Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene

Geometric Inhibition of Superflow in Single-Layer Graphene Suggests a Staggered-Flux Superconductivity in Bilayer and Trilayer Graphene

In great contrast to the numerous discoveries of superconductivity in layer-stacked graphene systems, the absence of superconductivity in the simplest monolayer graphene remains quite puzzling. Here, through realistic computation of the electronic structure, we identify a systematic trend that superconductivity emerges only upon alteration of the low-energy electronic lattice from the underlying honeycomb atomic structure. We then demonstrate that this inhibition can result from geometric frustration of the bond lattice that disables the quantum phase coherence of the order parameter residing on it. In comparison, upon deviation from the honeycomb lattice, relief of geometric frustration allows robust superfluidity with nontrivial spatial structures. For the specific examples of bilayer and trilayer graphene under an external electric field, such a bond-centered order parameter would develop superfluidity with staggered flux that breaks the time-reversal symmetry. Our study also suggests the possible realization of the long-sought superconductivity in single-layer graphene via the application of unidirectional strain.

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.

Evolution of superconductivity in twisted graphene multilayers

The group of moiré graphene superconductors keeps growing, and by now it contains twisted graphene multilayers as well as untwisted stacks. We analyze here the contribution of long-range charge fluctuations in the superconductivity of twisted double bilayers and helical trilayers, and compare the results to twisted bilayer graphene. A diagrammatic approach which depends on a few, well-known parameters is used. We find that the critical temperature and the order parameter differ significantly between twisted double bilayers and helical trilayers on one hand, and twisted bilayer graphene on the other. This trend, consistent with experiments, can be associated with the role played by moiré Umklapp processes in the different systems.

Collective Charge Excitations between Moiré Minibands in Twisted WSe_{2} Bilayers Probed with Resonant Inelastic Light Scattering

We establish low-temperature resonant inelastic light scattering (RILS) spectroscopy as a tool to probe the formation of a series of moiré bands in twisted WSe_{2} bilayers by accessing collective inter-moiré-band excitations (IMBEs). We observe resonances in RILS spectra at energies in agreement with inter-moiré-band transitions obtained from an ab initio based continuum model. Transitions between the first and second moiré band for a twist angle of about 8° are reported and between the first and the third, and higher bands for a twist of about 3°. The signatures from IMBE for the latter highlight a strong departure from parabolic bands with flat minibands exhibiting very high density of states in accord with theory. These observations allow one to quantify the transition energies at the K point where the states relevant for correlation physics are hosted.

Tunable Exciton Polaritons in Band-Gap Engineered Hexagonal Boron Nitride

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

Evidence of a distinct collective mode in Kagome superconductors

The collective modes of the superconducting order parameter fluctuation can provide key insights into the nature of the superconductor. Recently, a family of superconductors has emerged in non-magnetic kagome materials AV3Sb5 (A = K, Rb, Cs), exhibiting fertile emergent phenomenology. However, the collective behaviors of Cooper pairs have not been studied. Here, we report a distinct collective mode in CsV3-xTaxSb5 using scanning tunneling microscope/spectroscopy. The spectral line-shape is well-described by one isotropic and one anisotropic superconducting gap, and a bosonic mode due to electron-mode coupling. With increasing x, the two gaps move closer in energy, merge into two isotropic gaps of equal amplitude, and then increase synchronously. The mode energy decreases monotonically to well below 2 Δ and survives even after the charge density wave order is suppressed. We propose the interpretation of this collective mode as Leggett mode between different superconducting components or the Bardasis-Schrieffer mode due to a subleading superconducting component.

Enhanced Quantum Metric due to Vacancies in Graphene

Random vacancies in a graphene monolayer induce defect states that are known to form a narrow impurity band centered around zero energy at half filling. We use a space-resolved formulation of the quantum metric and establish a strong enhancement of the electronic correlations in this impurity band. The enhancement is primarily due to strong correlations between pairs of vacancies situated on different sublattices at anomalously large spatial distances. We trace the strong enhancement to both the multifractal vacancy wave functions, which ties the system exactly at the Anderson insulator transition for all defect concentrations, and preserving the chiral symmetry.

Acquisition of molecular rolling lubrication by self-curling of graphite nanosheet at cryogenic temperature

Friction as a fundamental physical phenomenon dominates nature and human civilization, among which the achievement of molecular rolling lubrication is desired to bring another breakthrough, like the macroscale design of wheel. Herein, an edge self-curling nanodeformation phenomenon of graphite nanosheets (GNSs) at cryogenic temperature is found, which is then used to promote the formation of graphite nanorollers in friction process towards molecular rolling lubrication. The observation of parallel nanorollers at the friction interface give the experimental evidence for the occurrence of molecular rolling lubrication, and the graphite exhibits abnormal lubrication performance in vacuum with ultra-low friction and wear at macroscale. The molecular rolling lubrication mechanism is elucidated from the electronic interaction perspective. Experiments and theoretical simulations indicate that the driving force of the self-curling is the uneven atomic shrinkage induced stress, and then the shear force promotes the intact nanoroller formation, while the constraint of atomic vibration decreases the dissipation of driving stress and favors the nanoroller formation therein. It will open up a new pathway for controlling friction at microscale and nanostructural manipulation.

