Electron Collimation in Twisted Bilayer Graphene via Gate-Defined Moiré Barriers

Electron collimation via a graphene p-n junction allows electrostatic control of ballistic electron trajectories akin to that of an optical circuit. Similar manipulation of novel correlated electronic phases in twisted-bilayer graphene (tBLG) can provide additional probes to the underlying physics and device components toward advanced quantum electronics. In this work, we demonstrate collimation of the electron flow via gate-defined moiré barriers in a tBLG device, utilizing the band-insulator gap of the moiré superlattice. A single junction can be tuned to host a chosen combination of conventional pseudo barrier and moiré tunnel barriers, from which we demonstrate improved collimation efficiency. By measuring transport through two consecutive moiré collimators separated by 1 μm, we demonstrate evidence of electron collimation in tBLG in the presence of realistic twist-angle inhomogeneity.

Chemically Reversible Translational Moiré Superlattice Formations in the Two-Dimensional Films of the Zinc Phthalate Complex

The exciting electronic properties of two-dimensional layered materials introduced by twist angle and lattice mismatch between two consecutive layers are well-recognized. The major challenge lies in the control over the moiré periodicity. Herein, we report a chemically directed way to achieve the desired precision over moiré periodicity of the assembly of a complex of zinc ions and o-phthalic acid utilizing soft bonds. The reaction of o-phthalic acid with zinc ions in the aqueous medium at 80 °C for 1 h followed by preserving the reaction mixture at ambient temperature (35 °C) resulted in translational moiré superlattices with precise periods. Those lattices are further stacked angularly to give rotational super-moiré lattices. Further, the role of the π-zinc ion interaction in the origin of moiré fringes was examined with the reaction with 8-hydroxyquinoline-5-sulfonic acid (HQS) that also established the reversible nature of the superlattices. The present observations also suggest the formation of moiré superlattice through ion insertion in a chemical lattice.

Deterministic fabrication of graphene hexagonal boron nitride moiré superlattices

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

Unraveling the origin of Kondo-like behavior in the 3d-electron heavy-fermion compound YFe2Ge2

The heavy fermion (HF) state of [Formula: see text]-electron systems is of great current interest since it exhibits various exotic phases and phenomena that are reminiscent of the Kondo effect in [Formula: see text]-electron HF systems. Here, we present a combined infrared spectroscopy and first-principles band structure calculation study of the [Formula: see text]-electron HF compound YFe[Formula: see text]Ge[Formula: see text]. The infrared response exhibits several charge-dynamical hallmarks of HF and a corresponding scaling behavior that resemble those of the [Formula: see text]-electron HF systems. In particular, the low-temperature spectra reveal a dramatic narrowing of the Drude response along with the appearance of a hybridization gap ([Formula: see text] 50 meV) and a strongly enhanced quasiparticle effective mass. Moreover, the temperature dependence of the infrared response indicates a crossover around [Formula: see text] 100 K from a coherent state at low temperature to a quasi-incoherent one at high temperature. Despite of these striking similarities, our band structure calculations suggest that the mechanism underlying the HF behavior in YFe[Formula: see text]Ge[Formula: see text] is distinct from the Kondo scenario of the [Formula: see text]-electron HF compounds and even from that of the [Formula: see text]-electron iron-arsenide superconductor KFe[Formula: see text]As[Formula: see text]. For the latter, the HF state is driven by orbital-selective correlations due to a strong Hund's coupling. Instead, for YFe[Formula: see text]Ge[Formula: see text] the HF behavior originates from the band flatness near the Fermi level induced by the combined effects of kinetic frustration from a destructive interference between the direct Fe-Fe and indirect Fe-Ge-Fe hoppings, band hybridization involving Fe [Formula: see text] and Y [Formula: see text] electrons, and electron correlations. This highlights that rather different mechanisms can be at the heart of the HF state in [Formula: see text]-electron systems.

Twist-Controlled Ferroelectricity and Emergent Multiferroicity in WSe2 Bilayers

Recently, researchers have been investigating artificial ferroelectricity, which arises when inversion symmetry is broken in certain R-stacked, i.e., zero-degree twisted, van der Waals (vdW) bilayers. Here, the study reports the twist-controlled ferroelectricity in tungsten diselenide (WSe2) bilayers. The findings show noticeable room temperature ferroelectricity that decreases with twist angle within the range 0° < θ < 3°, and disappears completely for θ ≥ 4°. This variation aligns with moiré length scale-controlled ferroelectric dynamics (0° < θ < 3°), while loss beyond 4° may relate to twist-controlled commensurate to non-commensurate transitions. This twist-controlled ferroelectricity serves as a spectroscopic tool for detecting transitions between commensurate and incommensurate moiré patterns. At 5.5 K, 3° twisted WSe2 exhibits ferroelectric and correlation-driven ferromagnetic ordering, indicating twist-controlled multiferroic behavior. The study offers insights into twist-controlled coexisting ferro-ordering and serves as valuable spectroscopic tools.

Nanoscale Optical Conductivity Imaging of Double-Moiré Twisted Bilayer Graphene

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

Van Hove Singularity-Enhanced Raman Scattering and Photocurrent Generation in Twisted Monolayer-Bilayer Graphene

Twisted monolayer-bilayer graphene (TMBG) has recently emerged as an exciting platform for exploring correlated physics and topological states with rich tunability. Strong light-matter interaction was realized in twisted bilayer graphene, boosting the development of broadband graphene photodetectors from the visible to infrared spectrum with high responsivity. Extending this approach to the case of TMBG will help design advanced quantum nano-optoelectronic devices because of the reduced symmetry of the system. Here, we observe the formation of van Hove singularities (VHSs) in TMBG by monitoring the significant enhancement of the Raman intensity of the G peak and the intensity ratio of G and 2D peaks. The strong interlayer coupling also leads to the appearance of twist-angle-dependent Raman R and R' peaks in TMBG. Furthermore, the constructed graphene photodetectors from 13.5°-TMBG show significantly enhanced photoresponsivity (∼31 folds of monolayer graphene and ∼15 folds of trilayer graphene) when the energy of incident photons matches the interval energy between the two VHSs in the conduction and valence bands. Our findings establish TMBG as a tunable platform for investigating the light-matter interaction and designing high-performance graphene photodetectors with combined high responsivity and high selectivity.

