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Abstract This study discusses the effect of long‐range interactions within the self‐consistent Hartree‐Fock (HF) approximation in comparison to short‐range atomic Hubbard interactions on the band structure of twisted bilayer graphene (TBG) at charge neutrality for various twist angles. Starting from atomistic calculations, it determines the quasi‐particle band structure of TBG with Hubbard interactions for three magnetic orderings: modulated anti‐ferromagnetic (MAFM), (NAFM) and hexagonal anti‐ferromagnetic (HAFM). Then, it develops an approach to incorporate these magnetic orderings along with the HF potential in the continuum approximation. Away from the magic angle, it observes a drastic effect of the magnetic order on the band structure of TBG compared to the influence of the HF potential. Near the magic angle, the HF potential plays a major role in the band structure, with HAFM and MAFM being secondary effects, but NAFM appears to still significantly distort the electronic structure at the magic angle. These findings suggest that the spin‐valley degenerate broken symmetry state often found in HF calculations of charge neutral TBG near the magic angle should favor magnetic order, since the atomistic Hubbard interaction will break this symmetry in favor of spin polarization.

The full optical response of twisted bilayer graphene at the neutrality point close to the magic angle within the continuum model (CM) is discussed. First, three different channels consistent with the underlying D 3 symmetry are identified, yielding the total, magnetic, and chiral response. Second, the full optical response in the immediate vicinity of the magic angle θ m is numerically calculated, which provides a direct mapping of the CM onto an effective two‐band model. It is, further, shown that the ground state of the CM in the immediate vicinity of θ m is unstable toward transverse current fluctuations, a so‐called Condon instability. Third, due to the large counterflow, the acoustic plasmonic excitations with typical wave numbers have larger energies than the optical ones and their energy density may be largely enhanced at certain frequencies which are denominated as chiral resonances. Finally, symmetry relations for the optical response and their consequences for the chiral response are discussed.

Abstract Twisted bilayer graphene (tBLG) possesses various novel physical properties. Most of tBLG are fabricated by using artificial methods of stacking or folding single‐layer graphene. Chemical vapor deposition (CVD) has been verified that it holds great potential for preparation of large‐size high‐quality graphene. Therefore, it is significant for preparing tBLG in situ by using CVD technology. In this work, a novel approach is developed to directly prepare tBLGs on liquid Cu substrate. When the growth temperature exceeds a certain critical value, the state of aligned high‐quality single‐layer graphene domains grown on liquid Cu will be broken. Then, tBLG with twisted double‐layer regions is prepared in situ by rotating and intercalating between graphene domains. Experimental observations suggest that the liquid phase of Cu substrate and gas flow play a crucial role for the formation of tBLGs. These results demonstrate that the liquid Cu is an ideal potential substrate for preparing tBLGs with a full range of twisted angles and studying the formation mechanism of layer‐stacked materials.

To pinpoint the electronic and structural mechanisms that affect intrinsic and extrinsic performance limits of 2D material devices, it is of critical importance to resolve the electronic properties on the mesoscopic length scale of such devices under operating conditions. Herein, angle‐resolved photoemission spectroscopy with nanoscale spatial resolution (nanoARPES) is used to map the quasiparticle electronic structure of a twisted bilayer graphene device. The dispersion and linewidth of the Dirac cones associated with top and bottom graphene layers are determined as a function of spatial position on the device under both static and operating conditions. The analysis reveals that microscopic rotational domains in the two graphene layers establish a range of twist angles from 9.8° to 12.7°. Application of current and electrostatic gating lead to strong electric fields with peak strengths of 0.75 V/μm at the rotational domain boundaries in the device. These proof‐of‐principle results demonstrate the potential of nanoARPES to link mesoscale structural variations with electronic states in operating device conditions and to disentangle such extrinsic factors from the intrinsic quasiparticle dispersion.

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"., (© 2024 The Authors. Small published by Wiley‐VCH GmbH.)

Twisted bilayer graphene (TBG) generates significant attention in the fundamental research of 2D materials due to its distinct twist-angle-dependent properties. Exploring the efficient production of TBG with a wide range of twist angles stands as one of the major frontiers in moiré materials. Here, the local space-confined chemical vapor deposition growth technique for high-quality single-crystal TBG with twist angles ranging from 0° to 30° on liquid copper substrates is reported. The clean surface, pristine interface, high crystallinity, and thermal stability of TBG are verified by using comprehensive characterization techniques including optical microscopy, electron microscopy, and secondary-ion mass spectrometry. The proportion of TBG in bilayer graphene reaches as high as 89%. In addition, the stacking structure and growth mechanism of TBG are investigated, revealing that the second graphene layer develops beneath the first one. A series of comparative experiments illustrates that the liquid copper surface, with its excellent fluidity, promotes the growth of TBG. Electrical measurements show the twist-angle-dependent electronic properties of as-grown TBG, achieving a room-temperature carrier mobility of 26640 cm 2 V -1 s -1 . This work provides an approach for the in situ preparation of 2D twisted materials and facilitates the application of TBG in the fields of electronics., (© 2023 Wiley-VCH GmbH.)

