Reconstruction of the atomic crystal structure in twisted 2D materials has been demonstrated to be responsible for multiple exciting phenomena in van der Waals heterostructures, from the appearance of flat bands in twisted bilayer graphene to Wigner crystallization in transition metal dichalcogenides (TMDs). However, there are still neither experimental methods for accessing the 3D atomic distributions nor models that describe the exact atomic shifts in such reconstructed structures, which significantly impedes the development of the field. Dark field (DF) transmission electron microscopy (TEM) has been conventionally employed to visualize the local in-plane atomic displacements. Here we expand this method to obtain a full description of the reconstructed atomic systems and demonstrate the quantitative relations between the local stacking and the intensity in the DF image. We show how local 3D atomic displacements and the interlayer distance can be extracted from a DF image.

We demonstrate that superconductivity driven by strong quantum-critical fluctuations can emerge near relativistic Mott transitions in twisted two-dimensional materials. In twisted double-bilayer WSe_{2}, all time-reversal-even, gap-opening collective modes promote pairing, whereas time-reversal-odd modes do not. In twisted bilayer graphene, all transitions into intervalley-coherent insulators give rise to superconductivity. Hence, the two separate superconducting domes of insulating or semimetallic undoped systems are expected to merge near the Gross-Neveu transition angle. A crucial ingredient of the theory is that critical fluctuations render the electronic states strongly incoherent, allowing attractive pairing channels to overcome the bare Dirac semimetal behavior. The richer the Dirac structure, the more readily pairs can form. Finally, we demonstrate a direct relation between boson-mediated pairing and the formation of charge-carrying skyrmions in the proximate insulating state.

In this article, we analyze the quantum and topological properties of graphene-based plasmonic systems. We consider the following plasmonic materials: single-layer graphene, twisted bilayer graphene, and other graphene stackings, as well as the following architectures: graphene-based gratings, grids, chains of graphene disks, and the kagomé lattice.

Abstract Emerging electronic, photonic, and mechanical properties exhibited by moiré superlattices formed through stacked twisted interfaces may revolutionize nano-opto-electro-mechanical systems, yet their impacts remain elusive. Here, we propose and demonstrate a multifunctional nano-opto-electro-mechanical system based on low-tension suspended twisted bilayer graphene. The mechanical properties of this system resemble those of other two-dimensional materials, exhibiting uniform membrane-like structures. Its tunable cavity length spans a broad range, with optical spectral signals significantly enhanced by approximately 8-fold when the length varies by about 50 nanometers. We further demonstrate that the microscopic degrees of freedom in twisted bilayer graphene can be effectively controlled through unique static and dynamic strain mechanisms. This work holds promise for unprecedented manipulation of electrons, photons, and phonons, and advances the development of hybrid quantum devices.

Electron interactions in quantum materials fundamentally shape their energy bands and, with them, the material's most intriguing quantum phases. Magic-angle twisted bilayer graphene (MATBG)1-3 has emerged as a model system in which flat bands lead to a variety of such phases, yet the precise nature of these bands has remained elusive owing to the lack of high-resolution momentum-space probes. Here we use the quantum twisting microscope (QTM) to directly image the interacting energy bands of MATBG with unprecedented momentum and energy resolution. Away from the magic angle, the observed bands closely follow the single-particle theory. At the magic angle, however, we observe bands that are completely transformed by interactions, exhibiting light and heavy electronic character at different parts of momentum space. On doping, the interplay between these light and heavy components leads to a variety of notable phenomena, including interaction-induced bandwidth renormalization, Mott-like cascades of the heavy particles and Dirac revivals of the light particles. We also uncover a persistent low-energy excitation tied to the heavy sector, suggesting a new unaccounted degree of freedom. These results resolve the long-standing puzzle in MATBG-the dual nature of its electrons-by showing that it originates from electrons at different momenta within the same topological heavy-fermion-like flat bands. More broadly, our results establish the QTM as a powerful tool for high-resolution spectroscopic studies of quantum materials previously inaccessible to conventional techniques.

