurations exist that "rectify" the field configuration, inducing band flattening. We present an explicit model where this localization scenario is energetically favorable-specifically in Dirac systems with nearly flat bands, where the energy cost of rectifying textures is quadratic in the order parameter, whereas the energy gain from flattening is linear. In conclusion, we discuss alternative symmetry-breaking channels, especially superconductivity, and propose that these interaction-induced band-flattening scenarios represent a generic nonperturbative mechanism for spontaneous symmetry breaking, pertinent to many strongly correlated electron systems.

Pentagonal Symmetry in Aperiodic Cyclic Multiply Twinned Nano- and Mesodiamonds

This Review provides the first comprehensive overview of the structure and properties of exotic sp3-crystalline aperiodic cyclic multiply twinned nano- (10-100 nm) and meso- (up to 1 mm) diamond particles (MTPs) exhibiting pentagonal symmetry. It spans their independent experimental discoveries (1963, 1964, 1972, and 1983) and theoretical structural insights (1993) to recent advancements. The Review focuses on high-symmetry MTPs formed by the fusion of multiple cubic diamond fragments through [111] facets. The sp3 diamond lattice of individual fragments offers a vast range of MTP varieties. These particles are shown to be a special case of aperiodic crystalline solids with limited dimensions and rotational symmetry, leading to a breakdown of translational invariance. Detailed mathematical analysis of the MTPs' lattices highlights the crucial role of central cores in determining the symmetry and effective dimensions of these structures. Both structural and kinetic aspects of the formation mechanisms of pentagonal diamond particles are considered, revealing the main role of embryo seeds (low fullerenes, polyhexacyclo[5.5.1.12,6.18,12.03,11.05,9]pentadecane (C15), and polyheptacyclo[5.5.1.12,7.19,14.03,13.06,11]octadecane (C18)) in determining the MTPs' symmetry and structure. The effective dimensions of multiply twinned diamonds are shown to be limited by structural stress caused by the mismatch of perfect pentagonal and tetrahedral dihedral angles. The extraordinary mechanical and electronic properties of multiply twinned diamonds are discussed, highlighting that hexagonal interfaces between cubic diamond fragments may determine exceptional ultrahard and quantum characteristics. The MTP X-ray diffraction spectra reveal clear pentagonal patterns with single (diamond decahedrons or dodecahedrons) or ten (diamond icosahedra) central 5-fold axes. A comparative analysis of experimental structural data and simulations at different theoretical levels demonstrates a perfect correspondence of theoretical models with crystalline lattices.

Robust flat bands in twisted trilayer graphene moiré quasicrystals

Moiré structures formed by twisting three layers of graphene with two independent twist angles present an ideal platform for studying correlated quantum phenomena, as an infinite set of angle pairs is predicted to exhibit flat bands. Moreover, the two mutually incommensurate moiré patterns among the twisted trilayer graphene (TTG) can form highly tunable moiré quasicrystals. This enables us to extend correlated physics in periodic moiré crystals to quasiperiodic systems. However, direct local characterization of the structure of the moiré quasicrystals and of the resulting flat bands are still lacking, which is crucial to fundamental understanding and control of the correlated moiré physics. Here, we demonstrate the existence of flat bands in a series of TTGs with various twist angle pairs and show that the TTGs with different magic angle pairs are strikingly dissimilar in their atomic and electronic structures. The lattice relaxation and the interference between moiré patterns are highly dependent on the twist angles. Our direct spatial mappings, supported by theoretical calculations, reveal that the localization of the flat bands exhibits distinct symmetries in different regions of the moiré quasicrystals.

Nanoscale Optical Conductivity Imaging of Double-Moiré Twisted Bilayer Graphene

A central paradigm of moiré materials relies on the formation of superlattices that yield enlarged effective crystal unit cells. While a critical consequence of this phenomenon is the celebrated flat electronic bands that foster strong interaction effects, the presence of superlattices has further implications. Here we explore the advantages of moiré superlattices in twisted bilayer graphene (TBG) aligned with hexagonal boron nitride (hBN) for passively enhancing optical conductivity in the low-energy regime. To probe the local optical response of TBG/hBN double-moiré lattices, we use infrared (IR) nano-imaging in conjunction with nanocurrent imaging to examine local optical conductivity over a wide range of TBG twist angles. We show that interband transitions associated with the multiple moiré flat and dispersive bands produce tunable transparent IR responses even at finite carrier densities, which is in stark contrast to the previously limited metallic near transparency observed only in undoped pristine graphene.

