Graphene bilayer with a twist: electronic structure

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

Near the magic angle, strong correlations drive many intriguing phases in twisted bilayer graphene (tBG) including unconventional superconductivity and chern insulation. Whether correlations can tune symmetry breaking phases in tBG at intermediate (≳ 2°) twist angles remains an open fundamental question. Here, using ARPES, we study the effects of many-body interactions and displacement field on the band structure of tBG devices at an intermediate (3°) twist angle. We observe a layer- and doping-dependent renormalization of bands at the K points that is qualitatively consistent with moiré models of the Hartree-Fock interaction. We provide evidence of correlation-enhanced inversion symmetry-breaking, manifested by gaps at the Dirac points that are tunable with doping. These results suggest that electronic interactions play a significant role in the physics of tBG even at intermediate twist angles and present a new pathway toward engineering band structure and symmetry-breaking phases in moiré heterostructures.

Polarizability characteristics of twisted bilayer graphene quantum dots in the absence of periodic moiré potential

Recent studies have documented a rich phenomenology in twisted bilayer graphene (TBG), which is significantly relevant to interlayer electronic coupling, in particular to the cases under an applied electric field. While polarizability measures the response of electrons against applied fields, this work adopts a unique strategy of decomposing global polarizability into distributional contributions to access the interlayer polarization in TBG, as a function of varying twisting angles (θ). Through the construction of a model of twisted graphene quantum dots, we assess distributional polarizability at the first-principles level. Our findings demonstrate that the polarizability perpendicular to the graphene plates can be decomposed into intralayer dipoles and interlayer charge-transfer (CT) components, the latter of which provides an explicit measurement of the interlayer coupling strength and charge transfer potential. Our analysis further reveals that interlayer polarizability dominates the polarizability variation during twisting. Intriguingly, the largest interlayer polarizability and CT driven by an external field occur in the misaligned structures with a size-dependent small angle corresponding to the first appearance of AB stacking, rather than the well-recognized Bernal structures. A derived equation is then employed to address the size dependence on the angle corresponding to the largest values in interlayer polarizability and CT. Our investigation not only characterizes the CT features in the interlayer polarizability of TBG quantum dots, but also sheds light on the existence of the strongest interlayer coupling and charge transfer at small twist angles in the presence of an external electric field, thereby providing a comprehensive understanding of the novel properties of graphene-based nanomaterials.

Tunable Interband Transitions in Twisted h-BN/Graphene Heterostructures

In twisted h-BN/graphene heterostructures, the complex electronic properties of the fast-traveling electron gas in graphene are usually considered to be fully revealed. However, the randomly twisted heterostructures may also have unexpected transition behaviors, which may influence the device performance. Here, we study the twist-angle-dependent coupling effects of h-BN/graphene heterostructures using monochromatic electron energy loss spectroscopy. We find that the moiré potentials alter the band structure of graphene, resulting in a redshift of the intralayer transition at the M point, which becomes more pronounced up to 0.22 eV with increasing twist angle. Furthermore, the twisting of the Brillouin zone of h-BN relative to the graphene M point leads to tunable vertical transition energies in the range of 5.1-5.6 eV. Our findings indicate that twist-coupling effects of van der Waals heterostructures should be carefully considered in device fabrications, and the continuously tunable interband transitions through the twist angle can serve as a new degree of freedom to design optoelectrical devices.

Ab Initio Spin Hamiltonian and Topological Noncentrosymmetric Magnetism in Twisted Bilayer CrI3

Twist engineering of van der Waals magnets has emerged as an outstanding platform for manipulating exotic magnetic states. However, the complicated form of spin interactions in the large moiré superlattice obstructs a concrete understanding of such spin systems. To tackle this problem, for the first time, we developed a generic ab initio spin Hamiltonian for twisted bilayer magnets. Our atomistic model reveals that strong AB sublattice symmetry breaking due to the twist introduces a promising route to realize the novel noncentrosymmetric magnetism. Several unprecedented features and phases are uncovered including the peculiar domain structure and skyrmion phase induced by noncentrosymmetricity. The diagram of those distinctive magnetic phases has been constructed, and the detailed nature of their transitions analyzed. Further, we established the topological band theory of moiré magnons relevant to each of these phases. By respecting the full lattice structure, our theory provides the characteristic features that can be detected in experiments.

Fast Twist Angle Mapping of Bilayer Graphene Using Spectroscopic Ellipsometric Contrast Microscopy

Twisted bilayer graphene provides an ideal solid-state model to explore correlated material properties and opportunities for a variety of optoelectronic applications, but reliable, fast characterization of the twist angle remains a challenge. Here we introduce spectroscopic ellipsometric contrast microscopy (SECM) as a tool for mapping twist angle disorder in optically resonant twisted bilayer graphene. We optimize the ellipsometric angles to enhance the image contrast based on measured and calculated reflection coefficients of incident light. The optical resonances associated with van Hove singularities correlate well to Raman and angle-resolved photoelectron emission spectroscopy, confirming the accuracy of SECM. The results highlight the advantages of SECM, which proves to be a fast, nondestructive method for characterization of twisted bilayer graphene over large areas, unlocking process, material, and device screening and cross-correlative measurement potential for bilayer and multilayer materials.

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

ARPES Signatures of Few-Layer Twistronic Graphenes

Diverse emergent correlated electron phenomena have been observed in twisted-graphene layers. Many electronic structure predictions have been reported exploring this new field, but with few momentum-resolved electronic structure measurements to test them. We use angle-resolved photoemission spectroscopy to study the twist-dependent (1° < θ < 8°) band structure of twisted-bilayer, monolayer-on-bilayer, and double-bilayer graphene (tDBG). Direct comparison is made between experiment and theory, using a hybrid k·p model for interlayer coupling. Quantitative agreement is found across twist angles, stacking geometries, and back-gate voltages, validating the models and revealing field-induced gaps in twisted graphenes. However, for tDBG at θ = 1.5 ± 0.2°, close to the magic angle θ = 1.3°, a flat band is found near the Fermi level with measured bandwidth E_w = 31 ± 5 meV. An analysis of the gap between the flat band and the next valence band shows deviations between experiment (Δ_h = 46 ± 5 meV) and theory (Δ_h = 5 meV), indicative of lattice relaxation in this regime.