Lifshitz transition enabling superconducting dome around a charge-order critical point

Superconductivity often emerges as a dome around a quantum critical point (QCP) where long-range order is suppressed to zero temperature, mostly in magnetically ordered materials. However, the emergence of superconductivity at charge-order QCPs remains shrouded in mystery, despite its relevance to high-temperature superconductors and other exotic phases of matter. Here, we present resistance measurements proving that a dome of superconductivity surrounds the putative charge-density-wave QCP in pristine samples of titanium diselenide tuned with hydrostatic pressure. In addition, our quantum oscillation measurements combined with electronic structure calculations show that superconductivity sets in precisely when large electron and hole pockets suddenly appear through an abrupt change of the Fermi surface topology, also known as a Lifshitz transition. Combined with the known repulsive interaction, this suggests that unconventional s± superconductivity is mediated by charge-density-wave fluctuations in titanium diselenide. These results highlight the importance of the electronic ground state and charge fluctuations in enabling unconventional superconductivity.

Tunable superconductivity in electron- and hole-doped Bernal bilayer graphene

Graphene-based, high-quality, two-dimensional electronic systems have emerged as a highly tunable platform for studying superconductivity1-21. Specifically, superconductivity has been observed in both electron- and hole-doped twisted graphene moiré systems1-17, whereas in crystalline graphene systems, superconductivity has so far been observed only in hole-doped rhombohedral trilayer graphene (RTG)18 and hole-doped Bernal bilayer graphene (BBG)19-21. Recently, enhanced superconductivity has been demonstrated20,21 in BBG because of the proximity to a monolayer WSe2. Here we report the observation of superconductivity and a series of flavour-symmetry-breaking phases in electron- and hole-doped BBG/WSe2 devices by electrostatic doping. The strength of the observed superconductivity is tunable by applied vertical electric fields. The maximum Berezinskii-Kosterlitz-Thouless transition temperature for the electron- and hole-doped superconductivity is about 210 mK and 400 mK, respectively. Superconductivities emerge only when the applied electric fields drive the BBG electron or hole wavefunctions towards the WSe2 layer, underscoring the importance of the WSe2 layer in the observed superconductivity. The hole-doped superconductivity violates the Pauli paramagnetic limit, consistent with an Ising-like superconductor. By contrast, the electron-doped superconductivity obeys the Pauli limit, although the proximity-induced Ising spin-orbit coupling is also notable in the conduction band. Our findings highlight the rich physics associated with the conduction band in BBG, paving the way for further studies into the superconducting mechanisms of crystalline graphene and the development of superconductor devices based on BBG.

Nematic Metal in a Multivalley Electron Gas: Variational Monte Carlo Analysis and Application to AlAs

The two-dimensional electron gas is of fundamental importance in quantum many-body physics. We study a minimal extension of this model with C_{4} (as opposed to full rotational) symmetry and an electronic dispersion with two valleys with anisotropic effective masses. Electrons in our model interact via Coulomb repulsion, screened by distant metallic gates. Using variational Monte Carlo simulations, we find a broad intermediate range of densities with a metallic valley-polarized, spin-unpolarized ground state. Our results are of direct relevance to the recently discovered "nematic" state in AlAs quantum wells. For the effective mass anisotropy relevant to this system, m_{x}/m_{y}≈5.2, we obtain a transition from an anisotropic metal to a valley-polarized metal at r_{s}≈12 (where r_{s} is the dimensionless Wigner-Seitz radius). At still lower densities, we find a (possibly metastable) valley and spin-polarized state with a reduced electronic anisotropy.

Directional Localization from a Magnetic Field in Moiré Systems

Moiré materials provide a highly tunable platform in which novel electronic phenomena can emerge. We study strained moiré materials in a uniform magnetic field and predict highly anisotropic electrical conductivity that switches easy axis as magnetic field or strain is varied. The dramatic anisotropy reflects one-dimensional localization (directional localization) of the electron wave functions along a crystal axis due to quantum interference effects. This can be understood in an effective one-dimensional quasiperiodic Aubry-André-Harper-like model, or in a complementary semiclassical picture. This phenomenon should be observable in strained moiré materials at realistic fields and low strain disorder, as well as unstrained systems with anisotropic Fermi surfaces.

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.