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.

Emergent phases in graphene flat bands

Electronic correlations in two-dimensional materials play a crucial role in stabilising emergent phases of matter. The realisation of correlation-driven phenomena in graphene has remained a longstanding goal, primarily due to the absence of strong electron-electron interactions within its low-energy bands. In this context, magic-angle twisted bilayer graphene has recently emerged as a novel platform featuring correlated phases favoured by the low-energy flat bands of the underlying moiré superlattice. Notably, the observation of correlated insulators and superconductivity, and the interplay between these phases have garnered significant attention. A wealth of correlated phases with unprecedented tunability was discovered subsequently, including orbital ferromagnetism, Chern insulators, strange metallicity, density waves, and nematicity. However, a comprehensive understanding of these closely competing phases remains elusive. The ability to controllably twist and stack multiple graphene layers has enabled the creation of a whole new family of moiré superlattices with myriad properties. Here, we review the progress and development achieved so far, encompassing the rich phase diagrams offered by these graphene-based moiré systems. Additionally, we discuss multiple phases recently observed in non-moiré multilayer graphene systems. Finally, we outline future opportunities and challenges for the exploration of hidden phases in this new generation of moiré materials.

Evolution of the flat band and the role of lattice relaxations in twisted bilayer graphene

Magic-angle twisted bilayer graphene exhibits correlated phenomena such as superconductivity and Mott insulating states related to the weakly dispersing flat band near the Fermi energy. Such a flat band is expected to be sensitive to both the moiré period and lattice relaxations. Thus, clarifying the evolution of the electronic structure with the twist angle is critical for understanding the physics of magic-angle twisted bilayer graphene. Here we combine nano-spot angle-resolved photoemission spectroscopy and atomic force microscopy to resolve the fine electronic structure of the flat band and remote bands, as well as their evolution with twist angle from 1.07° to 2.60°. Near the magic angle, the dispersion is characterized by a flat band near the Fermi energy with a strongly reduced band width. Moreover, we observe a spectral weight transfer between remote bands at higher binding energy, which allows to extract the modulated interlayer spacing near the magic angle. Our work provides direct spectroscopic information on flat band physics and highlights the important role of lattice relaxations.

Tunable Exciton Polaritons in Band-Gap Engineered Hexagonal Boron Nitride

We show that hexagonal boron nitride (hBN), a two-dimensional insulator, when subjected to an external superlattice potential forms a paradigm for electrostatically tunable excitons in the near- and mid-ultraviolet (UV). With a combination of analytical and numerical methods, we see that the imposed potential has three consequences: (i) It renormalizes the effective mass tensor, leading to anisotropic effective masses. (ii) It renormalizes the band gap, eventually reducing it. (iii) It reduces the exciton binding energies. All these consequences depend on a single dimensionless parameter, which includes the product of strength of the external potential with its period. In addition to the excitonic energy levels, we compute the optical conductivity along two orthogonal directions and from it the absorption spectrum. The results for the latter show that our system is able to mimic a grid polarizer. These characteristics make one-dimensional hBN superlattices a viable and meaningful platform for fine-tuned polaritonics in the UV to visible spectral range.

Ultra-flat bands at large twist angles in group-V twisted bilayer materials

Flat bands in 2D twisted materials are key to the realization of correlation-related exotic phenomena. However, a flat band often was achieved in the large system with a very small twist angle, which enormously increases the computational and experimental complexity. In this work, we proposed group-V twisted bilayer materials, including P, As, and Sb in the β phase with large twist angles. The band structure of twisted bilayer materials up to 2524 atoms has been investigated by a deep learning method DeepH, which significantly reduces the computational time. Our results show that the bandgap and the flat bandwidth of twisted bilayer β-P, β-As, and β-Sb reduce gradually with the decreasing of twist angle, and the ultra-flat band with bandwidth approaching 0 eV is achieved. Interestingly, we found that a twist angle of 9.43° is sufficient to achieve the band flatness for β-As comparable to that of twist bilayer graphene at the magic angle of 1.08°. Moreover, we also find that the bandgap reduces with decreasing interlayer distance while the flat band is still preserved, which suggests interlayer distance as an effective routine to tune the bandgap of flat band systems. Our research provides a feasible platform for exploring physical phenomena related to flat bands in twisted layered 2D materials.

Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields

We investigate the effect of a magnetic field on the band structure of bilayer graphene with a magic twist angle of 1.08∘. The coupling of a tight-binding model and the Peierls phase allows the calculation of the energy bands of periodic two-dimensional systems. For an orthogonal magnetic field, the Landau levels are dispersive, particularly for magnetic lengths comparable to or larger than the twisted bilayer cell size. A high in-plane magnetic field modifies the low-energy bands and gap, which we demonstrate to be a direct consequence of the minimal coupling.

Emergent Correlated Phases in Rhombohedral Trilayer Graphene Induced by Proximity Spin-Orbit and Exchange Coupling

The impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagram of rhombohedral trilayer graphene (RTG) is investigated theoretically. By employing ab initio-fitted effective models of RTG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr_{2}Ge_{2}Te_{6} (exchange proximity effect), we incorporate the Coulomb interactions within the random-phase approximation to explore potential correlated phases at different displacement fields and doping. We find a rich spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a spin-valley-coherent phase due to the presence of valley-Zeeman coupling. Similarly, proximity exchange removes the phase degeneracies by biasing the spin direction, enabling a magnetocorrelation effect-strong sensitivity of the correlated phases to the relative magnetization orientations (parallel or antiparallel) of the encapsulating ferromagnetic layers.

Waveguide-integrated twisted bilayer graphene photodetectors

Graphene photodetectors have exhibited high bandwidth and capability of being integrated with silicon photonics (SiPh), holding promise for future optical communication devices. However, they usually suffer from a low photoresponsivity due to weak optical absorption. In this work, we have implemented SiPh-integrated twisted bilayer graphene (tBLG) detectors and reported a responsivity of 0.65 A W-1 for telecom wavelength 1,550 nm. The high responsivity enables a 3-dB bandwidth of >65 GHz and a high data stream rate of 50 Gbit s-1. Such high responsivity is attributed to the enhanced optical absorption, which is facilitated by van Hove singularities in the band structure of high-mobility tBLG with 4.1o twist angle. The uniform performance of the fabricated photodetector arrays demonstrates a fascinating prospect of large-area tBLG as a material candidate for heterogeneous integration with SiPh.

Chirality Probe of Twisted Bilayer Graphene in the Linear Transport Regime

We propose minimal transport experiments in the coherent regime that can probe the chirality of twisted moiré structures. We show that only with a third contact and in the presence of an in-plane magnetic field (or another time-reversal symmetry breaking effect) a chiral system may display nonreciprocal transport in the linear regime. We then propose to use the third lead as a voltage probe and show that opposite enantiomers give rise to different voltage drops on the third lead. Additionally, in the scenario of layer-discriminating contacts, the third lead can serve as a current probe capable of detecting different handedness even in the absence of a magnetic field. In a complementary configuration, applying opposite voltages on the two layers of the third lead gives rise to a chiral (super)current in the absence of a source-drain voltage whose direction is determined by its chirality.

Strain Engineering of Twisted Bilayer Graphene: The Rise of Strain-Twistronics

The layer-by-layer stacked van der Waals structures (termed vdW hetero/homostructures) offer a new paradigm for materials design-their physical properties can be tuned by the vertical stacking sequence as well as by adding a mechanical twist, stretch, and hydrostatic pressure to the atomic structure. In particular, simple twisting and stacking of two layers of graphene can form a uniform and ordered Moiré superlattice, which can effectively modulate the electrons of graphene layers and lead to the discovery of unconventional superconductivity and strong correlations. However, the twist angle of twisted bilayer graphene (tBLG) is almost unchangeable once the interlayer stacking is determined, while applying mechanical elastic strain provides an alternative way to deeply regulate the electronic structure by controlling the lattice spacing and symmetry. In this review, diverse experimental advances are introduced in straining tBLG by in-plane and out-of-plane modes, followed by the characterizations and calculations toward quantitatively tuning the strain-engineered electronic structures. It is further discussed that the structural relaxation in strained Moiré superlattice and its influence on electronic structures. Finally, the conclusion entails prospects for opportunities of strained twisted 2D materials, discussions on existing challenges, and an outlook on the intriguing emerging field, namely "strain-twistronics".