Andreev Reflection in Scanning Tunneling Spectroscopy of Unconventional Superconductors

We evaluate the differential conductance measured in an STM setting at arbitrary electron transmission between STM tip and a 2D superconductor with arbitrary gap structure. Our analytical scattering theory accounts for Andreev reflections, which become prominent at larger transmissions. We show that this provides complementary information about the superconducting gap structure beyond the tunneling density of states, strongly facilitating the ability to extract the gap symmetry and its relation to the underlying crystalline lattice. We use the developed theory to discuss recent experimental results on superconductivity in twisted bilayer graphene.

Quantifying the local mechanical properties of twisted double bilayer graphene

Nanomechanical measurements of minimally twisted van der Waals materials remained elusive despite their fundamental importance for device realisation. Here, we use Ultrasonic Force Microscopy (UFM) to locally quantify the variation of out-of-plane Young's modulus in minimally twisted double bilayer graphene (TDBG). We reveal a softening of the Young's modulus by 7% and 17% along single and double domain walls, respectively. Our experimental results are confirmed by force-field relaxation models. This study highlights the strong tunability of nanomechanical properties in engineered twisted materials, and paves the way for future applications of designer 2D nanomechanical systems.

Current- and Field-Induced Topology in Twisted Nodal Superconductors

We show that interlayer current induces topological superconductivity in twisted bilayers of nodal superconductors. A bulk gap opens and achieves its maximum near a "magic" twist angle θ_{MA}. Chiral edge modes lead to a quantized thermal Hall effect at low temperatures. Furthermore, we show that an in-plane magnetic field creates a periodic lattice of topological domains with edge modes forming low-energy bands. We predict their signatures in scanning tunneling microscopy. Estimates for candidate materials indicate that twist angles θ∼θ_{MA} are optimal for observing the predicted effects.

Probing correlated states with plasmons

Understanding the nature of strongly correlated states in flat-band materials (such as moiré heterostructures) is at the forefront of both experimental and theoretical pursuits. While magnetotransport, scanning probe, and optical techniques are often very successful in investigating the properties of the underlying order, the exact nature of the ground state often remains unknown. Here, we propose to leverage strong light-matter coupling present in the flat-band systems to gain insight through dynamical dielectric response into the structure of the many-body ground state. We argue that because of the enlargement of the effective lattice of the system arising from correlations, conventional long-range plasmon becomes "folded" to yield a multiband plasmon spectrum. We detail several mechanisms through which the structure of the plasmon spectrum and that of the dynamical dielectric response is susceptible to the underlying order, revealing valued insights such as the interaction-driven band gaps, spin-structure, and the order periodicity.

Visualization of Moiré Magnons in Monolayer Ferromagnet

Two-dimensional magnetic materials provide an ideal platform to explore collective many-body excitations associated with spin fluctuations. In particular, it should be feasible to explore, manipulate, and ultimately design magnonic excitations in two-dimensional van der Waals magnets in a controllable way. Here we demonstrate the emergence of moiré magnon excitations, stemming from the interplay of spin-excitations in monolayer CrBr3 and the moiré pattern arising from the lattice mismatch with the underlying substrate. The existence of moiré magnons is further confirmed via inelastic quasiparticle interference, showing the appearance of a dispersion pattern correlated with the moiré length scale. Our results provide a direct visualization in real-space of the dispersion of moiré magnons, demonstrating the versatility of moiré patterns in creating emergent many-body excitations.

Chiral Decomposition of Twisted Graphene Multilayers with Arbitrary Stacking

We formulate the chiral decomposition rules that govern the electronic structure of a broad family of twisted N + M multilayer graphene configurations that combine arbitrary stacking order and a mutual twist. We show that at the magic angle in the chiral limit the low-energy bands of such systems are composed of chiral pseudospin doublets that are energetically entangled with two flat bands per valley induced by the moiré superlattice potential. The analytic construction is supported by explicit numerical calculations based on realistic parametrization. We further show that vertical displacement fields can open energy gaps between the pseudospin doublets and the two flat bands, such that the flat bands may carry nonzero valley Chern numbers. These results provide guidelines for the rational design of topological and correlated states in generic twisted graphene multilayers.

Moiré Lattice in One-Dimensional Synthetic Frequency Dimension

The moiré lattice has recently attracted broad interest in both solid-state physics and photonics where exotic phenomena in manipulating the quantum states are explored. In this work, we study the one-dimensional (1D) analogs of "moiré" lattices in a synthetic frequency dimension constructed by coupling two resonantly modulated ring resonators with different lengths. Unique features associated with the flatband manipulation as well as the flexible control of localization position inside each unit cell in the frequency dimension have been found, which can be controlled via the choice of flatband. Our work therefore provides insight into simulating moiré physics in 1D synthetic frequency space, which holds important promise for potential applications toward optical information processing.