Interplay of Landau Quantization and Interminivalley Scatterings in a Weakly Coupled Moiré Superlattice

Double-layer quantum systems are promising platforms for realizing novel quantum phases. Here, we report a study of quantum oscillations (QOs) in a weakly coupled double-layer system composed of a large-angle twisted-double-bilayer graphene (TDBG). We quantify the interlayer coupling strength by measuring the interlayer capacitance from the QOs pattern at low temperatures, revealing electron-hole asymmetry. At high temperatures when SdHOs are thermally smeared, we observe resistance peaks when Landau levels (LLs) from two moiré minivalleys are aligned, regardless of carrier density; eventually, it results in a 2-fold increase of oscillating frequency in D, serving as compelling evidence of the magneto-intersub-band oscillations (MISOs) in double-layer systems. The temperature dependence of MISOs suggests that electron-electron interactions play a crucial role and the scattering times obtained from MISO thermal damping are correlated with the interlayer coupling strength. Our study reveals intriguing interplays among Landau quantization, moiré band structure, and scatterings.

Uncovering the spin ordering in magic-angle graphene via edge state equilibration

The flat bands in magic-angle twisted bilayer graphene (MATBG) provide an especially rich arena to investigate interaction-driven ground states. While progress has been made in identifying the correlated insulators and their excitations at commensurate moiré filling factors, the spin-valley polarizations of the topological states that emerge at high magnetic field remain unknown. Here we introduce a technique based on twist-decoupled van der Waals layers that enables measurement of their electronic band structure and-by studying the backscattering between counter-propagating edge states-the determination of the relative spin polarization of their edge modes. We find that the symmetry-broken quantum Hall states that extend from the charge neutrality point in MATBG are spin unpolarized at even integer filling factors. The measurements also indicate that the correlated Chern insulator emerging from half filling of the flat valence band is spin unpolarized and suggest that its conduction band counterpart may be spin polarized.

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.

Toward Clean 2D Materials and Devices: Recent Progress in Transfer and Cleaning Methods

Two-dimensional (2D) materials have tremendous potential to revolutionize the field of electronics and photonics. Unlocking such potential, however, is hampered by the presence of contaminants that usually impede the performance of 2D materials in devices. This perspective provides an overview of recent efforts to develop clean 2D materials and devices. It begins by discussing conventional and recently developed wet and dry transfer techniques and their effectiveness in maintaining material "cleanliness". Multi-scale methodologies for assessing the cleanliness of 2D material surfaces and interfaces are then reviewed. Finally, recent advances in passive and active cleaning strategies are presented, including the unique self-cleaning mechanism, thermal annealing, and mechanical treatment that rely on self-cleaning in essence. The crucial role of interface wetting in these methods is emphasized, and it is hoped that this understanding can inspire further extension and innovation of efficient transfer and cleaning of 2D materials for practical applications.

Shaping Graphene Superconductivity with Nanometer Precision

Graphene holds great potential for superconductivity due to its pure 2D nature, the ability to tune its carrier density through electrostatic gating, and its unique, relativistic-like electronic properties. At present, still far from controlling and understanding graphene superconductivity, mainly because the selective introduction of superconducting properties to graphene is experimentally very challenging. Here, a method is developed that enables shaping at will graphene superconductivity through a precise control of graphene-superconductor junctions. The method combines the proximity effect with scanning tunnelling microscope (STM) manipulation capabilities. Pb nano-islands are first grown that locally induce superconductivity in graphene. Using a STM, Pb nano-islands can be selectively displaced, over different types of graphene surfaces, with nanometre scale precision, in any direction, over distances of hundreds of nanometres. This opens an exciting playground where a large number of predefined graphene-superconductor hybrid structures can be investigated with atomic scale precision. To illustrate the potential, a series of experiments are performed, rationalized by the quasi-classical theory of superconductivity, going from the fundamental understanding of superconductor-graphene-superconductor heterostructures to the construction of superconductor nanocorrals, further used as "portable" experimental probes of local magnetic moments in graphene.

Local gate control of Mott metal-insulator transition in a 2D metal-organic framework

Electron-electron interactions in materials lead to exotic many-body quantum phenomena, including Mott metal-insulator transitions (MITs), magnetism, quantum spin liquids, and superconductivity. These phases depend on electronic band occupation and can be controlled via the chemical potential. Flat bands in two-dimensional (2D) and layered materials with a kagome lattice enhance electronic correlations. Although theoretically predicted, correlated-electron Mott insulating phases in monolayer 2D metal-organic frameworks (MOFs) with a kagome structure have not yet been realised experimentally. Here, we synthesise a 2D kagome MOF on a 2D insulator. Scanning tunnelling microscopy (STM) and spectroscopy reveal a MOF electronic energy gap of ∼200 meV, consistent with dynamical mean-field theory predictions of a Mott insulator. Combining template-induced (via work function variations of the substrate) and STM probe-induced gating, we locally tune the electron population of the MOF kagome bands and induce Mott MITs. These findings enable technologies based on electrostatic control of many-body quantum phases in 2D MOFs.