Atomic-scale engineering typically involves bottom-up approaches, leveraging parameters such as temperature, partial pressures, and chemical affinity to promote spontaneous arrangement of atoms. These parameters are applied globally, resulting in atomic-scale features scattered probabilistically throughout the material. In a top-down approach, different regions of the material are exposed to different parameters, resulting in structural changes varying on the scale of the resolution. In this work, the application of global and local parameters is combined in an aberration-corrected scanning transmission electron microscope (STEM) to demonstrate atomic-scale precision patterning of atoms in twisted bilayer graphene. The focused electron beam is used to define attachment points for foreign atoms through the controlled ejection of carbon atoms from the graphene lattice. The sample environment is staged with nearby source materials such that the sample temperature can induce migration of the source atoms across the sample surface. Under these conditions, the electron-beam (top-down) enables carbon atoms in the graphene to be replaced spontaneously by diffusing adatoms (bottom-up). Using image-based feedback control, arbitrary patterns of atoms and atom clusters are attached to the twisted bilayer graphene with limited human interaction. The role of substrate temperature on adatom and vacancy diffusion is explored by first-principles simulations., (© 2023 Wiley-VCH GmbH.)

Twisted bilayer graphene (tBLG) exhibits a host of innovative physical phenomena owing to the formation of moiré superlattice. Especially, the discovery of superconducting behavior has generated new interest in graphene. The growing studies of tBLG mainly focus on its physical properties, while the fabrication of high-quality tBLG is a prerequisite for achieving the desired properties due to the great dependence on the twist angle and the interfacial contact. Here, the cutting-edge preparation strategies and challenges of tBLG fabrication are reviewed. The advantages and disadvantages of chemical vapor deposition, epitaxial growth on silicon carbide, stacking monolayer graphene, and folding monolayer graphene methods for the fabrication of tBLG are analyzed in detail, providing a reference for further development of preparation methods. Moreover, the characterization methods of twist angle for the tBLG are presented. Then, the unique physicochemical properties and corresponding applications of tBLG, containing correlated insulating and superconducting states, ferromagnetic state, soliton, enhanced optical absorption, tunable bandgap, and lithium intercalation and diffusion, are described. Finally, the opportunities and challenges for fabricating high-quality and large-area tBLG are discussed, unique physical properties are displayed, and new applications inferred from its angle-dependent features are explored, thereby impelling the commercialization of tBLG from laboratory to market., (© 2021 Wiley-VCH GmbH.)

The possibility of triggering correlated phenomena by placing a singularity of the density of states near the Fermi energy remains an intriguing avenue toward engineering the properties of quantum materials. Twisted bilayer graphene is a key material in this regard because the superlattice produced by the rotated graphene layers introduces a van Hove singularity and flat bands near the Fermi energy that cause the emergence of numerous correlated phases, including superconductivity. Direct demonstration of electrostatic control of the superlattice bands over a wide energy range has, so far, been critically missing. This work examines the effect of electrical doping on the electronic band structure of twisted bilayer graphene using a back-gated device architecture for angle-resolved photoemission measurements with a nano-focused light spot. A twist angle of 12.2° is selected such that the superlattice Brillouin zone is sufficiently large to enable identification of van Hove singularities and flat band segments in momentum space. The doping dependence of these features is extracted over an energy range of 0.4 eV, expanding the combinations of twist angle and doping where they can be placed at the Fermi energy and thereby induce new correlated electronic phases in twisted bilayer graphene., (© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Graphene has demonstrated great potential in new-generation electronic applications due to its unique electronic properties such as large carrier Fermi velocity, ultrahigh carrier mobility, and high material stability. Interestingly, the electronic structures can be further engineered in multilayer graphene by the introduction of a twist angle between different layers to create van Hove singularities (vHSs) at adjustable binding energy. In this work, using angle-resolved photoemission spectroscopy with sub-micrometer spatial resolution, the band structures and their evolution are systematically studied with twist angle in bilayer and trilayer graphene sheets. A doping effect is directly observed in graphene multilayer system as well as vHSs in bilayer graphene over a wide range of twist angles (from 5° to 31°) with wide tunable energy range over 2 eV. In addition, the formation of multiple vHSs (at different binding energies) is also observed in trilayer graphene. The large tuning range of vHS binding energy in twisted multilayer graphene provides a promising material base for optoelectrical applications with broadband wavelength selectivity from the infrared to the ultraviolet regime, as demonstrated by an example application of wavelength selective photodetector., (© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)