Cryogenic nano-imaging of second-order moiré superlattices

Second-order superlattices form when moiré superlattices with similar periodicities interfere with each other, leading to larger superlattice periodicities. These crystalline structures are engineered using two-dimensional materials such as graphene and hexagonal boron nitride, and the specific alignment plays a crucial role in facilitating correlation-driven topological phases. Signatures of second-order superlattices have been identified in magnetotransport experiments; however, real-space visualization is still lacking. Here we reveal the second-order superlattice in magic-angle twisted bilayer graphene closely aligned with hexagonal boron nitride through electronic transport measurements and cryogenic nanoscale photovoltage measurements and evidenced by long-range periodic photovoltage modulations. Our results show that even minuscule strain and twist-angle variations as small as 0.01° can lead to drastic changes in the second-order superlattice structure. Our real-space observations, therefore, serve as a 'magnifying glass' for strain and twist angle and can elucidate the mechanisms responsible for the breaking of spatial symmetries in twisted bilayer graphene.

Heterostrain-Induced Zeeman-like Splitting in h-BN-Encapsulated Bilayer WSe2

Heterostrain is predicted to induce exceptionally rich physics in atomically thin two-dimensional structures by modifying the symmetry and optical selection rules. In this work, we introduce heterostrain into WSe2 bilayers by combining h-BN encapsulation and high-temperature vacuum annealing. Nonvolatile heterostrain gives rise to a Zeeman-like splitting associated with the elliptically polarized optical emission of interlayer K-K excitons. Further manipulation of the interlayer exciton emission in an external magnetic field reveals that the Zeeman-like splitting cannot be eliminated even in a magnetic field of up to ±6 T. We propose a microscopic picture with respect to the layer and valley pseudospin to interpret the results. Our findings imply an intriguing way to encode binary information with the layer pseudospin enabled by the heterostrain and open a venue for manipulating the layer pseudospin with heterostrain engineering, optical pseudospin injection, and an external magnetic field.

Electronic and Transport Engineering of A-Type Antiferromagnets with Ferroelectric Sandwich Structure: Toward Multistate Nonvolatile Memory Applications

Achieving higher-order multistates with mutual interstate switching at the nanoscale is essential for high-density storage devices; yet, it remains a significant challenge. Here, we demonstrate that integrating A-type antiferromagnetic semiconductors sandwiched between ferroelectric layers is an effective strategy to achieve high-performance multistate data storage. Taking the Sc2CO2/VSi2P4 bilayer (bi-VSi2P4)/Sc2CO2 van der Waals multiferroic heterostructure as an example, our first-principles calculations show that by switching the polarization direction of the upper and bottom ferroelectric Sc2CO2 layers, antiferromagnetic bi-VSi2P4 can exhibit four distinct states with different band structures. The intriguing band structure engineering stems from the polarization-field-induced band shift and interface charge transfer. Accordingly, the proposed Sc2CO2/bi-VSi2P4/Sc2CO2-based multiferroic device can achieve four different resistance states, accompanied by fully spin-polarized currents and giant tunneling electroresistance ratios. Our results propose a viable strategy for realizing nonvolatile electrical control of antiferromagnets at the nanoscale and provide insights into the development of advanced memories.

Constructing Slip Stacking Diversity in Van der Waals Homobilayers

The van der Waals (vdW) interface provides two important degrees of freedom-twist and slip-to tune interlayer structures and inspire unique physics. However, constructing diversified high-quality slip stackings (i.e., lattice orientations between layers are parallel with only interlayer sliding) is more challenging than twisted stackings due to angstrom-scale structural discrepancies between different slip stackings, sparsity of thermodynamically stable candidates and insufficient mechanism understanding. Here, using transition metal dichalcogenide (TMD) homobilayers as a model system, this work theoretically elucidates that vdW materials with low lattice symmetry and weak interlayer coupling allow the creation of multifarious thermodynamically advantageous slip stackings, and experimentally achieves 13 and 9 slip stackings in 1T″-ReS2 and 1T″-ReSe2 bilayers via direct growth, which are systematically revealed by atomic-resolution scanning transmission electron microscopy (STEM), angle-resolved polarization Raman spectroscopy, and second harmonic generation (SHG) measurements. This work also develops modulation strategies to switch the stacking via grain boundaries (GBs) and to expand the slip stacking library from thermodynamic to kinetically favored structures via in situ thermal treatment. Finally, density functional theory (DFT) calculations suggest a prominent dependence of the pressure-induced electronic band structure transition on stacking configurations. These studies unveil a unique vdW epitaxy and offer a viable means for manipulating interlayer atomic registries.

Engineered moiré photonic and phononic superlattices

Recent discoveries of Mott insulating and unconventional superconducting states in twisted bilayer graphene with moiré superlattices have not only reshaped the landscape of 'twistronics' but also sparked the rapidly growing fields of moiré photonic and phononic structures. These innovative moiré structures have opened new routes of exploration for classical wave physics, leading to intriguing phenomena and robust control of electromagnetic and mechanical waves. Drawing inspiration from the success of twisted bilayer graphene, this Perspective describes an overarching framework of the emerging moiré photonic and phononic structures that promise novel classical wave devices. We begin with the fundamentals of moiré superlattices, before highlighting recent studies that exploit twist angle and interlayer coupling as new ingredients with which to engineer and tailor the band structures and effective material properties of photonic and phononic structures. Finally, we discuss the future directions and prospects of this emerging area in materials science and wave physics.