The discovery of three-dimensional Van Hove singularity

Arising from the extreme/saddle point in electronic bands, Van Hove singularity (VHS) manifests divergent density of states (DOS) and induces various new states of matter such as unconventional superconductivity. VHS is believed to exist in one and two dimensions, but rarely found in three dimension (3D). Here, we report the discovery of 3D VHS in a topological magnet EuCd2As2 by magneto-infrared spectroscopy. External magnetic fields effectively control the exchange interaction in EuCd2As2, and shift 3D Weyl bands continuously, leading to the modification of Fermi velocity and energy dispersion. Above the critical field, the 3D VHS forms and is evidenced by the abrupt emergence of inter-band transitions, which can be quantitatively described by the minimal model of Weyl semimetals. Three additional optical transitions are further predicted theoretically and verified in magneto-near-infrared spectra. Our results pave the way to exploring VHS in 3D systems and uncovering the coordination between electronic correlation and the topological phase.

Stacking engineering in layered homostructures: transitioning from 2D to 3D architectures

Artificial materials, characterized by their distinctive properties and customized functionalities, occupy a central role in a wide range of applications including electronics, spintronics, optoelectronics, catalysis, and energy storage. The emergence of atomically thin two-dimensional (2D) materials has driven the creation of artificial heterostructures, harnessing the potential of combining various 2D building blocks with complementary properties through the art of stacking engineering. The promising outcomes achieved for heterostructures have spurred an inquisitive exploration of homostructures, where identical 2D layers are precisely stacked. This perspective primarily focuses on the field of stacking engineering within layered homostructures, where precise control over translational or rotational degrees of freedom between vertically stacked planes or layers is paramount. In particular, we provide an overview of recent advancements in the stacking engineering applied to 2D homostructures. Additionally, we will shed light on research endeavors venturing into three-dimensional (3D) structures, which allow us to proactively address the limitations associated with artificial 2D homostructures. We anticipate that the breakthroughs in stacking engineering in 3D materials will provide valuable insights into the mechanisms governing stacking effects. Such advancements have the potential to unlock the full capability of artificial layered homostructures, propelling the future development of materials, physics, and device applications.

Emerging van der Waals Dielectrics of Inorganic Molecular Crystals for 2D Electronics

In the landscape of continuous downscaling metal-oxide-semiconductor field-effect transistors, two-dimensional (2D) semiconductors with atomic thinness emerge as promising channel materials for ultimate scaled devices. However, integrating compatible dielectrics with 2D semiconductors, particularly in a scalable way, remains a critical challenge that hinders the development of 2D devices. Recently, 2D inorganic molecular crystals (IMCs), which are free of dangling bonds and possess excellent dielectric properties and simplicity for scalable fabrication, have emerged as alternatives for gate dielectric integration in 2D devices. In this Perspective, we start with the introduction of structure and synthesis methods of IMCs and then discuss the explorations of using IMCs as the dielectrics, as well as some remaining relevant issues to be unraveled. Moreover, we look at the future opportunities of IMC dielectrics in 2D devices both for practical applications and fundamental research.

Local atomic stacking and symmetry in twisted graphene trilayers

Moiré superlattices formed by twisting trilayers of graphene are a useful model for studying correlated electron behaviour and offer several advantages over their formative bilayer analogues, including a more diverse collection of correlated phases and more robust superconductivity. Spontaneous structural relaxation alters the behaviour of moiré superlattices considerably and has been suggested to play an important role in the relative stability of superconductivity in trilayers. Here we use an interferometric four-dimensional scanning transmission electron microscopy approach to directly probe the local graphene layer alignment over a wide range of trilayer graphene structures. Our results inform a thorough understanding of how reconstruction modulates the local lattice symmetries crucial for establishing correlated phases in twisted graphene trilayers, evincing a relaxed structure that is markedly different from that proposed previously.

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

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

Vestigial singlet pairing in a fluctuating magnetic triplet superconductor and its implications for graphene superlattices

Stacking and twisting graphene layers allows to create and control a two-dimensional electron liquid with strong correlations. Experiments indicate that these systems exhibit strong tendencies towards both magnetism and triplet superconductivity. Motivated by this phenomenology, we study a 2D model of fluctuating triplet pairing and spin magnetism. Individually, their respective order parameters, d and N, cannot order at finite temperature. Nonetheless, the model exhibits a variety of vestigial phases, including charge-4e superconductivity and broken time-reversal symmetry. Our main focus is on a phase characterized by finite d ⋅ N, which has the same symmetries as the BCS state, a Meissner effect, and metastable supercurrents, yet rather different spectral properties: most notably, the suppression of the electronic density of states at the Fermi level can resemble that of either a fully gapped or nodal superconductor, depending on parameters. This provides a possible explanation for recent tunneling experiments in the superconducting phase of graphene moiré systems.