Weak localization and universal conductance fluctuations in large-area twisted bilayer graphene

Opening a bandgap in bilayer graphene typically requires either structural modification or continuous external electric fields, while twisted bilayer graphene configurations remain largely gapless without additional perturbation. Here, we demonstrate bandgap opening of up to 50meV in structurally intact bilayer graphene by in-plane strain fields imposed by an interfaced porous organic 2D crystal. These sandwich graphene/organic 2D crystal/graphene (G-O2DC-G) heterostructures, with O2DCs of honeycomb lattice structure and with pore sizes ranging from 9.6 to 31.0Å, template corrugation that brings graphene layers into localized Bernal-stacked contact within the pores. We identify a critical pore size threshold of ∼18Å, above which the graphene layers establish direct contact with interlayer spacing of ∼3.34Å as in Bernal-stacked bilayer. The bandgap exhibits a non-monotonic dependence on pore size, reaching its maximum at ∼19Å (G-TTI-G) before declining with further pore expansion. We propose this strain-based approach as a design principle for bandgap engineering in graphene, leveraging the chemical diversity of O2DCs for potential applications in graphene-based semiconductor devices.

Optical signatures of flat bands and anisotropic quantum geometry in magic-angle twisted bilayer graphene

Nanoscale polar structures are essential for understanding polarization processes in low-dimensional systems and offer exciting prospects for high-performance electronics. Here, we reveal the signatures of a flexoelectric polar vortex superstructure in twisted bilayer graphene aligned with hexagonal boron nitride (TBG/hBN), where strong coupling between two moiré patterns induces pronounced structural relaxation. Scanning tunneling microscopy uncovers moiré-scale flat-band bending, distinct from domain-wall-confined polarization in minimally twisted graphene. Theoretical simulations demonstrate that the lowering of point-group symmetry plays a crucial role and indicate that the in-plane polarization field forms an array of polar vortices. Moreover, near the magic angle, the polarization becomes highly gate-tunable and couples to electron correlations, leading to spatially modulated correlated gaps. Our findings establish the coupling of multiple moiré patterns as a powerful strategy for engineering nanoscale polar structures and emergent quantum states.

Dirac cones and magic angles in the Bistritzer–MacDonald twisted bilayer graphene Hamiltonian

Observation of superconductivity, magnetism, and correlated insulating phases driven by the moiré potential in twisted graphene bilayer has opened the exciting new field of "twistronics". Even richer physics is expected if moiré superlattice could be generated on topological insulators; however, until now, experimental studies have been scarce. Here, we demonstrate topological moirés generated by adsorbing a monolayer of noble gas on a topological insulator. By angle-resolved photoemission spectroscopy, we show that the moiré potential replicates the topological surface state and affects it in a way fundamentally different from the trivial states. Replicated Dirac cones generally avoid crossings, except at the time-reversal invariant momenta that remain gapless. This creates van Hove singularities at the moiré Brillouin zone corners, providing the mechanism of enhancing correlations. Indeed, we observe a strong enhancement of the electron-phonon coupling strength that, if properly tuned, might lead to topological superconductivity and Majorana Fermions.

Recent work investigated graphene's hydrogenation with independent control of the electric field, E, and charge density, n, in the crystal and showed that the process is controlled by n. Here, we demonstrate layer-selective conductor-insulator transitions in twisted bilayer graphene, driven by hydrogenation at fixed n under strong E. This process is accompanied by proton transport through the bilayer, enabling several parallel and configurable logic gates in the devices. Selectivity arises because the large twist angle decouples the two layers' electronic systems, enabling independent control of their charge densities. Polarisation by the field then induces a charge imbalance at fixed total n, triggering hydrogenation when one of the layers' charge densities reaches the threshold for monolayer hydrogenation. Our results introduce a new type of electrode-electrolyte interface in which electrochemical processes are controlled with two decoupled 2D electron gases, opening new design opportunities for energy and information processing devices.