Evidence of abnormal hot carrier thermalization at van Hove singularity of twisted bilayer graphene

Interlayer twist evokes revolutionary changes to the optical and electronic properties of twisted bilayer graphene (TBG) for electronics, photonics and optoelectronics. Although the ground state responses in TBG have been vastly and clearly studied, the dynamic process of its photoexcited carrier states mainly remains elusive. Here, we unveil the photoexcited hot carrier dynamics in TBG by time-resolved ultrafast photoluminescence (PL) autocorrelation spectroscopy. We demonstrate the unconventional ultrafast PL emission between the van Hove singularities (VHSs) with a ∼4 times prolonged relaxation lifetime. This intriguing photoexcited carrier behavior is ascribed to the abnormal hot carrier thermalization brought by bottleneck effects at VHSs and interlayer charge distribution process. Our study on hot carrier dynamics in TBG offers new insights into the excited states and correlated physics of graphene twistronics systems.

Theory of topological exciton insulators and condensates in flat Chern bands

Excitons are the neutral quasiparticles that form when Coulomb interactions create bound states between electrons and holes. Due to their bosonic nature, excitons are expected to condense and exhibit superfluidity at sufficiently low temperatures. In interacting Chern insulators, excitons may inherit the nontrivial topology and quantum geometry from the underlying electron wavefunctions. We theoretically investigate the excitonic bound states and superfluidity in flat-band insulators pumped with light. We find that the exciton wavefunctions exhibit vortex structures in momentum space, with the total vorticity being equal to the difference of Chern numbers between the conduction and valence bands. Moreover, both the exciton binding energy and the exciton superfluid density are proportional to the Brillouin-zone average of the quantum metric and the Coulomb potential energy per unit cell. Spontaneous emission of circularly polarized light from radiative decay is a detectable signature of the exciton vorticity. We propose that the vorticity can also be experimentally measured via the nonlinear anomalous Hall effect, whereas the exciton superfluidity can be detected by voltage-drop quantization through a combination of quantum geometry and Aharonov-Casher effect. Topological excitons and their superfluid phase could be realized in flat bands of twisted Van der Waals heterostructures.

Helicity-Resolved Vibrational Coupling in Twist WS2/WSe2 Heterostructures

Helicity-resolved Raman spectra can provide an intricate view into lattice structural details. Through the analysis of peak positions, intensities, and circular polarized Raman signals, a wealth of information about chiral structure arrangement within the moiré superlattice, interlayer interaction strength, polarizability change in chemical bond, and beyond can be unveiled. However, the relationship between the circular polarization of high-frequency Raman and twist angle is still not clear. Here, we utilize helicity-resolved Raman spectroscopy to explore the interlayer interactions and the effect of the moiré superlattice in WS2/WSe2 heterostructures. For the out-of-plane Raman mode A1g of WS2 (A1g and 1E2g of WSe2), its intensity is significantly enhanced (suppressed) in WS2/WSe2 heterostructures when θ is less than 10° or greater than 50°. This observation could be attributed to the large polarizability changes in both W-S and W-Se covalent bonds. The circular polarization of 2LA(M) in WSe2 of the WS2/WSe2 heterostructure (θ < 10° or θ > 50°) is significantly enhanced compared to that of 2LA(M) in the monolayer WSe2. We deduce that the circular polarization of the Raman mode correlates with the proportion of high-symmetry area within a supercell of the moiré lattice. Our findings improve the understanding of twist-angle-modulated Raman modes in TMD heterostructures.

Giant Second Harmonic Generation in Supertwisted WS2 Spirals Grown in Step-Edge Particle-Induced Non-Euclidean Surfaces

In moiré crystals resulting from the stacking of twisted two-dimensional (2D) layered materials, a subtle adjustment in the twist angle surprisingly gives rise to a wide range of correlated optical and electrical properties. Herein, we report the synthesis of supertwisted WS2 spirals and the observation of giant second harmonic generation (SHG) in these spirals. Supertwisted WS2 spirals featuring different twist angles are synthesized on a Euclidean or step-edge particle-induced non-Euclidean surface using carefully designed water-assisted chemical vapor deposition. We observed an oscillatory dependence of SHG intensity on layer number, attributed to atomically phase-matched nonlinear dipoles within layers of supertwisted spiral crystals where inversion symmetry is restored. Through an investigation into the twist angle evolution of SHG intensity, we discovered that the stacking model between layers plays a crucial role in determining the nonlinearity, and the SHG signals in supertwisted spirals exhibit enhancements by a factor of 2 to 136 when compared with the SHG of the single-layer structure. These findings provide helpful perspectives on the rational growth of 2D twisted structures and the implementation of twist angle adjustable endowing them great potential for exploring strong coupling correlation physics and applications in the field of twistronics.

Floquet engineering of the orbital Hall effect and valleytronics in two-dimensional topological magnets

We show that circularly polarized light is a versatile way to manipulate both the orbital Hall effect and band topology in two-dimensional ferromagnets. Employing the hexagonal lattice, we proposed that interactions between light and matter allow for the modulation of the valley polarization effect, and then band inversions, accompanied by the band gap closing and reopening processes, can be achieved subsequently at two valleys. Remarkably, the distribution of orbital angular momentum can be controlled by the band inversions, leading to the Floquet engineering of the orbital Hall effect, as well as the topological phase transition from a second-order topological insulator to a Chern insulator with in-plane magnetization, and then to a normal insulator. Furthermore, first-principles calculations validate the feasibility with the 2H-ScI2 monolayer as a candidate material, paving a technological avenue to bridge the orbitronics and nontrivial topology using Floquet engineering.

Quantum Anomalous Hall Crystal at Fractional Filling of Moiré Superlattices

We predict the emergence of a state of matter with intertwined ferromagnetism, charge order, and topology in fractionally filled moiré superlattice bands. Remarkably, these quantum anomalous Hall crystals exhibit a quantized integer Hall conductance that is different than expected from the filling and Chern number of the band. Microscopic calculations show that this phase is robustly favored at half-filling (ν=1/2) at larger twist angles of the twisted semiconductor bilayer tMoTe_{2}.

