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Twisted two-dimensional materials have recently attracted tremendous interest owing to their unique structures and fantastic electronic properties. However, the effect of interlayer twisting on the phonon transport properties is less known, especially for the twist-angle-dependent lattice thermal conductivity ( κ L ). Using the emerging Janus SnSSe bilayer as a prototypical example, we develop an accurate machine learning potential, which is adopted to efficiently predict the κ L at a series of twist angles via iterative solution of the Boltzmann transport equation. It is found that the κ L exhibits a distinct non-monotonous dependence on the twist angle, which can be traced back to the bonding heterogeneity between high-symmetry stacking regions inside the moiré unit cell. In contrast to the general belief, the optical phonons make a major contribution toward the κ L of the twisted structures. Moreover, we demonstrate that four-phonon scattering can significantly reduce the κ L of SnSSe bilayer at higher temperatures, which becomes more pronounced by interlayer twisting. Our work not only highlights the strong predictive power of machine learning potential, but also offers new insights into the design of thermal smart materials with tunable κ L .

Graphene is an atomically thin material that supports highly confined plasmon polaritons, or nano-light, with very low loss. The properties of graphene can be made richer by introducing and then rotating a second layer so that there is a slight angle between the atomic registry. Sunku et al. show that the moiré patterns that result from such twisted bilayer graphene also provide confined conducting channels that can be used for the directed propagation of surface plasmons. Controlling the structure thereby provides a pathway to control and route surface plasmons for a nanophotonic platform. Science , this issue p. 1153 Twisted bilayer graphene hosts periodic arrays of conducting channels for the directed propagation of surface plasmons. Graphene is an atomically thin plasmonic medium that supports highly confined plasmon polaritons, or nano-light, with very low loss. Electronic properties of graphene can be drastically altered when it is laid upon another graphene layer, resulting in a moiré superlattice. The relative twist angle between the two layers is a key tuning parameter of the interlayer coupling in thus-obtained twisted bilayer graphene (TBG). We studied the propagation of plasmon polaritons in TBG by infrared nano-imaging. We discovered that the atomic reconstruction occurring at small twist angles transforms the TBG into a natural plasmon photonic crystal for propagating nano-light. This discovery points to a pathway for controlling nano-light by exploiting quantum properties of graphene and other atomically layered van der Waals materials, eliminating the need for arduous top-down nanofabrication.

Bilayer graphene can be modified by rotating (twisting) one layer with respect to the other. The interlayer twist gives rise to a moiré superlattice that affects the electronic motion and alters the band structure 1 – 4 . Near a ‘magic angle’ of twist 2 , 4 , where the emergence of a flat band causes the charge carriers to slow down 3 , correlated electronic phases including Mott-like insulators and superconductors were recently discovered 5 – 8 by using electronic transport. These measurements revealed an intriguing similarity between magic-angle twisted bilayer graphene and high-temperature superconductors, which spurred intensive research into the underlying physical mechanism 9 – 14 . Essential clues to this puzzle, such as the symmetry and spatial distribution of the spectral function, can be accessed through scanning tunnelling spectroscopy. Here we use scanning tunnelling microscopy and spectroscopy to visualize the local density of states and charge distribution in magic-angle twisted bilayer graphene. Doping the sample to partially fill the flat band, we observe a pseudogap phase accompanied by a global stripe charge order that breaks the rotational symmetry of the moiré superlattice. Both the pseudogap and the stripe charge order disappear when the band is either empty or full. The close resemblance to similar observations in high-temperature superconductors 15 – 21 provides new evidence of a deeper link underlying the phenomenology of these systems. When scanning tunnelling spectroscopy is used to map the electronic structure of magic-angle twisted bilayer graphene, a pseudogap phase is found, accompanied by a global charge-ordered stripe phase.