Sensitivity enhanced tunable plasmonic biosensor using two-dimensional twisted bilayer graphene superlattice

This study theoretically demonstrated an insight for designing a novel tunable plasmonic biosensor, which was created by simply stacking a twisted bilayer graphene (TBG) superlattice onto a plasmonic gold thin film. To achieve ultrasensitive biosensing, the plasmonic biosensor was modulated by Goos-Hänchen (GH) shift. Interestingly, our proposed biosensor exhibited tunable biosensing ability, largely depending on the twisted angle. When the relative twisted angle was optimized to be 55.3°, such a configuration: 44 nm Au film/1-TBG superlattice could produce an ultralow reflectivity of 2.2038 × 10-9 and ultra-large GH shift of 4.4785 × 104 µm. For a small refractive index (RI) increment of 0.0012 RIU (refractive index unit) in sensing interface, the optimal configuration could offer an ultra-high GH shift detection sensitivity of 3.9570 × 107 µm/RIU. More importantly, the optimal plasmonic configuration demonstrated a theoretical possibility of quantitatively monitoring severe acute respiratory syndrome coronavirus (SARS-CoV-2) and human hemoglobin. Considering an extremely small RI change as little as 3 × 10-7 RIU, a good linear response between detection concentration of SARS-CoV-2 and changes in differential GH shift was studied. For SARS-CoV-2, a linear detection interval was obtained from 0 to 2 nM. For human hemoglobin, a linear detection range was achieved from 0 to 0.002 g/L. Our work will be important to develop novel TBG-enhanced biosensors for quantitatively detecting microorganisms and biomolecules in biomedical application.

Moiré magnetic exchange interactions in twisted magnets

In addition to moiré superlattices, twisting can also generate moiré magnetic exchange interactions (MMEIs) in van der Waals magnets. However, owing to the extreme complexity and twist-angle-dependent sensitivity, all existing models fail to fully capture MMEIs and thus cannot provide an understanding of MMEI-induced physics. Here, we develop a microscopic moiré spin Hamiltonian that enables the effective description of MMEIs via a sliding-mapping approach in twisted magnets, as demonstrated in twisted bilayer CrI3. We show that the emergence of MMEIs can create a magnetic skyrmion bubble with non-conserved helicity, a 'moiré-type skyrmion bubble'. This represents a unique spin texture solely generated by MMEIs and ready to be detected under the current experimental conditions. Importantly, the size and population of skyrmion bubbles can be finely controlled by twist angle, a key step for skyrmion-based information storage. Furthermore, we reveal that MMEIs can be effectively manipulated by substrate-induced interfacial Dzyaloshinskii-Moriya interactions, modulating the twist-angle-dependent magnetic phase diagram, which solves outstanding disagreements between theories and experiments.

Pair-Density-Wave and Chiral Superconductivity in Twisted Bilayer Transition Metal Dichalcogenides

We theoretically explore possible orders induced by weak repulsive interactions in twisted bilayer transition metal dichalcogenides (e.g., WSe_{2}) in the presence of an out-of-plane electric field. Using renormalization group analysis, we show that superconductivity survives even with the conventional van Hove singularities. We find that topological chiral superconducting states with Chern number N=1, 2, 4 (namely, p+ip, d+id, and g+ig) appear over a large parameter region with a moiré filling factor around n=1. At some special values of applied electric field and in the presence of a weak out-of-plane Zeeman field, spin-polarized pair-density-wave (PDW) superconductivity can emerge. This spin-polarized PDW state can be probed by experiments such as spin-polarized STM measuring spin-resolved pairing gap and quasiparticle interference. Moreover, the spin-polarized PDW could lead to a spin-polarized superconducting diode effect.

An Atomistic Insight into Moiré Reconstruction in Twisted Bilayer Graphene beyond the Magic Angle

Twisted bilayer graphene exhibits electronic properties strongly correlated with the size and arrangement of moiré patterns. While rigid rotation of the two graphene layers results in a moiré interference pattern, local rearrangements of atoms due to interlayer van der Waals interactions result in atomic reconstruction within the moiré cells. Manipulating these patterns by controlling the twist angle and externally applied strain provides a promising route to tuning their properties. Atomic reconstruction has been extensively studied for angles close to or smaller than the magic angle (θ _m = 1.1°). However, this effect has not been explored for applied strain and is believed to be negligible for high twist angles. Using interpretive and fundamental physical measurements, we use theoretical and numerical analyses to resolve atomic reconstruction in angles above θ _m . In addition, we propose a method to identify local regions within moiré cells and track their evolution with strain for a range of representative high twist angles. Our results show that atomic reconstruction is actively present beyond the magic angle, and its contribution to the moiré cell evolution is significant. Our theoretical method to correlate local and global phonon behavior further validates the role of reconstruction at higher angles. Our findings provide a better understanding of moiré reconstruction in large twist angles and the evolution of moiré cells under the application of strain, which might be potentially crucial for twistronics-based applications.

Preparation, properties and applications of two-dimensional superlattices

As a combination concept of a 2D material and a superlattice, two-dimensional superlattices (2DSs) have attracted increasing attention recently. The natural advantages of 2D materials in their properties, dimension, diversity and compatibility, and their gradually improved technologies for preparation and device fabrication serve as solid foundations for the development of 2DSs. Compared with the existing 2D materials and even their heterostructures, 2DSs relate to more materials and elaborate architectures, leading to novel systems with more degrees of freedom to modulate material properties at the nanoscale. Here, three typical types of 2DSs, including the component, strain-induced and moiré superlattices, are reviewed. The preparation methods, properties and state-of-the-art applications of each type are summarized. An outlook of the challenges and future developments is also presented. We hope that this work can provide a reference for the development of 2DS-related research.