Interaction-Driven Quasi-Insulating Ground States of Gapped Electron-Doped Bilayer Graphene

Bernal bilayer graphene has recently been discovered to exhibit a wide range of unique ordered phases resulting from interaction-driven effects and encompassing spin and valley magnetism, correlated insulators, correlated metals, and superconductivity. This Letter reports on a novel family of correlated phases characterized by spin and valley ordering, distinct from those reported previously. These phases emerge in electron-doped bilayer graphene where the energy bands are exceptionally flat, manifested through an intriguing nonlinear current-bias behavior that occurs at the onset of the phases and is accompanied by an insulating temperature dependence. These characteristics align with the presence of charge- or spin-density-wave states that open a gap on a portion of the Fermi surface or fully gapped Wigner crystals, resulting in an exceptionally intricate phase diagram.

Emergent phases in graphene flat bands

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

Nonlinear Electrical Transport Unveils Fermi Surface Malleability in a Moiré Heterostructure

Van Hove singularities enhance many-body interactions and induce collective states of matter ranging from superconductivity to magnetism. In magic-angle twisted bilayer graphene, van Hove singularities appear at low energies and are malleable with density, leading to a sequence of Lifshitz transitions and resets observable in Hall measurements. However, without a magnetic field, linear transport measurements have limited sensitivity to the band's topology. Here, we utilize nonlinear longitudinal and transverse transport measurements to probe these unique features in twisted bilayer graphene at zero magnetic field. We demonstrate that the nonlinear responses, induced by the Berry curvature dipole and extrinsic scattering processes, intricately map the Fermi surface reconstructions at various fillings. Importantly, our experiments highlight the intrinsic connection of these features with the moiré bands. Beyond corroborating the insights from linear Hall measurements, our findings establish nonlinear transport as a pivotal tool for probing band topology and correlated phenomena.

Realizing Topological Superconductivity in Tunable Bose-Fermi Mixtures with Transition Metal Dichalcogenide Heterostructures

Heterostructures of two-dimensional transition metal dichalcogenides are emerging as a promising platform for investigating exotic correlated states of matter. Here, we propose to engineer Bose-Fermi mixtures in these systems by coupling interlayer excitons to doped charges in a trilayer structure. Their interactions are determined by the interlayer trion, whose spin-selective nature allows excitons to mediate an attractive interaction between charge carriers of only one spin species. Remarkably, we find that this causes the system to become unstable to topological p+ip superconductivity at low temperatures. We then demonstrate a general mechanism to develop and control this unconventional state by tuning the trion binding energy using a solid-state Feshbach resonance.

Anomalous h/2e Periodicity and Majorana Zero Modes in Chiral Josephson Junctions

Recent experiments reported that quantum Hall chiral edge state-mediated Josephson junctions (chiral Josephson junctions) could exhibit Fraunhofer oscillations with a periodicity of either h/e [Vignaud et al., Nature (London) 624, 545 (2023)NATUAS0028-083610.1038/s41586-023-06764-4] or h/2e [Amet et al., Science 352, 966 (2016)SCIEAS0036-807510.1126/science.aad6203]. While the h/e-periodic component of the supercurrent had been anticipated theoretically before, the emergence of the h/2e periodicity is still not fully understood. In this Letter, we systematically study the Fraunhofer oscillations of chiral Josephson junctions. In chiral Josephson junctions, the chiral edge states coupled to the superconductors become chiral Andreev edge states. We find that in short junctions, the coupling of the chiral Andreev edge states can trigger the h/2e-magnetic flux periodicity. Our theory resolves the important puzzle concerning the appearance of the h/2e periodicity in chiral Josephson junctions. Furthermore, we explain that when the chiral Andreev edge states couple, a pair of localized Majorana zero modes appear at the ends of the Josephson junction, which are robust and independent of the phase difference between the two superconductors. As the h/2e periodicity and the Majorana zero modes have the same physical origin in the wide junction limit, the Fraunhofer oscillation period could be useful in identifying the regime with Majorana zero modes.

Interface Design beyond Epitaxy: Oxide Heterostructures Comprising Symmetry-Forbidden Interfaces

Epitaxial growth of thin-film heterostructures is generally considered the most successful procedure to obtain interfaces of excellent structural and electronic quality between 3D materials. However, these interfaces can only join material systems with crystal lattices of matching symmetries and lattice constants. This article presents a novel category of interfaces, the fabrication of which is membrane-based and does not require epitaxial growth. These interfaces therefore overcome the limitations imposed by epitaxy. Leveraging the additional degrees of freedom gained, atomically clean interfaces are demonstrated between threefold symmetric sapphire and fourfold symmetric SrTiO3. Atomic-resolution imaging reveals structurally well-defined interfaces with a novel moiré-type reconstruction.

Spontaneous Supercrystal Formation During a Strain-Engineered Metal-Insulator Transition

Mott metal-insulator transitions possess electronic, magnetic, and structural degrees of freedom promising next-generation energy-efficient electronics. A previously unknown, hierarchically ordered, and anisotropic supercrystal state is reported and its intrinsic formation characterized in-situ during a Mott transition in a Ca2RuO4 thin film. Machine learning-assisted X-ray nanodiffraction together with cryogenic electron microscopy reveal multi-scale periodic domain formation at and below the film transition temperature (TFilm ≈ 200-250 K) and a separate anisotropic spatial structure at and above TFilm. Local resistivity measurements imply an intrinsic coupling of the supercrystal orientation to the material's anisotropic conductivity. These findings add a new degree of complexity to the physical understanding of Mott transitions, opening opportunities for designing materials with tunable electronic properties.