Spin Polarization: A New Frontier in Efficient Photocatalysis for Environmental Purification and Energy Conversion

As a promising strategy to improve photocatalytic efficiency, spin polarization has attracted enormous attention in recent years, which could be involved in various steps of photoreaction. The Pauli repulsion principle and the spin selection rule dictate that the behavior of two electrons in a spatial eigenstate is based on their spin states, and this fact opens up a new avenue for manipulating photocatalytic efficiency. In this review, recent advances in modulating the photocatalytic activity with spin polarization are systematically summarized. Fundamental insights into the influence of spin-polarization effects on photon absorption, carrier separation, and migration, and the behaviors of reaction-related substances from the photon uptake to reactant desorption are highlighted and discussed in detail, and various photocatalytic applications for environmental purification and energy conversion are presented. This review is expected to deliver a timely overview of the recent developments in spin-polarization-modulated photocatalysis for environmental purification and energy conversion in terms of their practical applications.

Graphene removal by water-assisted focused electron-beam-induced etching - unveiling the dose and dwell time impact on the etch profile and topographical changes in SiO2 substrates

Graphene is one of the most extensively studied 2D materials, exhibiting extraordinary mechanical and electronic properties. Although many years have passed since its discovery, manipulating single graphene layers is still challenging using standard resist-based lithography techniques. Recently, it has been shown that it is possible to etch graphene directly in water-assisted processes using the so-called focused electron-beam-induced etching (FEBIE), with a spatial resolution of ten nanometers. Nanopatterning graphene with such a method in one single step and without using a physical mask or resist is a very appealing approach. During the process, on top of graphene nanopatterning, we have found significant morphological changes induced in the SiO2 substrate even at low electron dose values (<8 nC/μm2). We demonstrate that graphene etching and topographical changes in SiO2 substrates can be controlled via electron beam parameters such as dwell time and dose.

Twisted-layer boron nitride ceramic with high deformability and strength

Moiré superlattices formed by twisted stacking in van der Waals materials have emerged as a new platform for exploring the physics of strongly correlated materials and other emergent phenomena1-5. However, there remains a lack of research on the mechanical properties of twisted-layer van der Waals materials, owing to a lack of suitable strategies for making three-dimensional bulk materials. Here we report the successful synthesis of a polycrystalline boron nitride bulk ceramic with high room-temperature deformability and strength. This ceramic, synthesized from an onion-like boron nitride nanoprecursor with conventional spark plasma sintering and hot-pressing sintering, consists of interlocked laminated nanoplates in which parallel laminae are stacked with varying twist angles. The compressive strain of this bulk ceramic can reach 14% before fracture, about one order of magnitude higher compared with traditional ceramics (less than 1% in general), whereas the compressive strength is about six times that of ordinary hexagonal boron nitride layered ceramics. The exceptional mechanical properties are due to a combination of the elevated intrinsic deformability of the twisted layering in the nanoplates and the three-dimensional interlocked architecture that restricts deformation from propagating across individual nanoplates. The advent of this twisted-layer boron nitride bulk ceramic opens a gate to the fabrication of highly deformable bulk ceramics.

Fluidization and Application of Carbon Nano Agglomerations

Carbon nanomaterials are unique with excellent functionality and diverse structures. However, agglomerated structures are commonly formed because of small-size effects and surface effects. Their hierarchical assembly into micro particles enables carbon nanomaterials to break the boundaries of classical Geldart particle classification before stable fluidization under gas-solid interactions. Currently, there are few systematic reports regarding the structural evolution and fluidization mechanism of carbon nano agglomerations. Based on existing research on carbon nanomaterials, this article reviews the fluidized structure control and fluidization principles of prototypical carbon nanotubes (CNTs) as well as their nanocomposites. The controlled agglomerate fluidization technology leads to the successful mass production of agglomerated and aligned CNTs. In addition, the self-similar agglomeration of individual ultralong CNTs and nanocomposites with silicon as model systems further exemplify the important role of surface structure and particle-fluid interactions. These emerging nano agglomerations have endowed classical fluidization technology with more innovations in advanced applications like energy storage, biomedical, and electronics. This review aims to provide insights into the connections between fluidization and carbon nanomaterials by highlighting their hierarchical structural evolution and the principle of agglomerated fluidization, expecting to showcase the vitality and connotation of fluidization science and technology in the new era.