Topological Flat Bands in Graphene Super-Moiré Lattices

Moiré-pattern-based potential engineering has become an important way to explore exotic physics in a variety of two-dimensional condensed matter systems. While these potentials have induced correlated phenomena in almost all commonly studied 2D materials, monolayer graphene has remained an exception. We demonstrate theoretically that a single layer of graphene, when placed between two bulk boron nitride crystal substrates with the appropriate twist angles, can support a robust topological ultraflat band emerging as the second hole band. This is one of the simplest platforms to design and exploit topological flat bands.

Twisted van der Waals Quantum Materials: Fundamentals, Tunability, and Applications

Twisted van der Waals (vdW) quantum materials have emerged as a rapidly developing field of two-dimensional (2D) semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single photon emission, nonlinear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moiré patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This paper offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moiré superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes, lasers, and photodetectors. It highlights the unique ability of moiré superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moiré superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.

Second-harmonic generation in 2D moiré superlattices composed of bilayer transition metal dichalcogenides

Moiré superlattices (MSLs) in twisted two-dimensional van der Waals materials feature twist-angle-dependent crystal symmetry and strong optical nonlinearities. By adjusting the twist angle in bilayer van der Waals materials, the second-harmonic generation (SHG) can be controlled. Here, we focus on exploring the electronic and SHG properties of MSLs in 2D bilayer transition metal dichalcogenides (TMDs) with different twist angles through first-principles calculations. We constructed MSL structures of five TMD materials, including three single-phase materials (MoS2, WS2, and MoSe2) and two heterojunctions (MoS2/MoSe2 and MoS2/WS2) with twist angles of 9.4°, 13.2°, 21.8°, 32.2°, and 42.1° without lattice mismatch. Our findings demonstrate a consistent variation in the SHG susceptibility among different TMD MSLs as a response to twist-angle changes. The underlying reason for the twist-angle dependence of SHG is that the twist angle regulates the interlayer coupling strength, affecting the optical band gap of MSLs and subsequently tuning the SHG susceptibility. Through a comparison of the static SHG susceptibility values, we identified the twist angle of 9.4° as the configuration that yields the highest SHG susceptibility (e.g. 358.5 pm V-1 for the 9.4° MoSe2 MSL). This value is even twice that of the monolayer (173.3 pm V-1 for monolayer MoSe2) and AA'-stacked bilayer structures (139.8 pm V-1 for AA' MoSe2). This high SHG susceptibility is attributed to the strong interlayer coupling in the 9.4° MSL, which enhances the valence band energy (contributed by the antibonding orbitals of chalcogen-pz and transition metal-dz2) and consequently leads to a small optical band gap, thus improving the optical transitions. The findings of this study provide a straightforward way to improve the SHG performance of bilayer TMDs and also throw light on the sensitive relationship between the twist angle, band structure and SHG properties of TMD MSLs.

Transfer learning from Hermitian to non-Hermitian quantum many-body physics

Identifying phase boundaries of interacting systems is one of the key steps to understanding quantum many-body models. The development of various numerical and analytical methods has allowed exploring the phase diagrams of many Hermitian interacting systems. However, numerical challenges and scarcity of analytical solutions hinder obtaining phase boundaries in non-Hermitian many-body models. Recent machine learning methods have emerged as a potential strategy to learn phase boundaries from various observables without having access to the full many-body wavefunction. Here, we show that a machine learning methodology trained solely on Hermitian correlation functions allows identifying phase boundaries of non-Hermitian interacting models. These results demonstrate that Hermitian machine learning algorithms can be redeployed to non-Hermitian models without requiring further training to reveal non-Hermitian phase diagrams. Our findings establish transfer learning as a versatile strategy to leverage Hermitian physics to machine learning non-Hermitian phenomena.

Magic Momenta and Three-Dimensional Landau Levels from a Three-Dimensional Graphite Moiré Superlattice

In this Letter, we theoretically explore the physical properties of a new type of three-dimensional graphite moiré superlattice, the bulk alternating twisted graphite (ATG) system with homogeneous twist angle, which is grown by in situ chemical vapor decomposition method. Compared to twisted bilayer graphene (TBG), the bulk ATG system is bestowed with an additional wave vector degree of freedom due to the extra dimensionality. As a result, when the twist angle of bulk ATG is smaller than twice of the magic angle of TBG, there always exist "magic momenta" which host topological flat bands with vanishing in-plane Fermi velocities. Most saliently, when the twist angle is relatively large, a dispersionless three-dimensional zeroth Landau level would emerge in the bulk ATG, which may give rise to robust three-dimensional quantum Hall effects and unusual quantum-Hall physics over a large range of twist angles.