Spin Gapless Quantum Materials and Devices

Quantum materials, with nontrivial quantum phenomena and mechanisms, promise efficient quantum technologies with enhanced functionalities. Quantum technology is held back because a gap between fundamental science and its implementation is not fully understood yet. In order to capitalize the quantum advantage, a new perspective is required to figure out and close this gap. In this review, spin gapless quantum materials, featured by fully spin-polarized bands and the electron/hole transport, are discussed from the perspective of fundamental understanding and device applications. Spin gapless quantum materials can be simulated by minimal two-band models and could help to understand band structure engineering in various topological quantum materials discovered so far. It is explicitly highlighted that various types of spin gapless band dispersion are fundamental ingredients to understand quantum anomalous Hall effect. Based on conventional transport in the bulk and topological transport on the boundaries, various spintronic device aspects of spin gapless quantum materials as well as their advantages in different models for topological field effect transistors are reviewed.

The Rise of Xene Hybrids

Xenes, mono-elemental atomic sheets, exhibit Dirac/Dirac-like quantum behavior. When interfaced with other 2D materials such as boron nitride, transition metal dichalcogenides, and metal carbides/nitrides/carbonitrides, it enables them with unique physicochemical properties, including structural stability, desirable bandgap, efficient charge carrier injection, flexibility/breaking stress, thermal conductivity, chemical reactivity, catalytic efficiency, molecular adsorption, and wettability. For example, BN acts as an anti-oxidative shield, MoS2 injects electrons upon laser excitation, and MXene provides mechanical flexibility. Beyond precise compositional modulations, stacking sequences, and inter-layer coupling controlled by parameters, achieving scalability and reproducibility in hybridization is crucial for implementing these quantum materials in consumer applications. However, realizing the full potential of these hybrid materials faces challenges such as air gaps, uneven interfaces, and the formation of defects and functional groups. Advanced synthesis techniques, a deep understanding of quantum behaviors, precise control over interfacial interactions, and awareness of cross-correlations among these factors are essential. Xene-based hybrids show immense promise for groundbreaking applications in quantum computing, flexible electronics, energy storage, and catalysis. In this timely perspective, recent discoveries of novel Xenes and their hybrids are highlighted, emphasizing correlations among synthetic parameters, structure, properties, and applications. It is anticipated that these insights will revolutionize diverse industries and technologies.

Ultra-Long Carrier Lifetime of Spiral Perovskite Nanowires Realized through Cooperative Strategy of Selective Etching and Passivation

Spiral inorganic perovskite nanowires (NWs) possess unique morphologies and properties that allow them highly attractive for applications in optoelectronic and catalytic fields. In popular solution-based synthesis methodology, however, challenges persist in simultaneously achieving precise and facile control over morphological twisting and fantastic carrier lifetimes. Here, a cooperative strategy of concurrently employing selective etching and ligand engineering is applied to facilitate the formation of spiral CsPbBr3 perovskite NWs with an ultralong carrier lifetime of ≈2 µs. Specifically, a novel amine of 1-(p-tolyl)ethanamine is introduced to functionalize as both a selective etchant and the source of forming an effective ligand to passivate the exposed facets, favoring the structural twisting and the enhancement of carrier lifetimes. The twisting behaviors are dependent on the etch ratios, which are essentially associated with the densities of grain boundaries and dislocations in the NWs. The ultralong carrier lifetime and long-term stability of the spiral NWs open up new possibilities for all-inorganic perovskites in optoelectronic and photocatalytic fields, while the cooperative synthesis strategy paves the way for exploring complex spiral structures with tunable morphology and functionality.

Enhancing shift current response via virtual multiband transitions

Materials exhibiting a significant shift current response could potentially outperform conventional solar cell materials. The myriad of factors governing shift-current response, however, poses significant challenges in finding such strong shift-current materials. Here we propose a general design principle that exploits inter-orbital mixing to excite virtual multiband transitions in materials with multiple flat bands to achieve an enhanced shift current response. We further relate this design principle to maximizing Wannier function spread as expressed through the formalism of quantum geometry. We demonstrate the viability of our design using a 1D stacked Rice-Mele model. Furthermore, we consider a concrete material realization - alternating angle twisted multilayer graphene (TMG) - a natural platform to experimentally realize such an effect. We identify a set of twist angles at which the shift current response is maximized via virtual transitions for each multilayer graphene and highlight the importance of TMG as a promising material to achieve an enhanced shift current response at terahertz frequencies. Our proposed mechanism also applies to other 2D systems and can serve as a guiding principle for designing multiband systems that exhibit an enhanced shift current response.

Theory of spin and orbital Edelstein effects

In systems with broken spatial inversion symmetry, such as surfaces, interfaces, or bulk systems lacking an inversion center, the application of a charge current can generate finite spin and orbital densities associated with a nonequilibrium magnetization, which is known as spin and orbital Edelstein effect (SEE and OEE), respectively. Early reports on this current-induced magnetization focus on two-dimensional Rashba systems, in which an in-plane nonequilibrium spin density is generated perpendicular to the applied charge current. However, until today, a large variety of materials have been theoretically predicted and experimentally demonstrated to exhibit a sizeable Edelstein effect, which comprises contributions from the spin as well as the orbital degrees of freedom, and whose associated magnetization may be out of plane, nonorthogonal, and even parallel to the applied charge current, depending on the system's particular symmetries. In this review, we give an overview on the most commonly used theoretical approaches for the discussion and prediction of the SEE and OEE. Further, we introduce a selection of the most intensely discussed materials exhibiting a finite Edelstein effect, and give a brief summary of common experimental techniques.