Optical properties and plasmons in moiré structures

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

The Integration of Two-Dimensional Materials and Ferroelectrics for Device Applications

In recent years, there has been growing interest in functional devices based on two-dimensional (2D) materials, which possess exotic physical properties. With an ultrathin thickness, the optoelectrical and electrical properties of 2D materials can be effectively tuned by an external field, which has stimulated considerable scientific activities. Ferroelectric fields with a nonvolatile and electrically switchable feature have exhibited enormous potential in controlling the electronic and optoelectronic properties of 2D materials, leading to an extremely fertile area of research. Here, we review the 2D materials and relevant devices integrated with ferroelectricity. This review starts to introduce the background about the concerned themes, namely 2D materials and ferroelectrics, and then presents the fundamental mechanisms, tuning strategies, as well as recent progress of the ferroelectric effect on the optical and electrical properties of 2D materials. Subsequently, the latest developments of 2D material-based electronic and optoelectronic devices integrated with ferroelectricity are summarized. Finally, the future outlook and challenges of this exciting field are suggested.

Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands

Kekulé-O order in graphene, which has recently been realized experimentally, induces Dirac electron masses on the order of m∼100  meV. We show that twisted bilayer graphene in which one or both layers have Kekulé-O order exhibits nontrivial flat electronic bands on honeycomb and kagome lattices. When only one layer has Kekulé-O order, there is a parameter regime for which the lowest four bands at charge neutrality form an isolated two-orbital honeycomb lattice model with two flat bands. The bandwidths are minimal at a magic twist angle θ≈0.7° and Dirac mass m≈100  meV. When both layers have Kekulé-O order, there is a large parameter regime around θ≈1° and m≳100  meV in which the lowest three valence and conduction bands at charge neutrality each realize isolated kagome lattice models with one flat band, while the next three valence and conduction bands are flat bands on triangular lattices. These flat band systems may provide a new platform for strongly correlated phases of matter.

Charge-4e superconductivity and chiral metal in 45°-twisted bilayer cuprates and related bilayers

The material realization of charge-4e/6e superconductivity (SC) is a big challenge. Here, we propose to realize charge-4e SC in maximally-twisted homobilayers, such as 45∘-twisted bilayer cuprates and 30∘-twisted bilayer graphene, referred to as twist-bilayer quasicrystals (TB-QC). When each monolayer hosts a pairing state with the largest pairing angular momentum, previous studies have found that the second-order interlayer Josephson coupling would drive chiral topological SC (TSC) in the TB-QC. Here we propose that, above the Tc of the chiral TSC, either charge-4e SC or chiral metal can arise as vestigial phases, depending on the ordering of the total- and relative-pairing-phase fields of the two layers. Based on a thorough symmetry analysis to get the low-energy effective Hamiltonian, we conduct a combined renormalization-group and Monte-Carlo study and obtain the phase diagram, which includes the charge-4e SC and chiral metal phases.

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

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

Nodal band-off-diagonal superconductivity in twisted graphene superlattices

The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. Recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of consequences: most notably, the pairing invariant under all symmetries can have Bogoliubov Fermi surfaces in the superconducting state with protected nodal lines, or may be fully gapped, depending on parameters, and the band-off-diagonal chiral p-wave state exhibits transitions between gapped and nodal regions upon varying the doping. We demonstrate that band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.

Sharpness of the Berezinskii-Kosterlitz-Thouless Transition in Disordered NbN Films

We present a comprehensive investigation of the Berezinskii-Kosterlitz-Thouless transition in ultrathin strongly disordered NbN films. Measurements of resistance, current-voltage characteristics, and kinetic inductance on the very same device reveal a consistent picture of a sharp unbinding transition of vortex-antivortex pairs that fit standard renormalization group theory without extra assumptions in terms of inhomogeneity. Our experiments demonstrate that the previously observed broadening of the transition is not an intrinsic feature of strongly disordered superconductors and provide a clean starting point for the study of dynamical effects at the Berezinskii-Kosterlitz-Thouless transition.

Superconductivity in twisted double bilayer graphene stabilized by WSe2

Identifying the essential components of superconductivity in graphene-based systems remains a critical problem in two-dimensional materials research. This field is connected to the mysteries that underpin investigations of unconventional superconductivity in condensed-matter physics. Superconductivity has been observed in magic-angle twisted stacks of monolayer graphene but conspicuously not in twisted stacks of bilayer graphene, although both systems host topological flat bands and symmetry-broken states. Here we report the discovery of superconductivity in twisted double bilayer graphene (TDBG) in proximity to WSe2. Samples with twist angles 1.24° and 1.37° superconduct in small pockets of the gate-tuned phase diagram within the valence and conduction band, respectively. Superconductivity emerges from unpolarized phases near van Hove singularities and next to regions with broken isospin symmetry. Our results show the correlation between a high density of states and the emergence of superconductivity in TDBG while revealing a possible role for isospin fluctuations in the pairing.