Optical properties and plasmons in moiré structures

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.

Photonic Flatband Resonances in Multiple Light Scattering

We introduce the concept of photonic flatband resonances and demonstrate it for an array of high-index dielectric particles. We employ the multiple Mie scattering theory and demonstrate that both short- and long-range interactions between the resonators are crucial for the emerging collective resonances and their associated photonic flatbands. By examining both near- and far-field characteristics, we uncover how the flatbands emerge due to a fine tuning of resonators' radiation fields, and predict that hybridization of a flatband resonance with an electric hot spot can lead to giant values of the Purcell factor for the electric dipolar emitters.

Terahertz linear/non-linear anomalous Hall conductivity of moiré TMD hetero-nanoribbons as topological valleytronics materials

Twisted moiré van der Waals heterostructures hold promise to provide a robust quantum simulation platform for strongly correlated materials and realize elusive states of matter such as topological states in the laboratory. We demonstrated that the moiré bands of twisted transition metal dichalcogenide (TMD) hetero-nanoribbons exhibit non-trivial topological order due to the tendency of valence and conduction band states in K valleys to form giant band gaps when spin-orbit coupling (SOC) is taken into account. Among the features of twisted WS[Formula: see text]/MoS[Formula: see text] and WSe[Formula: see text]/MoSe[Formula: see text], we found that the heavy fermions associated with the topological flat bands and the presence of strongly correlated states, enhance anomalous Hall conductivity (AHC) away from the magic angle. By band analysis, we showed that the topmost conduction bands from the ± K-valleys are perfectly flat and carry a spin/valley Chern number. Moreover, we showed that the non-linear anomalous Hall effect in moiré TMD hetero-nanoribbons can be used to manipulate terahertz (THz) radiation. Our findings establish twisted heterostructures of group-VI TMD nanoribbons as a tunable platform for engineering topological valley quantum phases and THz non-linear Hall conductivity.

Tuning the Through-Plane Lattice Thermal Conductivity in van der Waals Structures through Rotational (Dis)ordering

It has recently been demonstrated that MoS2 with irregular interlayer rotations can achieve an extreme anisotropy in the lattice thermal conductivity (LTC), which is, for example, of interest for applications in waste heat management in integrated circuits. Here, we show by atomic-scale simulations based on machine-learned potentials that this principle extends to other two-dimensional materials, including C and BN. In all three materials, introducing rotational disorder drives the through-plane LTC to the glass limit, while the in-plane LTC remains almost unchanged compared to those of the ideal bulk materials. We demonstrate that the ultralow through-plane LTC is connected to the collapse of their transverse acoustic modes in the through-plane direction. Furthermore, we find that the twist angle in periodic moiré structures representing rotational order provides an efficient means for tuning the through-plane LTC that operates for all chemistries considered here. The minimal through-plane LTC is obtained for angles between 1 and 4° depending on the material, with the biggest effect in MoS2. The angular dependence is correlated with the degree of stacking disorder in the materials, which in turn is connected to the slip surface. This provides a simple descriptor for predicting the optimal conditions at which the LTC is expected to become minimal.

Controlled light energy and perfect absorption in twisted bilayer graphene

We theoretically study the components of the dynamical optical conductivity tensor and associated finite-frequency dielectric response of bilayer graphene (BLG), where one graphene layer can slide in-plane or commensurably twist on top of the other. Our results reveal that even slight deviations from the conventional AA, AB, or AC stacking orders yield a finite transverse conductivity. Upon calculating the optical conductivity of the BLG at any arbitrary interlayer displacement, Δ, and chemical potential, µ, it is utilized for a layered device with an epsilon-near-zero (ENZ) insert and metallic back plate. We find that both Δ and µ can effectively control the polarization, energy flow direction, and absorptivity of linearly polarized incident light. By appropriately tailoring Δ and µ, near-perfect absorption and tunable dissipation can be accessible through particular angles of incidence and a broad range of ENZ layer thicknesses. Our findings can be applied to the design of programmable optoelectronics devices.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