Exploring unconventional ferromagnetism in hole-doped LaCrAsO: insights into charge-transfer and magnetic interactions

Itinerant ferromagnetism due to the canonical double exchange (CDE) mechanism always occurs at low doping concentrations. Here we demonstrate the occurrence of robust itinerant ferromagnetism that can persist high doping concentrations. Using experimentally synthesized LaCrAsO as an illustrative example, we study the effects of hole doping via first-principles calculations and observe that the parent G-type antiferromagnetism vanishes quickly at a low doping concentration (∼0.20) and the system becomes a ferromagnetic metal due to the CDE mechanism. As the doping concentration continues to increase, the As 4p orbitals are gradually pushed up to the Fermi level and doped with holes. These ligand holes participate in the exchange interactions and drive the system toward ferromagnetism. Therefore, itinerant ferromagnetism doesn't terminate at an intermediate doping concentration as the CDE mechanism usually predicts. Furthermore, our results reveal that both the nearest and the next-nearest ferromagnetic exchange coupling strengths keep growing with doping concentration monotonically, showing that the emergent ferromagnetism mediated by As 4p orbitals is "stronger" than that of the CDE picture. Our work unlocks a new mechanism of itinerant ferromagnetism and potentially paves the way towards novel magneto-transport properties.

Large-scale 2D heterostructures from hydrogen-bonded organic frameworks and graphene with distinct Dirac and flat bands

The current strategies for building 2D organic-inorganic heterojunctions involve mostly wet-chemistry processes or exfoliation and transfer, leading to interface contaminations, poor crystallizing, or limited size. Here we show a bottom-up procedure to fabricate 2D large-scale heterostructure with clean interface and highly-crystalline sheets. As a prototypical example, a well-ordered hydrogen-bonded organic framework is self-assembled on the highly-oriented-pyrolytic-graphite substrate. The organic framework adopts a honeycomb lattice with faulted/unfaulted halves in a unit cell, resemble to molecular "graphene". Interestingly, the topmost layer of substrate is self-lifted by organic framework via strong interlayer coupling, to form effectively a floating organic framework/graphene heterostructure. The individual layer of heterostructure inherits its intrinsic property, exhibiting distinct Dirac bands of graphene and narrow bands of organic framework. Our results demonstrate a promising approach to fabricate 2D organic-inorganic heterostructure with large-scale uniformity and highly-crystalline via the self-lifting effect, which is generally applicable to most of van der Waals materials.

Multiferroicity and Topology in Twisted Transition Metal Dichalcogenides

Van der Waals heterostructures have recently emerged as an exciting platform for investigating the effects of strong electronic correlations, including various forms of magnetic or electrical orders. Here, we perform an unbiased exact diagonalization study of the effects of interactions on topological flat bands of twisted transition metal dichalcogenides (TMDs) at odd integer fillings. For hole-filling ν_{h}=1, we find that the Chern insulator phase, expected from interaction-induced spin-valley polarization of the bare bands, is quite fragile, and gives way to spontaneous multiferroic order-coexisting ferroelectricity and ferromagnetism, in the presence of long-range Coulomb repulsion. We provide a simple real-space picture to understand the phase diagram as a function of interaction range and strength. Our findings establish twisted TMDs as a novel and highly tunable platform for multiferroicity, and we outline a potential route towards electrical control of magnetism in the multiferroic phase.

Exchange Energy of the Ferromagnetic Electronic Ground State in a Monolayer Semiconductor

Mobile electrons in the semiconductor monolayer MoS_{2} form a ferromagnetic state at low temperature. The Fermi sea consists of two circles: one at the K point, the other at the K[over ˜] point, both with the same spin. Here, we present an optical experiment on gated MoS_{2} at low electron density in which excitons are injected with known spin and valley quantum numbers. The resulting trions are identified using a model which accounts for the injection process, the formation of antisymmetrized trion states, electron-hole scattering from one valley to the other, and recombination. The results are consistent with a complete spin polarization. From the splittings between different trion states, we measure the exchange energy Σ, the energy required to flip a single spin within the ferromagnetic state, as well as the intervalley Coulomb exchange energy J. We determine Σ=11.2  meV and J=5  meV at n=1.5×10^{12}  cm^{-2} and find that J depends strongly on the electron density n.

Inversion Symmetry-Broken Tetralayer Graphene Probed by Second-Harmonic Generation

Stacking orders provide a unique way to tune the properties of two-dimensional materials. Recently, ABCB-stacked tetralayer graphene has been predicted to possess atypical elemental ferroelectricity arising from its symmetry breaking but has been experimentally explored very little. Here, we observe pronounced nonlinear optical second-harmonic generation (SHG) in ABCB-stacked tetralayer graphene while absent in both ABAB- and ABCA-stacked allotropes. Our results provide direct evidence of symmetry breaking in ABCB-stacked tetralayer graphene. The remarkable contrast in the SHG spectra of tetralayer graphene allows straightforward identification of ABCB domains from the other two kinds of stacking order and facilitates the characterization of their crystalline orientation. The employed SHG technique serves as a convenient tool for exploring the intriguing physics and novel nonlinear optics in ABCB-stacked graphene, where spontaneous polarization and intrinsically gapped flat bands coexist. Our results establish ABCB-stacked graphene as a unique platform for studying the rare ferroelectricity in noncentrosymmetric elemental structures.

Layer-Dependent Electromechanical Response in Twisted Graphene Moiré Superlattices

The coupling of mechanical deformation and electrical stimuli at the nanoscale has been the subject of intense investigation in the realm of materials science. Recently, twisted van der Waals (vdW) materials have emerged as a platform for exploring exotic quantum states. These states are intimately tied to the formation of moiré superlattices, which can be visualized by directly exploiting the electromechanical response. However, the origin of the response, even in twisted bilayer graphene (tBLG), remains unsettled. Here, employing lateral piezoresponse force microscopy (LPFM), we investigate the electromechanical responses of marginally twisted graphene moiré superlattices with different layer thicknesses. We observe distinct LPFM amplitudes and spatial profiles in tBLG and twisted monolayer-bilayer graphene (tMBG), exhibiting effective in-plane piezoelectric coefficients of 0.05 and 0.35 pm/V, respectively. Force tuning experiments further underscored a marked divergence in their responses. The contrasting behaviors suggest different electromechanical couplings in tBLG and tMBG. In tBLG, the response near the domain walls is attributed to the flexoelectric effect, while in tMBG, the behaviors can be comprehended within the context of the piezoelectric effect. Our results not only provide insights into electromechanical and corporative effects in twisted vdW materials with different stacking symmetries but may also offer a way to engineer them at the nanoscale.