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

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

Moiré Superlattice Structure of Pleated Trilayer Graphene Imaged by 4D Scanning Transmission Electron Microscopy

Moiré superlattices in graphene arise from rotational twists in stacked 2D layers, leading to specific band structures, charge density and interlayer electron and excitonic interactions. The periodicities in bilayer graphene moiré lattices are given by a simple moiré basis vector that describes periodic oscillations in atomic density. The addition of a third layer to form trilayer graphene generates a moiré lattice comprised of multiple harmonics that do not occur in bilayer systems, leading to nontrivial crystal symmetries. Here, we use atomic resolution 4D-scanning transmission electron microscopy to study atomic structure in bilayer and trilayer graphene moiré superlattices and use 4D-STEM to map the electric fields to show subtle variations in the long-range moiré patterns. We show that monolayer graphene folded into an S-bend graphene pleat produces trilayer moiré superlattices with both small (<2°) and larger twist angles (7-30°). Annular in-plane electric field concentrations are detected in high angle bilayers due to overlapping rotated graphene hexagons in each layer. The presence of a third low angle twisted layer in S-bend trilayer graphene, introduces a long-range modulation of the atomic structure so that no real space unit cell is detected. By directly imaging trilayer moiré harmonics that span from picoscale to nanoscale using 4D-STEM, we gain insights into the complex spatial distributions of atomic density and electric fields in trilayer twisted layered materials.

In Situ Twistronics: A New Platform Based on Superlubricity

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

Observation of quadrupolar and dipolar excitons in a semiconductor heterotrilayer

Van der Waals (vdW) materials have opened up many avenues for discovery through layer assembly, as epitomized by interlayer dipolar excitons that exhibit electrically tunable luminescence, lasing and exciton condensation. Extending interlayer excitons to more vdW layers, however, raises fundamental questions concerning coherence within excitons and coupling between moiré superlattices at multiple interfaces. Here, by assembling angle-aligned WSe2/WS2/WSe2 heterotrilayers, we demonstrate the emergence of quadrupolar excitons. We confirm the exciton's quadrupolar nature by the decrease in its energy of 12 meV from coherent hole tunnelling between the two outer layers, its tunable static dipole moment under an external electric field and the reduced exciton-exciton interactions. At high exciton density, we also see signatures of a phase of oppositely aligned dipolar excitons, consistent with a staggered dipolar phase predicted to be driven by attractive dipolar interactions. Our demonstration paves the way for discovering emergent exciton orderings for three vdW layers and beyond.

A Universal Approach to Determine the Atomic Layer Numbers in Two-Dimensional Materials Using Dark-Field Optical Contrast

Two-dimensional (2D) materials possess unique properties primarily due to the quantum confinement effect, which highly depends on their thicknesses. Identifying the number of atomic layers in these materials is a crucial, yet challenging step. However, the commonly used optical reflection method offers only very low contrast. Here, we develop an approach that shows unprecedented sensitivity by analyzing the brightness of dark-field optical images. The brightness of the 2D material edges has a linear dependence on the number of atomic layers. The findings are modeled by Rayleigh scattering, and the results agree well with the experiments. The relative contrast of single-layer graphene can reach 70% under white-light incident conditions. Furthermore, different 2D materials were successfully tested. By adjusting the exposure conditions, we can identify the number of atomic layers ranging from 1 to over 100. Finally, this approach can be applied to various substrates, even transparent ones, making it highly versatile.

Gate-Defined Topological Josephson Junctions in Bernal Bilayer Graphene

Recent experiments on Bernal bilayer graphene (BLG) deposited on monolayer WSe_{2} revealed robust, ultraclean superconductivity coexisting with sizable induced spin-orbit coupling. Here, we propose BLG/WSe_{2} as a platform to engineer gate-defined planar topological Josephson junctions, where the normal and superconducting regions descend from a common material. More precisely, we show that if superconductivity in BLG/WSe_{2} is gapped and emerges from a parent state with intervalley coherence, then Majorana zero-energy modes can form in the barrier region upon applying weak in-plane magnetic fields. Our results spotlight a potential pathway for "internally engineered" topological superconductivity that minimizes detrimental disorder and orbital-magnetic-field effects.

A quantum ruler for orbital magnetism in moiré quantum matter

For almost a century, magnetic oscillations have been a powerful "quantum ruler" for measuring Fermi surface topology. In this study, we used Landau-level spectroscopy to unravel the energy-resolved valley-contrasting orbital magnetism and large orbital magnetic susceptibility that contribute to the energies of Landau levels of twisted double-bilayer graphene. These orbital magnetism effects led to substantial deviations from the standard Onsager relation, which manifested as a breakdown in scaling of Landau-level orbits. These substantial magnetic responses emerged from the nontrivial quantum geometry of the electronic structure and the large length scale of the moiré lattice potential. Going beyond traditional measurements, Landau-level spectroscopy performed with a scanning tunneling microscope offers a complete quantum ruler that resolves the full energy dependence of orbital magnetic properties in moiré quantum matter.