Atomic Bose-Einstein condensate in twisted-bilayer optical lattices

Observation of strong correlations and superconductivity in twisted-bilayer graphene^1-4 has stimulated tremendous interest in fundamental and applied physics^5-8. In this system, the superposition of two twisted honeycomb lattices, generating a moiré pattern, is the key to the observed flat electronic bands, slow electron velocity and large density of states^9-12. Extension of the twisted-bilayer system to new configurations is highly desired, which can provide exciting prospects to investigate twistronics beyond bilayer graphene. Here we demonstrate a quantum simulation of superfluid to Mott insulator transition in twisted-bilayer square lattices based on atomic Bose-Einstein condensates loaded into spin-dependent optical lattices. The lattices are made of two sets of laser beams that independently address atoms in different spin states, which form the synthetic dimension accommodating the two layers. The interlayer coupling is highly controllable by a microwave field, which enables the occurrence of a lowest flat band and new correlated phases in the strong coupling limit. We directly observe the spatial moiré pattern and the momentum diffraction, which confirm the presence of two forms of superfluid and a modified superfluid to insulator transition in twisted-bilayer lattices. Our scheme is generic and can be applied to different lattice geometries and for both boson and fermion systems. This opens up a new direction for exploring moiré physics in ultracold atoms with highly controllable optical lattices.

Optimal twist angle for a graphene-like bilayer

The first optimal-or 'magic'-angle leading to the nullity of the Dirac/Fermi velocity for twisted bilayer graphene is re-evaluated in the Bistritzer-MacDonald set-up (Bistritzer and MacDonald 2011Proc. Natl Acad. Sci.10812233-7). From the details of that calculation we study the resulting alterations when the properties of the two layers are not exactly the same. A moiré combination of lattices without relative rotation but with different spacing lengths may also lead to a vanishing Dirac velocity. Hopping amplitudes can vary as well, and curvature is one of the possible causes for their change. In the case of small curvature values and situations dominated by hopping energy scales, the optimal angle becomes wider than in the 'flat' case.

Ideal acoustic quantum spin Hall phase in a multi-topology platform

Fermionic time-reversal symmetry ([Formula: see text])-protected quantum spin Hall (QSH) materials feature gapless helical edge states when adjacent to arbitrary trivial cladding materials. However, due to symmetry reduction at the boundary, bosonic counterparts usually exhibit gaps and thus require additional cladding crystals to maintain robustness, limiting their applications. In this study, we demonstrate an ideal acoustic QSH with gapless behaviour by constructing a global T_f on both the bulk and the boundary based on bilayer structures. Consequently, a pair of helical edge states robustly winds several times in the first Brillouin zone when coupled to resonators, promising broadband topological slow waves. We further reveal that this ideal QSH phase behaves as a topological phase transition plane that bridges trivial and higher-order phases. Our versatile multi-topology platform sheds light on compact topological slow-wave and lasing devices.

A primer on twistronics: a massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene

The recent discovery of superconductivity in magic-angle twisted bilayer graphene (TBLG) has sparked a renewed interest in the strongly-correlated physics ofsp²carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moiré pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and TBLG. Subsequently, we illuminate the origin of flat bands in TBLG at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of TBLG not covered by this review but may readily be approached with the help of this primer.

Tunable Superconductivity and Möbius Fermi Surfaces in an Inversion-Symmetric Twisted van der Waals Heterostructure

We theoretically study a moiré superlattice geometry consisting of mirror-symmetric twisted trilayer graphene surrounded by identical transition metal dichalcogenide layers. We show that this setup allows us to switch on or off and control the spin-orbit splitting of the Fermi surfaces via application of a perpendicular displacement field D_{0} and explore two manifestations of this control: first, we compute the evolution of superconducting pairing with D_{0}; this features a complex admixture of singlet and triplet pairing and, depending on the pairing state in the parent trilayer system, phase transitions between competing superconducting phases. Second, we reveal that, with application of D_{0}, the spin-orbit-induced spin textures exhibit vortices which lead to "Möbius fermi surfaces" in the interior of the Brillouin zone: diabatic electron trajectories, which are predicted to dominate quantum oscillation experiments, require encircling the Γ point twice, making their Möbius nature directly observable. Further, we show that the superconducting order parameter inherits the unconventional, Möbius spin textures. Our findings suggest that this system provides a promising experimental avenue for systematically studying the impact of spin-orbit coupling on the multitude of topological and correlated phases in near-magic-angle twisted trilayer graphene.

Emerging topics in nanophononics and elastic, acoustic, and mechanical metamaterials: an overview

This broad review summarizes recent advances and "hot" research topics in nanophononics and elastic, acoustic, and mechanical metamaterials based on results presented by the authors at the EUROMECH 610 Colloquium held on April 25-27, 2022 in Benicássim, Spain. The key goal of the colloquium was to highlight important developments in these areas, particularly new results that emerged during the last two years. This work thus presents a "snapshot" of the state-of-the-art of different nanophononics- and metamaterial-related topics rather than a historical view on these subjects, in contrast to a conventional review article. The introduction of basic definitions for each topic is followed by an outline of design strategies for the media under consideration, recently developed analysis and implementation techniques, and discussions of current challenges and promising applications. This review, while not comprehensive, will be helpful especially for early-career researchers, among others, as it offers a broad view of the current state-of-the-art and highlights some unique and flourishing research in the mentioned fields, providing insight into multiple exciting research directions.

Switching between Mott-Hubbard and Hund Physics in Moiré Quantum Simulators

Mott-Hubbard and Hund electron correlations have been realized thus far in separate classes of materials. Here, we show that a single moiré homobilayer encompasses both kinds of physics in a controllable manner. We develop a microscopic multiband model that we solve by dynamical mean-field theory to nonperturbatively address the local many-body correlations. We demonstrate how tuning with twist angle, dielectric screening, and hole density allows us to switch between Mott-Hubbard and Hund correlated states in a twisted WSe₂ bilayer. The underlying mechanism is based on controlling Coulomb-interaction-driven orbital polarization and the energetics of concomitant local singlet and triplet spin configurations. From a comparison to recent experimental transport data, we find signatures of a filling-controlled transition from a triplet charge-transfer insulator to a Hund-Mott metal. Our finding establishes twisted transition-metal dichalcogenides as a tunable platform for exotic phases of quantum matter emerging from large local spin moments.