Emerging 2D Ferromagnetism in Graphenized GdAlSi

2D magnets are expected to give new insights into the fundamentals of magnetism, host novel quantum phases, and foster development of ultra-compact spintronics. However, the scarcity of 2D magnets often makes a bottleneck in the research efforts, prompting the search for new magnetic systems and synthetic routes. Here, an unconventional approach is adopted to the problem, graphenization - stabilization of layered honeycomb materials in the 2D limit. Tetragonal GdAlSi, stable in the bulk, in ultrathin films gives way to its layered counterpart - graphene-like anionic AlSi layers coupled to Gd cations. A series of inch-scale films of layered GdAlSi on silicon is synthesized, down to a single monolayer, by molecular beam epitaxy. Graphenization induces an easy-plane ferromagnetic order in GdAlSi. The magnetism is controlled by low magnetic fields, revealing its 2D nature. Remarkably, it exhibits a non-monotonic evolution with the number of monolayers. The results provide a fresh platform for research on 2D magnets by design.

Nanoironing van der Waals Heterostructures toward Electrically Controlled Quantum Dots

Assembling two-dimensional van der Waals (vdW)-layered materials into heterostructures is an exciting development that sparked the discovery of rich correlated electronic phenomena. vdW heterostructures also offer possibilities for designer device applications in areas such as optoelectronics, valley- and spintronics, and quantum technology. However, realizing the full potential of these heterostructures requires interfaces with exceptionally low disorder which is challenging to engineer. Here, we show that thermal scanning probes can be used to create pristine interfaces in vdW heterostructures. Our approach is compatible at both the material- and device levels, and monolayer WS2 transistors show up to an order of magnitude improvement in electrical performance from this technique. We also demonstrate vdW heterostructures with low interface disorder enabling the electrical formation and control of quantum dots that can be tuned from macroscopic current flow to the single-electron tunneling regime.

Topological heavy fermions in magnetic field

The recently introduced topological heavy fermion model (THFM) provides a means for interpreting the low-energy electronic degrees of freedom of the magic angle twisted bilayer graphene as hybridization amidst highly dispersing topological conduction and weakly dispersing localized heavy fermions. In order to understand the Landau quantization of the ensuing electronic spectrum, a generalization of THFM to include the magnetic field B is desired, but currently missing. Here we provide a systematic derivation of the THFM in B and solve the resulting model to obtain the interacting Hofstadter spectra for single particle charged excitations. While naive minimal substitution within THFM fails to correctly account for the total number of magnetic subbands within the narrow band i.e., its total Chern number, our method-based on projecting the light and heavy fermions onto the irreducible representations of the magnetic translation group- reproduces the correct total Chern number. Analytical results presented here offer an intuitive understanding of the nature of the (strongly interacting) Hofstadter bands.

Thermodynamics of resonating-valence-bond states toward the understanding of quantum spin liquid phenomena

A quantum spin liquid (QSL) is a state of matter in which spins do not exhibit magnetic order. In contrast to paramagnets, the spins in a QSL interact strongly, similar to conventional ordered magnets; however the thermodynamic stability of QSLs is rarely studied. Here, the thermodynamic properties of centered hexagon nanoclusters were investigated using the Hubbard model, which was solved using exact numerical diagonalization. The total spin, spin-spin correlation functions, local magnetic moments, charge and spin gaps, and magnetocaloric effect were analyzed for a half-filled band as a function of the ratio between the on-site Coulomb repulsion and electronic hopping (U/t). The centered hexagon nanocluster exhibited an antiferromagnetic (AFM) behavior with exotic magnetic ordering. Resonating-valence-bond (RVB) states were observed for intermediate values of U/t, in which short-range spin-spin correlation functions were suppressed to minimize spin frustration. The AFM order was examined in terms of the Néel-like temperature derived from the temperature dependence of the magnetic susceptibility. An interesting result is that the systems under external magnetic fields exhibited an inverse magnetocaloric effect, which was remarkable for intermediate values of U/t, where the RVB state was observed. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene (TBLG) systems, these results provide insights into the onset of magnetism and the possible spin liquid states in these graphene moiré materials.

Double and Quadruple Flat Bands Tuned by Alternative Magnetic Fluxes in Twisted Bilayer Graphene

Twisted bilayer graphene (TBG) can host the moiré energy flat bands with twofold degeneracy serving as a fruitful playground for strong correlations and topological phases. However, the number of degeneracy is not limited to two. Introducing a spatially alternative magnetic field, we report that the induced magnetic phase becomes an additional controllable parameter and leads to an undiscovered generation of fourfold degenerate flat bands. This emergence stems from the band inversion at the Γ point near the Fermi level with a variation of both twisted angle and magnetic phase. We present the conditions for the emergence of multifold degenerate flat bands, which are associated with the eigenvalue degeneracy of a Birman-Schwinger operator. Using holomorphic functions, which explain the origin of the double flat bands in the conventional TBG, we can generate analytical wave functions in the magnetic TBG to show absolute flatness with fourfold degeneracy. Moreover, we identify an orbital-related intervalley coherent state as the many-body ground state at charge neutrality. In contrast, the conventional TBG has only two moiré energy flat bands, and the highly degenerate flat bands with additional orbital channels in this magnetic platform might bring richer correlation physics.