In twisted bilayer graphene (TBG) devices, local strain frequently coexists with the twist-angle-dependent moiré superlattice and strongly influences the electronic properties, yet their combined effects remain incompletely understood. Here, using low-temperature scanning tunneling microscopy, we study a TBG device exhibiting both a continuous twist-angle gradient from 0.35° to 1.30° and spatially varying strain fields, spanning the first (1.1°), second (0.5°), and third (0.3°) magic angles. We directly visualize the evolution of flat and remote bands in both energy and real space with atomic resolution. By comparing regions dominated by shear, uniaxial, and mixed strain, we find that shear strain plays a decisive role in controlling flat-band separation, linewidth, and spectral-weight redistribution. Near the first magic angle, this manifests as an anomalous transfer of spectral weight between the two flat-band peaks, accompanied by an unusual spatial dispersion of flat-band states within a moiré unit cell. In contrast, the energy of the remote bands provides a robust, strain-insensitive indicator of the local twist angle. Structural analysis reveals that shear strain dominates over large regions of the sample, consistent with its lower elastic energy cost. All observations are quantitatively reproduced by a continuum model incorporating heterostrain and electron-electron interactions, establishing shear strain as a central ingredient in shaping the low-energy electronic landscape of TBG.

Theoretical modeling and performance prediction of magic-angle twisted bilayer graphene Sodium-Ion batteries: a multi-scale computational framework

Moiré superstructures in stacked two-dimensional (2D) materials offer a promising means for tailoring tribological properties, yet the experimental dependence of friction on continuously varying moiré patterns remains unexplored. Here, we systematically investigate the frictional response of twisted bilayer graphene (TBG) across twist angles from 0.3° to 10.8°. Both lateral force modulation amplitude and frictional dissipation exhibit nonmonotonic variations. For lateral force amplitude, it peaks at ∼3.0°, validating the prior predictions based on the geometric interplay. In contrast, frictional energy dissipation reaches its extremum at a notably smaller twist angle of ∼1.2°. This distinct nonmonotonic trend is attributed to the competition between the local in-plane stiffness and its atomic reconstruction state, both of which influence the onset of unstable moiré-scale slip. Our results highlight the critical role of local in-plane stiffness of superstructures in governing sliding dynamics and energy dissipation, offering insights into moiré engineering for controlling surface friction.

We consider a lattice model of twisted bilayer graphene (TBG) for incommensurate twist angles, focusing on the role of large-momentum-transfer umklapp terms. These terms, which nearly connect the Fermi points of different layers, are typically neglected in effective continuum descriptions but could, in principle, destroy the Dirac cones; they are indeed closely analogous to those appearing in fermions within quasiperiodic potentials, where they play a crucial role. We prove that, for small but finite interlayer coupling, the semimetallic phase is stable provided the angles belong to a fractal set of large measure (which decreases with the hopping strength) characterized by a number-theoretic Diophantine condition. In particular, this set excludes the (zero measure) commensurate angles. Our method combines a renormalization group (RG) analysis of the imaginary-time, zero-temperature Green's functions, with number theoretic properties, and it is similar to the technique used in the Lindstedt series approach to Kolmogorov-Arnold-Moser (KAM) theory. The convergence of the resulting series allows us to rule out nonperturbative effects. The result provides a partial justification of the effective continuum description of TBG in which such large-momentum interlayer hopping processes are neglected.