New two-dimensional flat band materials: B3C11O6 and B3C15O6

Recently, there has been growing interest in the field of flat-band physics due to its attractive properties and wide range of practical applications. In this study, we introduce two novel two-dimensional monolayers, namely B3C11O6 and B3C15O6, which exhibit a flat band near the Fermi level. These monolayers have been found to be energetically favorable, dynamically stable, and thermodynamically stable based on formation energies, phonon spectra, and molecular dynamics simulations. The nearly flat band (NFB) in B3C11O6 arises from the extended kagome sublattice of carbon atoms. Due to the strong interaction between carbon atoms beyond their nearest neighbors, the bandwidth of the initial flat band is extended to approximately 0.5 eV. Nevertheless, there is still a prominent peak in the density of states near the Fermi level. On the other hand, the NFB in B3C15O6 originates from the localized states of the carbon five-ring structure, which forms a distorted kagome lattice. The presence and characteristics of the NFB strongly depend on the interactions between next-nearest neighbors. Interestingly, the partially occupied NFB in B3C11O6 leads to spin splitting, resulting in a transformation of the system into a ferromagnetic metal. Our research not only presents two types of lattices capable of hosting flat bands or NFBs, but also provides two monolayers that can be employed to investigate various intriguing quantum phases.

Imaging inter-valley coherent order in magic-angle twisted trilayer graphene

Magic-angle twisted trilayer graphene (MATTG) exhibits a range of strongly correlated electronic phases that spontaneously break its underlying symmetries1,2. Here we investigate the correlated phases of MATTG using scanning tunnelling microscopy and identify marked signatures of interaction-driven spatial symmetry breaking. In low-strain samples, over a filling range of about two to three electrons or holes per moiré unit cell, we observe atomic-scale reconstruction of the graphene lattice that accompanies a correlated gap in the tunnelling spectrum. This short-scale restructuring appears as a Kekulé supercell-implying spontaneous inter-valley coherence between electrons-and persists in a wide range of magnetic fields and temperatures that coincide with the development of the gap. Large-scale maps covering several moiré unit cells further reveal a slow evolution of the Kekulé pattern, indicating that atomic-scale reconstruction coexists with translation symmetry breaking at a much longer moiré scale. We use auto-correlation and Fourier analyses to extract the intrinsic periodicity of these phases and find that they are consistent with the theoretically proposed incommensurate Kekulé spiral order3,4. Moreover, we find that the wavelength characterizing moiré-scale modulations monotonically decreases with hole doping away from half-filling of the bands and depends weakly on the magnetic field. Our results provide essential insights into the nature of the correlated phases of MATTG in the presence of strain and indicate that superconductivity can emerge from an inter-valley coherent parent state.

The influence of twist angle on the electronic and phononic band of 2D twisted bilayer SiC

Silicon carbide has a planar two-dimensional structure; therefore it is a potential material for constructing twisted bilayer systems for applications. In this study, DFT calculations were performed on four models with different twist angles. We chose angles of 21.8°, 17.9°, 13.2°, and 5.1° to estimate the dependence of the electronic and phononic properties on the twist angle. The results show that the band gap of bilayer SiC can be changed proportionally by changing the twist angle. However, there are only small variations in the band gaps, with an increment of 0.24 eV by changing the twist angle from 5.1° to 21.8°. At four considered twist angles, the band gaps decrease significantly when fixing the structure of each layer and pressing the separation distance down to 3.5 Å, 3.0 Å, 2.7 Å, and 2.5 Å. A noteworthy point is that the pressing also makes the band linearly smaller at a certain rate regardless of the twist angles. Meanwhile, the phonon bands are not affected by the value of the twist angle. The optical bands are between 900 cm-1 and 1100 cm-1 and the acoustic bands are between 0 cm-1 and 650 cm-1 at four twist angles.