Thermodynamic Characteristic for a Correlated Flat-Band System with a Quantum Anomalous Hall Ground State

While the ground-state phase diagram of the correlated flat-band systems has been intensively investigated, the dynamic and thermodynamic properties of such lattice models are less explored, but it is the latter which is most relevant to the experimental probes (transport, quantum capacitance, and spectroscopy) of the quantum moiré materials such as twisted bilayer graphene. Here we show, by means of momentum-space quantum Monte Carlo and exact diagonalization, in chiral limit there exists a unique thermodynamic characteristic for the correlated flat-band model with interaction-driven quantum anomalous Hall (QAH) ground state, namely, the transition from the QAH insulator to the metallic state takes place at a much lower temperature compared with the zero-temperature single-particle gap generated by the long-range Coulomb interaction. Such low transition temperature comes from the proliferation of excitonic particle-hole excitations, which transfers the electrons across the gap between different topological bands to restore the broken time-reversal symmetry and gives rise to a pronounced enhancement in the charge compressibility. Future experiments, to verify such generic thermodynamic characteristics, are proposed.

Intercalation of argon in honeycomb structures towards promising strategy for rechargeable Li-ion batteries

High-performance rechargeable batteries are becoming very important for high-end technologies with their ever increasing application areas. Hence, improving the performance of such batteries has become the main bottleneck to transferring high-end technologies to end users. In this study, we propose an argon intercalation strategy to enhance battery performance via engineering the interlayer spacing of honeycomb structures such as graphite, a common electrode material in lithium-ion batteries (LIBs). Herein, we systematically investigated the LIB performance of graphite and hexagonal boron nitride (h-BN) when argon atoms were sent into between their layers by using first-principles density-functional-theory calculations. Our results showed enhanced lithium binding for graphite and h-BN structures when argon atoms were intercalated. The increased interlayer space doubles the gravimetric lithium capacity for graphite, while the volumetric capacity also increased by around 20% even though the volume was also increased. Theab initiomolecular dynamics simulations indicate the thermal stability of such graphite structures against any structural transformation and Li release. The nudged-elastic-band calculations showed that the migration energy barriers were drastically lowered, which promises fast charging capability for batteries containing graphite electrodes. Although a similar level of battery promise was not achieved for h-BN material, its enhanced battery capabilities by argon intercalation also support that the argon intercalation strategy can be a viable route to enhance such honeycomb battery electrodes.

Local atomic-morphology-resolved edge states in twisted bilayer graphene nanoribbons

We study the properties of edge states for a selected (10,1)[(4,3)] twisted bilayer graphene (TBG) nanoribbon with minimal edges but a majority of zigzag edges. By using the tight-binding and Green's function methods, we find a remarkable rule of a local electronic transfer for the edge states. As the energy away from the Fermi level, the transfer is in the order of convex AB-, concave AB-, concave AA- and convex AA-stacked regions of the ribbon curve edges. We illustrate that this rule comes from the difference in interlayer couplings among the four types of local geometries at edges. Further, an in-plane transverse electric field can rearrange the edge bands and enlarge the energy regimes, leading to the lowest energy states modified from AB-stacked edge states to AA-stacked ones. The realignment of the edge bands results from the interplay between the interlayer coupling and the potential difference induced by the transverse electric field, which results in different bonding and antibonding edge states, i.e. the edge bands. In contrast, the total energy regime of the edge bands remain nearly unchanged under a relative strong off-plane perpendicular electric field, and the typical AA-stacked edge states are still maintained even the rotational symmetry of two layers is broken. Until a sufficiently strong value, the TBG nanoribbon tends to behave as two noninteracting monolayer ribbons except for a band distortion in low-energy regime. The conductance spectra reflects the edge bands well. We also discussed the influence of edge defects in the TBG nanoribbon on transport properties. It is found that the contributed conductance of each type of edge states shows different degrees of suppression for a monatomic vacancy in the corresponding region of edges.

Atomic-Scale Confinement and Negative Refraction of Plasmons by Twisted Bilayer Graphene

Moiré superlattices provide in-plane quantum restriction for light-matter interactions in twisted bilayer graphene (tBLG), leading to the exotic photon-Moiré physics and potential applications for light manipulation. Recently, our experiment identified a highly confined slow surface plasmons polaritons (SPPs) mode in tBLG. Here, we demonstrate that the propagation of the slow SPPs mode in tBLG is spatially tailored and steered at deep subwavelengths. Analysis by the perturbation theory indicates that the coupling between the slow SPPs mode and the Moiré system is greatly strengthened, which regulates the wavefront at the atomic scale and makes tBLG serve as a universal optical metamaterial. Consequently, the negative refraction is achieved at the interface of monolayer graphene and tBLG, by which a metalens with a controllable focal length and an extremely high resolution up to 1/150 of wavelength is devised. Our work paves the way for constructing optical metamaterial at the atomic scale and develops future photon-Moiré interaction systems.

Omnidirectional flat bands in chiral magnonic crystals

The magnonic band structure of two-dimensional chiral magnonic crystals is theoretically investigated. The proposed metamaterial involves a three-dimensional architecture, where a thin ferromagnetic layer is in contact with a two-dimensional periodic array of heavy-metal square islands. When these two materials are in contact, an anti-symmetric exchange coupling known as the Dzyaloshinskii–Moriya interaction (DMI) arises, which generates nonreciprocal spin waves and chiral magnetic order. The Landau–Lifshitz equation and the plane-wave method are employed to study the dynamic magnetic behavior. A systematic variation of geometric parameters, the DMI constant, and the filling fraction allows the examination of spin-wave propagation features, such as the spatial profiles of the dynamic magnetization, the isofrequency contours, and group velocities. In this study, it is found that omnidirectional flat magnonic bands are induced by a sufficiently strong Dzyaloshinskii–Moriya interaction underneath the heavy-metal islands, where the spin excitations are active. The theoretical results were substantiated by micromagnetic simulations. These findings are relevant for envisioning applications associated with spin-wave-based logic devices, where the nonreciprocity and channeling of the spin waves are of fundamental and practical scientific interest.