Moiré materials have emerged as a rich platform for exploring strong correlation effects in low dimensions, with twisted bilayer graphene (TBG) as a paradigmatic example. To distill the essential ingredients driving moiré-induced phases, a simplified one-dimensional analog -- a two-leg ladder with spatially modulated interleg hopping and a uniform magnetic flux -- was recently introduced. This model, which we refer to as the moiré ladder, features a nearly flat lowest-energy band in a suitable parameter regime, capturing the band-flattening mechanism of TBG. We investigate the ground-state phase diagram of the moiré ladder using a combination of bosonization and density matrix renormalization group (DMRG) techniques, and systematically disentangle the respective roles of the flux and the hopping modulation. At half filling, previous numerical work identified a metal-insulator transition at finite interaction strength and an unexpected ferromagnetic ground state. Revisiting this, we show that the metal-insulator transition can be understood perturbatively within bosonization, governed by the number of Fermi points. In contrast, the ferromagnetic correlations are nonperturbative and require both flux and spatial modulation -- neither alone is sufficient. We extend our analysis to other fillings: one-quarter, three-quarters, slightly above half filling (half filling plus two electrons), and slightly below half filling (half filling minus two electrons). At moderate interactions, we observe ferromagnetism below half filling and antiferromagnetism above; at stronger interactions, ferromagnetism dominates across all studied fillings. Crucially, the analysis demonstrates that periodic interleg hopping alone does not engender new correlated phases; the magnetic flux is essential for the observed unconventional behavior.

Skyrmionic transport and first-order phase transitions in a twisted bilayer graphene quantum hall ferromagnet

bonded carbon structures exhibit a rich variety of morphologies depending on how the graphene as basic unit is laterally constrained and topologically connected to itself. Here, we demonstrate that the connection that forms between two adjacent layers of graphene after cutting by focused electron beam can be exploited in a controlled fashion to induce a spontaneous reconstruction from the flat to a tubular or even more complex geometry. In particular, we demonstrate the cutting of twisted bilayer graphene to create chiral carbon nanotubes (CNTs), using a scanning transmission electron microscope operated at 200 kV and with line doses of electrons per nanometer. By choosing the cutting angle halfway between the two graphene orientations, a seamless tube could be formed in principle, and relatively straight tube sectionsare obtained in practice. Bilayer graphene ribbons with a width of less than approximately 4 nm spontaneously convert to CNTs, while no nanotubes are formed from wider ribbons. Moreover, CNT arrays and CNT junctions are prepared in a controlled way. The transformations from a nanoribbon to a nanotube are also reproduced via analytical potential molecular dynamics simulations. Devices made from such junctions could be useful for nanoelectronics, quantum transport, interconnects ornanofluidics.

Twist-angle engineering in van der Waals homo- and hetero-bilayers introduces profound modifications in their electronic, optical, and mechanical properties due to lattice reconstruction. In these systems, the interlayer coupling and atomic rearrangement strongly depend on the twist angle, leading to the formation of periodic moiré superlattices. At small twist angles, significant lattice relaxation results in the emergence of domain structures separated by one-dimensional (1D) soliton networks, influencing electronic band structures and phonon modes. In this study, we systematically investigate the impact of lattice reconstruction on phonon renormalization in twisted bilayer graphene (TBLG) and graphene-hBN moiré superlattices, representing homo- and hetero-bilayer system, respectively. Using Raman spectroscopy, we identify distinct phonon behaviors across different twist angle regimes. In TBLG, we observe the evolution of the G peak, including broadening, splitting, and the emergence of additional peaks in the small angle range (0.3°−1°), attributed to moiré-modified phonon interactions. At large twist angles, the peaks gradually merge back into a single feature, reflecting the reduced impact of lattice reconstruction. Similarly, in hBN–graphene moiré superlattices, we detect moiré-induced Raman peaks above and below the G peak, while the central G peak remains largely invariant to twist angle variation. The theoretical calculations based on classical force-field uncover moiré phonon modes originating from different stacking regions, including AB (AB′), AA, and SP configurations, providing insights into phonon renormalization driven by lattice reconstruction. Our results establish a direct link between twist angle, lattice reconstruction, moiré phonons, and interlayer coupling, offering a fundamental framework for understanding phonon engineering in twisted bilayer systems. These findings pave the way for controlling phononic, optoelectronic, and heat flow properties in next generation van der Waals heterostructures.