Twist piezoelectricity: giant electromechanical coupling in magic-angle twisted bilayer LiNbO3

Twisted a pair of stacked two-dimensional materials exhibit many exotic electronic and photonic properties, leading to the emergence of flat-band superconductivity, moiré engineering and topological polaritons. These remarkable discoveries make twistronics the focus point of tremendous interest, but mostly limited to the concept of electrons, phonons or photons. Here, we present twist piezoelectricity as a fascinating paradigm to modulate polarization and electromechanical coupling by twisting precisely the stacked lithium niobate slabs due to the interlayer coupling effect. Particularly, the inversed and twisted bilayer lithium niobate is constructed to overcome the intrinsic mutual limitation of single crystals and giant effective electromechanical coupling coefficientk t 2 is unveiled at magic angle of 11 1 ∘ , reaching 85.5%. Theoretical analysis based on mutual energy integrals shows well agreements with numerical and experimental results. Our work opens new venues to flexibly control multi-physics with magic angle, stimulating progress in wideband acoustic-electric, and acoustic-optic components, which has great potential in wireless communication, timing, sensing, and hybrid integrated photonics.

Twisto-Electrochemical Activity Volcanoes in Trilayer Graphene

In this work, we develop a twist-dependent electrochemical activity map, combining a low-energy continuum electronic structure model with modified Marcus-Hush-Chidsey kinetics in trilayer graphene. We identify a counterintuitive rate enhancement region spanning the magic angle curve and incommensurate twists in the system geometry. We find a broad activity peak with a ruthenium hexamine redox couple in regions corresponding to both magic angles and incommensurate angles, a result qualitatively distinct from the twisted bilayer case. Flat bands and incommensurability offer new avenues for reaction rate enhancements in electrochemical transformations.

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

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

Moiré Pattern Controlled Phonon Polarizer Based on Twisted Graphene

Twisted van der Waals materials featuring Moiré patterns present new design possibilities and demonstrate unconventional behaviors in electrical, optical, spintronic, and superconducting properties. However, experimental exploration of thermal transport across Moiré patterns has not been as extensive, despite its critical role in nanoelectronics, thermal management, and energy technologies. Here, the first experimental study is conducted on thermal transport across twisted graphene, demonstrating a phonon polarizer concept from the rotational misalignment between stacked layers. The direct thermal and acoustic measurements, structural characterizations, and atomistic modeling, reveal a modulation up to 631% in thermal conductance with various Moiré angles, while maintaining a high acoustic transmission. By comparing experiments with density functional theory and molecular dynamics simulations, mode-dependent phonon transmissions are quantified based on the angle alignment of graphene band structures and attributed to the coupling among flexural phonon modes. The agreement confirms the dominant tuning mechanisms in adjusting phonon transmission from high-frequency thermal modes while having negligible effects on low-frequency acoustic modes near Brillouin zone center. This study offers crucial insights into the fundamental thermal transport in Moiré structures, opening avenues for the invention of quantum thermal devices and new design methodologies based on manipulations of vibrational band structures and phonon spectra.

Engineering the Band Topology in a Rhombohedral Trilayer Graphene Moiré Superlattice

Moiré superlattices have become a fertile playground for topological Chern insulators, where the displacement field can tune the quantum geometry and Chern number of the topological band. However, in experiments, displacement field engineering of spontaneous symmetry-breaking Chern bands has not been demonstrated. Here in a rhombohedral trilayer graphene moiré superlattice, we use a thermodynamic probe and transport measurement to monitor the Chern number evolution as a function of the displacement field. At a quarter filling of the moiré band, a novel Chern number of three is unveiled to compete with the well-established number of two upon turning on the electric field and survives when the displacement field is sufficiently strong. The transition can be reconciled by a nematic instability on the Fermi surface due to the pseudomagnetic vector field potentials associated with moiré strain patterns. Our work opens more opportunities to active control of Chern numbers in van der Waals moiré systems.

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

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

Moiré band renormalization due to lattice mismatch in bilayer graphene

We investigated the band renormalization caused by the compressive-strain-induced lattice mismatch in parallel AA stacked bilayer graphene using two complementary methods: the tight-binding approach and the low-energy continuum theory. While a large mismatch does not alter the low-energy bands, a small one reduces the bandwidth of the low-energy bands along with a decrease in the Fermi velocity. In the tiny-mismatch regime, the low-energy continuum theory reveals that the long-period moiré pattern extensively renormalizes the low-energy bands, resulting in a significant reduction of bandwidth. Meanwhile, the Fermi velocity exhibits an oscillatory behavior and approaches zero at specific mismatches. However, the resulting low-energy bands are not perfectly isolated flat, as seen in twisted bilayer graphene at magic angles. These findings provide a deeper understanding of moiré physics and offer valuable guidance for related experimental studies in creating moiré superlattices using two-dimensional van der Waals heterostructures.

Observation of dichotomic field-tunable electronic structure in twisted monolayer-bilayer graphene

Twisted bilayer graphene (tBLG) provides a fascinating platform for engineering flat bands and inducing correlated phenomena. By designing the stacking architecture of graphene layers, twisted multilayer graphene can exhibit different symmetries with rich tunability. For example, in twisted monolayer-bilayer graphene (tMBG) which breaks the C2z symmetry, transport measurements reveal an asymmetric phase diagram under an out-of-plane electric field, exhibiting correlated insulating state and ferromagnetic state respectively when reversing the field direction. Revealing how the electronic structure evolves with electric field is critical for providing a better understanding of such asymmetric field-tunable properties. Here we report the experimental observation of field-tunable dichotomic electronic structure of tMBG by nanospot angle-resolved photoemission spectroscopy (NanoARPES) with operando gating. Interestingly, selective enhancement of the relative spectral weight contributions from monolayer and bilayer graphene is observed when switching the polarity of the bias voltage. Combining experimental results with theoretical calculations, the origin of such field-tunable electronic structure, resembling either tBLG or twisted double-bilayer graphene (tDBG), is attributed to the selectively enhanced contribution from different stacking graphene layers with a strong electron-hole asymmetry. Our work provides electronic structure insights for understanding the rich field-tunable physics of tMBG.

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

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