Baby skyrmions in Chern ferromagnets and topological mechanism for spin-polaron formation in twisted bilayer graphene

The advent of moiré materials has galvanized interest in the nature of charge carriers in topological bands. In contrast to conventional materials with electron-like charge carriers, topological bands allow for more exotic possibilities where charge is carried by nontrivial topological textures, such as skyrmions. However, the real-space description of skyrmions is ill-suited to address the limit of small skyrmions and to account for momentum-space band features. Here, we develop a momentum-space approach to study the formation of the smallest skyrmions – spin polarons, formed as bound states of an electron and a spin flip – in topological ferromagnets. We show that, quite generally, there is an attraction between an electron and a spin flip that is purely topological in origin, promoting the formation of spin polarons. Applying our results to twisted bilayer graphene, we identify a range of parameters where spin polarons are formed and discuss their possible experimental signatures.

In conventional materials, charge carriers are electron-like quasiparticles, but topological bands allow for more exotic possibilities. Here, the authors predict that in the Chern-ferromagnet phase of twisted bilayer graphene charge is carried by spin polarons, bound states of an electron and a spin flip.

Controlling magnetic frustration in 1T-TaS2via Coulomb engineered long-range interactions

Magnetic frustrations in two-dimensional materials provide a rich playground to engineer unconventional phenomena. However, despite intense efforts, a realization of tunable frustrated magnetic order in two-dimensional materials remains an open challenge. Here we propose Coulomb engineering as a versatile strategy to tailor magnetic ground states in layered materials. Using the frustrated van der Waals monolayer 1T-TaS₂as an example, we show how long-range Coulomb interactions renormalize the low energy nearly flat band structure, leading to a Heisenberg model which depends on the Coulomb interactions. Based on this, we show that superexchange couplings in the material can be precisely tailored by means of environmental dielectric screening, ultimately allowing to externally drive the material towards a tunable frustrated regime. Our results put forward Coulomb engineering as a powerful tool to manipulate magnetic properties of van der Waals materials.

Strain-induced stacking transition in bilayer graphene

Strain, both naturally occurring and deliberately engineered, can have a considerable effect on the structural and electronic properties of 2D and layered materials. Uniaxial or biaxial heterostrain modifies the stacking arrangement of bilayer graphene (BLG) which subsequently influences the electronic structure of the bilayer. Here, we use density functional theory (DFT) calculations to investigate the interplay between an external applied heterostrain and the resulting stacking in BLG. We determine how a strain applied to one layer is transferred to a second, 'free' layer and at what critical strain the ground-state AB-stacking is disrupted. To overcome limitations introduced by periodic boundary conditions, we consider an approximate system consisting of an infinite graphene sheet and an armchair graphene nanoribbon. We find that above a critical strain of∼1%, it is energetically favourable for the free layer to be unstrained, indicating a transition between uniform AB-stacking and non-uniform mixed stacking. This is in agreement with a simple model estimate based on the individual energy contributions of strain and stacking effects. Our findings suggest that small levels of strain provide a platform to reversibly engineer stacking order and Moiré features in bilayers, providing a viable alternative to twistronics to engineer topological and exotic physical phenomena in such systems.

Strong interlayer coupling and stable topological flat bands in twisted bilayer photonic Moiré superlattices

The moiré superlattice of misaligned atomic bilayers paves the way for designing a new class of materials with wide tunability. In this work, we propose a photonic analog of the moiré superlattice based on dielectric resonator quasi-atoms. In sharp contrast to van der Waals materials with weak interlayer coupling, we realize the strong coupling regime in a moiré superlattice, characterized by cascades of robust flat bands at large twist-angles. Surprisingly, we find that these flat bands are characterized by a non-trivial band topology, the origin of which is the moiré pattern of the resonator arrangement. The physical manifestation of the flat band topology is a robust one-dimensional conducting channel on edge, protected by the reflection symmetry of the moiré superlattice. By explicitly breaking the underlying reflection symmetry on the boundary terminations, we show that the first-order topological edge modes naturally deform into higher-order topological corner modes. Our work pioneers the physics of topological phases in the designable platform of photonic moiré superlattices beyond the weakly coupled regime.

Promotion of superconductivity in magic-angle graphene multilayers

Graphene moiré superlattices show an abundance of correlated insulating, topological, and superconducting phases. Whereas the origins of strong correlations and nontrivial topology can be directly linked to flat bands, the nature of superconductivity remains enigmatic. We demonstrate that magic-angle devices made of twisted tri-, quadri-, and pentalayer graphene placed on monolayer tungsten diselenide exhibit flavor polarization and superconductivity. We also observe insulating states in the tril- and quadrilayer arising at finite electric displacement fields. As the number of layers increases, superconductivity emerges over an enhanced filling-factor range, and in the pentalayer it extends well beyond the filling of four electrons per moiré unit cell. Our results highlight the role of the interplay between flat and more dispersive bands in extending superconducting regions in graphene moiré superlattices.

Spectroscopy of Twisted Bilayer Graphene Correlated Insulators

We analytically compute the scanning tunneling microscopy (STM) signatures of integer-filled correlated ground states of the magic angle twisted bilayer graphene (TBG) narrow bands. After experimentally validating the strong-coupling approach at ±4  electrons/moiré unit cell, we consider the spatial features of the STM signal for 14 different many-body correlated states and assess the possibility of Kekulé distortion (KD) emerging at the graphene lattice scale. Remarkably, we find that coupling the two opposite graphene valleys in the intervalley-coherent (IVC) TBG insulators does not always result in KD. As an example, we show that the Kramers IVC state and its nonchiral U(4) rotations do not exhibit any KD, while the time-reversal-symmetric IVC state does. Our results, obtained over a large range of energies and model parameters, show that the STM signal and Chern number of a state can be used to uniquely determine the nature of the TBG ground state.