Inverse design of chiral functional films by a robotic AI-guided system

Artificial chiral materials and nanostructures with strong and tuneable chiroptical activities, including sign, magnitude, and wavelength distribution, are useful owing to their potential applications in chiral sensing, enantioselective catalysis, and chiroptical devices. Thus, the inverse design and customized manufacturing of these materials is highly desirable. Here, we use an artificial intelligence (AI) guided robotic chemist to accurately predict chiroptical activities from the experimental absorption spectra and structure/process parameters, and generate chiral films with targeted chiroptical activities across the full visible spectrum. The robotic AI-chemist carries out the entire process, including chiral film construction, characterization, and testing. A machine learned reverse design model using spectrum embedded descriptors is developed to predict optimal structure/process parameters for any targeted chiroptical property. A series of chiral films with a dissymmetry factor as high as 1.9 (gabs ~ 1.9) are identified out of more than 100 million possible structures, and their feasible application in circular polarization-selective color filters for multiplex laser display and switchable circularly polarized (CP) luminescence is demonstrated. Our findings not only provide chiral films with the highest reported chiroptical activity, but also have great fundamental value for the inverse design of chiroptical materials.

Probing the Twist-Controlled Interlayer Coupling in Artificially Stacked Transition Metal Dichalcogenide Bilayers by Second-Harmonic Generation

Interlayer coupling plays a critical role in the electronic band structures and optoelectronic properties of van der Waals (vdW) materials and heterostructures. Here, we utilize optical second-harmonic generation (SHG) measurements to probe the twist-controlled interlayer coupling in artificially stacked WSe2/WSe2 homobilayers and WSe2/WS2 and WSe2/MoS2 heterobilayers with a postannealing procedure. In the large angle twisted WSe2/WSe2 and WSe2/WS2, the angular dependence of the SHG intensity follows the interference relations up to angles above 10°. For lower angles, the SHG is significantly suppressed. Furthermore, for the twisted WSe2/MoS2 the SHG intensity largely deviates from the coherent superposition model and shows consistent quenching for all the stacking angles. The suppressed SHG in twisted transition metal dichalcogenide (TMDC) bilayers is predominantly attributed to the interlayer coupling between the two adjacent monolayers. The evolution of the interlayer Raman mode in WSe2 demonstrates that the interlayer coupling in the twisted WSe2/WSe2 and WSe2/WS2 is highly angle-dependent. Alternatively, the interlayer coupling generally exists in the twisted WSe2/MoS2, regardless of the different angles. The interlayer coupling is further confirmed by the quenching and red-shift of the photoluminescence of WSe2 in the twisted TMDC bilayers. Combined with density functional theory calculations, we reveal that the stacking-angle-modulated interlayer coupling originates from the variation of the interlayer spacing and the binding energy in the twisted TMDC bilayers.

Recent Advances in Moiré Superlattice Systems by Angle-Resolved Photoemission Spectroscopy

The last decade has witnessed a flourish in 2D materials including graphene and transition metal dichalcogenides (TMDs) as atomic-scale Legos. Artificial moiré superlattices via stacking 2D materials with a twist angle and/or a lattice mismatch have recently become a fertile playground exhibiting a plethora of emergent properties beyond their building blocks. These rich quantum phenomena stem from their nontrivial electronic structures that are effectively tuned by the moiré periodicity. Modern angle-resolved photoemission spectroscopy (ARPES) can directly visualize electronic structures with decent momentum, energy, and spatial resolution, thus can provide enlightening insights into fundamental physics in moiré superlattice systems and guides for designing novel devices. In this review, first, a brief introduction is given on advanced ARPES techniques and basic ideas of band structures in a moiré superlattice system. Then ARPES research results of various moiré superlattice systems are highlighted, including graphene on substrates with small lattice mismatches, twisted graphene/TMD moiré systems, and high-order moiré superlattice systems. Finally, it discusses important questions that remain open, challenges in current experimental investigations, and presents an outlook on this field of research.

Magic-angle helical trilayer graphene

We propose magic-angle helical trilayer graphene (HTG), a helical structure featuring identical rotation angles between three consecutive layers of graphene, as a unique and experimentally accessible platform for realizing exotic correlated topological states of matter. While nominally forming a supermoiré (or moiré-of-moiré) structure, we show that HTG locally relaxes into large regions of a periodic single-moiré structure realizing flat topological bands carrying nontrivial valley Chern number. These bands feature near-ideal quantum geometry and are isolated from remote bands by a very large energy gap, making HTG a promising platform for experimental realization of correlated topological states such as integer and fractional quantum anomalous Hall states.