In Situ Twistronics: A New Platform Based on Superlubricity

Twistronics, an emerging field focused on exploring the unique electrical properties induced by twist interface in graphene multilayers, has garnered significant attention in recent years. The general manipulation of twist angle depends on the assembly of van der Waals (vdW) layered materials, which has led to the discovery of unconventional superconductivity, ferroelectricity, and nonlinear optics, thereby expanding the realm of twistronics. Recently, in situ tuning of interlayer conductivity in vdW layered materials has been achieved based on scanning probe microscope. In this Perspective, the advancements in in situ twistronics are focused on by reviewing the state-of-the-art in situ manipulating technology, discussing the underlying mechanism based on the concept of structural superlubricity, and exploiting the real-time twistronic tests under scanning electron microscope (SEM). It is shown that the real-time manipulation under SEM allows for visualizing and monitoring the interface status during in situ twistronic testing. By harnessing the unique tribological properties of vdW layered materials, this novel platform not only enhances the fabrication of twistronic devices but also facilitates the fundamental understanding of interface phenomena in vdW layered materials. Moreover, this platform holds great promise for the application of twistronic-mechanical systems, providing avenues for the integration of twistronics into various mechanical frameworks.

Strain-Induced Quasi-1D Channels in Twisted Moiré Lattices

We study the effects of strain in moiré systems composed of honeycomb lattices. We elucidate the formation of almost perfect one-dimensional moiré patterns in twisted bilayer systems. The formation of such patterns is a consequence of an interplay between twist and strain which gives rise to a collapse of the reciprocal space unit cell. As a criterion for such collapse we find a simple relation between the two quantities and the material specific Poisson ratio. The induced one-dimensional behavior is characterized by two, usually incommensurate, periodicities. Our results offer explanations for the complex patterns of one-dimensional channels observed in low angle twisted bilayer graphene systems and twisted bilayer dicalcogenides. Our findings can be applied to any hexagonal twisted moiré pattern and can be easily extended to other geometries.

Giant Atomic Swirl in Graphene Bilayers with Biaxial Heterostrain

The study of moiré engineering started with the advent of van der Waals heterostructures, in which stacking 2D layers with different lattice constants leads to a moiré pattern controlling their electronic properties. The field entered a new era when it was found that adjusting the twist between two graphene layers led to strongly-correlated-electron physics and topological effects associated with atomic relaxation. A twist is now routinely used to adjust the properties of 2D materials. This study investigates a new type of moiré superlattice in bilayer graphene when one layer is biaxially strained with respect to the other-so-called biaxial heterostrain. Scanning tunneling microscopy measurements uncover spiraling electronic states associated with a novel symmetry-breaking atomic reconstruction at small biaxial heterostrain. Atomistic calculations using experimental parameters as inputs reveal that a giant atomic swirl forms around regions of aligned stacking to reduce the mechanical energy of the bilayer. Tight-binding calculations performed on the relaxed structure show that the observed electronic states decorate spiraling domain wall solitons as required by topology. This study establishes biaxial heterostrain as an important parameter to be harnessed for the next step of moiré engineering in van der Waals multilayers.

Kinetics of Nanobubbles in Tiny-Angle Twisted Bilayer Graphene

Realization of high-quality van der Waals (vdWs) heterostructures by stacking two-dimensional (2D) layers requires atomically clean interfaces. Because of strong adhesion between the constituent layers, the vdWs forces could drive trapped contaminants together into submicron-size "bubbles", which leaves large interfacial areas atomically clean. Here, we study the kinetics of nanobubbles in tiny-angle twisted bilayer graphene (TBG) and our results reveal a substantial influence of the moiré superlattice on the motion of nanoscale interfacial substances. Our experiments indicate that the bubbles will mainly move along the triangular network of domain boundaries in the tiny-angle TBG when the sizes of the bubbles are comparable to that of an AA-stacking region. When the size of the bubble is smaller than that of an AA-stacking region, the bubble becomes motionless and is fixed in the AA-stacking region, because of its large out-of-plane corrugation.

Heavy quasiparticles and cascades without symmetry breaking in twisted bilayer graphene

Among the variety of correlated states exhibited by twisted bilayer graphene, cascades in the spectroscopic properties and in the electronic compressibility occur over larger ranges of energy, twist angle and temperature compared to other effects. This suggests a hierarchy of phenomena. Using a combined dynamical mean-field theory and Hartree calculation, we show that the spectral weight reorganisation associated with the formation of local moments and heavy quasiparticles can explain the cascade of electronic resets without invoking symmetry breaking orders. The phenomena reproduced here include the cascade flow of spectral weight, the oscillations of remote band energies, and the asymmetric jumps of the inverse compressibility. We also predict a strong momentum differentiation in the incoherent spectral weight associated with the fragile topology of twisted bilayer graphene.