Moiré metasurfaces for dynamic beamforming

Recent advances in digitally programmable metamaterials have accelerated the development of reconfigurable intelligent surfaces (RIS). However, the excessive use of active components (e.g., pin diodes and varactor diodes) leads to high costs, especially for those operating at millimeter-wave frequencies, impeding their large-scale deployments in RIS. Here, we introduce an entirely different approach-moiré metasurfaces-to implement dynamic beamforming through mutual twists of two closely stacked metasurfaces. The superposition of two high-spatial-frequency patterns produces a low-spatial-frequency moiré pattern through the moiré effect, which provides the surface impedance profiles to generate desired radiation patterns. We demonstrate experimentally that the direction of the radiated beams can continuously sweep over the entire reflection space along predesigned trajectories by simply adjusting the twist angle and the overall orientation. Our work opens previously unexplored directions for synthesizing far-field scattering through the direct contact of mutually twisted metallic patterns with different plane symmetry groups.

Pressure Tunable van Hove Singularities of Twisted Bilayer Graphene

The giant light-matter interaction induced by van Hove singularities (vHSs) of twisted bilayer graphene (tBLG) is responsible for enhanced optical absorption and strong photoresponse. Here, we investigated the evolution of vHSs in tBLG under pressure by using Raman spectroscopy. Pressure not only induces a blue shift of the G/R band but also tunes the intensity of the G/R band. The blue shift of the G/R band is due to the reduction of the in-plane lattice constant, and the variation of the G/R band intensity is due to the vHSs' shift of tBLG. Moreover, the main band in the absorption spectrum of tBLG is attributed to multiple transitions from valence to conduction bands. Because the ratio of R to G band intensity increases under pressure and the origins of R and G bands are different, we claim that pressure enhances intervalley electron scattering. This study paves the way for pressure engineering of vHS and the corresponding photon-electron-phonon interaction in tBLG.

First-principles calculation of gate-tunable ferromagnetism in magic-angle twisted bilayer graphene under pressure

Magic-angle twisted bilayer graphene (MATBG) is notable as a highly tunable platform for investigating strongly correlated phenomena such as unconventional superconductivity and quantum spin liquids, due to easy control of doping level through gating and sensitive dependence of the magic angle on hydrostatic pressure. Experimental observations of correlated insulating states, unconventional superconductivity and ferromagnetism in MATBG indicate that this system exhibits rich exotic phases. In this work, using density functional theory calculations in conjunction with the effective screening medium method, we find the MATBG under pressure at a twisting angle of 2.88^∘and simulate how its electronic states evolve when doping level and electric field perpendicular to plane are tuned by gating. Our calculations show that, at doping levels between two electrons and four holes per moiré unit cell, a ferromagnetic (FM) solution with spin density localized at AA stacking sites is lower in energy than the nonmagnetic solution. The magnetic moment of this FM state decreases with both electron and hole doping and vanishes at four electrons/holes doped per moiré unit cell. Hybridization between the flat bands at the Fermi level and the surrounding dispersive bands can take place at finite doping. On increasing the out-of-plane electric field at zero doping, a transition from the FM state to the nonmagnetic one is seen. An investigation of impurity effects shows that both absorption ofO2molecules and occurrence of Stone-Wales impurities suppress the FM state, and the mechanisms are understood from our calculations. We also analyze the interlayer bonding character due to flat bands via Wannier functions. Finally, we report trivial band topology of the flat bands in the FM state at a certain doping level.

Moiré Quasibound States in the Continuum

The novel physics of twisted bilayer graphene has motivated extensive studies of magic-angle flat bands hosted by moiré structures in electronic, photonic, and acoustic systems. On the other hand, bound states in the continuum (BICs) have also attracted great attention in recent years because of their potential applications in the field of designing superior optical devices. Here, we combine these two independent concepts to construct a new optical state in a twisted bilayer photonic crystal slab, which is called as moiré quasi-BIC, and numerically demonstrate that such an exotic optical state possesses dual characteristics of moiré flat bands and quasi-BICs. To illustrate the mechanism for the formation of moiré flat bands, we develop an effective model at the center of the Brillouin zone and show that moiré flat bands could be fulfilled by balancing the interlayer coupling strength and the twist angle around the band edge above the light line. Moreover, by decreasing the twist angle of moiré photonic crystal slabs with flat bands, it is shown that the moiré flat-band mode at the Brillouin center gradually approaches a perfect BIC, where the total radiation loss from all diffraction channels is significantly suppressed. To clarify the advantage of moiré quasi-BICs, enhanced second-harmonic generation (SHG) is numerically proven with a wide-angle optical source. The efficiency of SHG assisted by designed moiré quasi-BICs can be greatly improved compared with that based on dispersive quasi-BICs with similar quality factors.

Influence of Hexagonal Boron Nitride on Electronic Structure of Graphene

By performing first-principles calculations, we studied hexagonal-boron-nitride (hBN)-supported graphene, in which moiré structures are formed due to lattice mismatch or interlayer rotation. A series of graphene/hBN systems has been studied to reveal the evolution of properties with respect to different twisting angles (21.78°, 13.1°, 9.43°, 7.34°, 5.1°, and 3.48°). Although AA- and AB-stacked graphene/hBN are gapped at the Dirac point by about 50 meV, the energy gap of the moiré graphene/hBN, which is much more asymmetric, is only about several meV. Although the Dirac cone of graphene residing in the wide gap of hBN is not much affected, the calculated Fermi velocity is found to decrease with the increase in the moiré super lattice constant due to charge transfer. The periodic potential imposed by hBN modulated charge distributions in graphene, leading to the shift of graphene bands. In agreement with experiments, there are dips in the calculated density of states, which get closer and closer to the Fermi energy as the moiré lattice grows larger.

Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models

We propose models of twisted multilayer graphene that exhibit exactly flat Bloch bands with arbitrary Chern numbers and ideal band geometries. The models are constructed by twisting two sheets of Bernal-stacked multiple graphene layers with only intersublattice couplings. Analytically we show that flatband wave functions in these models exhibit a momentum space holomorphic character, leading to ideal band geometries. We also explicitly demonstrate a generic "wave function exchange" mechanism that generates the high Chern numbers of these ideal flatbands. The ideal band geometries and high Chern numbers of the flatbands imply the possibility of hosting exotic fractional Chern insulators which do not have analogues in continuum Landau levels. We numerically verify that these exotic fractional Chern insulators are model states for short-range interactions, characterized by exact ground-state degeneracies at zero energy and infinite particle-cut entanglement gaps.

Twisted graphene stabilized by organic linkers pillaring

Twisted graphene, including magic angle graphene, has attracted extensive attentions for its novel properties recently. However, twisted graphene is intrinsically unstable and this will obstruct their application in practice, especially for twisted nano graphene. The twist angles between adjacent layers will change spontaneously. This relaxation process will be accelerated under heat and strain. To solve this problem, we propose a strategy of pillaring twisted graphene by organic linkers in theory. The necessity and feasibility of this strategy is proved by numerical calculation.

Deep Elastic Strain Engineering of 2D Materials and Their Twisted Bilayers

Conventionally, tuning materials' properties can be done through strategies such as alloying, doping, defect engineering, and phase engineering, while in fact mechanical straining can be another effective approach. In particular, elastic strain engineering (ESE), unlike conventional strain engineering mainly based on epitaxial growth, allows for continuous and reversible modulation of material properties by mechanical loading/unloading. The exceptional intrinsic mechanical properties (including elasticity and strength) of two-dimensional (2D) materials make them naturally attractive candidates for potential ESE applications. Here, we demonstrated that using the strain effect to modulate the physical and chemical properties toward novel functional device applications, which could be a general strategy for various 2D materials and their heterostructures. We then show how ultralarge, uniform elastic strain in free-standing 2D monolayers can permit deep elastic strain engineering (DESE), which can result in fundamentally changed electronic and optoelectronic properties for unconventional device applications. In addition to monolayers and van der Waals (vdW) heterostructures, we propose that DESE can be also applied to twisted bilayer graphene and other emerging twisted vdW structures, allowing for unprecedented functional 2D material applications.

Moiré Superlattice Effects and Band Structure Evolution in Near-30-Degree Twisted Bilayer Graphene

In stacks of two-dimensional crystals, mismatch of their lattice constants and misalignment of crystallographic axes lead to formation of moiré patterns. We show that moiré superlattice effects persist in twisted bilayer graphene (tBLG) with large twists and short moiré periods. Using angle-resolved photoemission, we observe dramatic changes in valence band topology across large regions of the Brillouin zone, including the vicinity of the saddle point at M and across 3 eV from the Dirac points. In this energy range, we resolve several moiré minibands and detect signatures of secondary Dirac points in the reconstructed dispersions. For twists θ > 21.8°, the low-energy minigaps are not due to cone anticrossing as is the case at smaller twist angles but rather due to moiré scattering of electrons in one graphene layer on the potential of the other which generates intervalley coupling. Our work demonstrates the robustness of the mechanisms which enable engineering of electronic dispersions of stacks of two-dimensional crystals by tuning the interface twist angles. It also shows that large-angle tBLG hosts electronic minigaps and van Hove singularities of different origin which, given recent progress in extreme doping of graphene, could be explored experimentally.

Degradation of Phonons in Disordered Moiré Superlattices

The elastic collective modes of a moiré superlattice arise not from vibrations of a rigid crystal but from the relative displacement between the constituent layers. Despite their similarity to acoustic phonons, these modes, called phasons, are not protected by any conservation law. Here, we show that disorder in the relative orientation between the layers and thermal fluctuations associated with their sliding motion degrade the propagation of sound in the moiré superlattice. Specifically, the phason modes become overdamped at low energies and acquire a finite gap, which displays a universal dependence on the twist-angle variance. Thus, twist-angle inhomogeneity is manifested not only in the noninteracting electronic structure of moiré systems, but also in their phononlike modes. More broadly, our results have important implications for the electronic properties of twisted moiré systems that are sensitive to the electron-phonon coupling.

Scattering between Minivalleys in Twisted Double Bilayer Graphene

A unique feature of the complex band structures of moiré materials is the presence of minivalleys, their hybridization, and scattering between them. Here, we investigate magnetotransport oscillations caused by scattering between minivalleys-a phenomenon analogous to magnetointersubband oscillations-in a twisted double bilayer graphene sample with a twist angle of 1.94°. We study and discuss the potential scattering mechanisms and find an electron-phonon mechanism and valley conserving scattering to be likely. Finally, we discuss the relevance of our findings for different materials and twist angles.

Gapping Fragile Topological Bands by Interactions

We consider the stability of fragile topological bands protected by space-time inversion symmetry in the presence of strong electron-electron interactions. At the single-particle level, the topological nature of the bands prevents the opening of a gap between them. In contrast, we show that when the fragile bands are half filled, interactions can open a gap in the many-body spectrum without breaking any symmetry or mixing degrees of freedom from remote bands. Furthermore, the resulting ground state is not topologically ordered. Thus, a fragile topological band structure does not present an obstruction to forming a "featureless insulator" ground state. Our construction relies on the formation of fermionic bound states of two electrons and one hole known as "trions." The trions form a band whose coupling to the electronic band enables the gap opening. This result may be relevant to the gapped state indicated by recent experiments in magic angle twisted bilayer graphene at charge neutrality.