The coupling between electrons and phonons is one of the fundamental interactions in solids, underpinning a wide range of phenomena, such as resistivity, heat conductivity and superconductivity. However, direct measurements of this coupling for individual phonon modes remain a substantial challenge. In this work, we introduce a new technique for mapping phonon dispersions and electron–phonon coupling (EPC) in van der Waals (vdW) materials. By generalizing the quantum twisting microscope 1 (QTM) to cryogenic temperatures, we demonstrate its capability to map not only electronic dispersions through elastic momentum-conserving tunnelling but also phononic dispersions through inelastic momentum-conserving tunnelling. Crucially, the inelastic tunnelling strength provides a direct and quantitative measure of the momentum and mode-resolved EPC. We use this technique to measure the phonon spectrum and EPC of twisted bilayer graphene (TBG) with twist angles larger than 6°. Notably, we find that, unlike standard acoustic phonons, whose coupling to electrons diminishes as their momentum tends to zero, TBG exhibits a low-energy mode whose coupling increases with decreasing twist angle. We show that this unusual coupling arises from the modulation of the interlayer tunnelling by a layer-antisymmetric ‘phason’ mode of the moiré system. The technique demonstrated here opens the way for examining a large variety of other neutral collective modes that couple to electronic tunnelling, including plasmons 2 , magnons 3 and spinons 4 in quantum materials. Generalization of a quantum twisting microscope to cryogenic temperatures in twisted bilayer graphene shows the ability to map phononic dispersions through inelastic momentum-conserving tunnelling and reveals an angle-dependent coupling between electrons and phonons.

Van der Waals heterostructures obtained via stacking and twisting have been used to create moiré superlattices1, enabling new optical and electronic properties in solid-state systems. Moiré lattices in twisted bilayers of transition metal dichalcogenides (TMDs) result in exciton trapping2–5, host Mott insulating and superconducting states6 and act as unique Hubbard systems7–9 whose correlated electronic states can be detected and manipulated optically. Structurally, these twisted heterostructures feature atomic reconstruction and domain formation10–14. However, due to the nanoscale size of moiré domains, the effects of atomic reconstruction on the electronic and excitonic properties have not been systematically investigated. Here we use near-0°-twist-angle MoSe2/MoSe2 bilayers with large rhombohedral AB/BA domains15 to directly probe the excitonic properties of individual domains with far-field optics. We show that this system features broken mirror/inversion symmetry, with the AB and BA domains supporting interlayer excitons with out-of-plane electric dipole moments in opposite directions. The dipole orientation of ground-state Γ–K interlayer excitons can be flipped with electric fields, while higher-energy K–K interlayer excitons undergo field-asymmetric hybridization with intralayer K–K excitons. Our study reveals the impact of crystal symmetry on TMD excitons and points to new avenues for realizing topologically non-trivial systems16,17, exotic metasurfaces18, collective excitonic phases19 and quantum emitter arrays20,21 via domain-pattern engineering.Domain-resolved spectroscopy reveals the impact of local atomic registry and crystal symmetry on the exciton properties of individual domains in near-0°-twist-angle MoSe2/MoSe2.

Twisting or sliding two-dimensional crystals with respect to each other gives rise to moiré patterns determined by the difference in their periodicities. Such lattice mismatches can exist for several reasons: differences between the intrinsic lattice constants of the two layers, as is the case for graphene on BN 1 ; rotations between the two lattices, as is the case for twisted bilayer graphene 2 ; and strains between two identical layers in a bilayer 3 . Moiré patterns are responsible for a number of new electronic phenomena observed in recent years in van der Waals heterostructures, including the observation of superlattice Dirac points for graphene on BN 1 , collective electronic phases in twisted bilayers and twisted double bilayers 4 – 8 , and trapping of excitons in the moiré potential 9 – 12 . An open question is whether we can use moiré potentials to achieve strong trapping potentials for electrons. Here, we report a technique to achieve deep, deterministic trapping potentials via strain-based moiré engineering in van der Waals materials. We use strain engineering to create on-demand soliton networks in transition metal dichalcogenides. Intersecting solitons form a honeycomb-like network resulting from the three-fold symmetry of the adhesion potential between layers. The vertices of this network occur in bound pairs with different interlayer stacking arrangements. One vertex of the pair is found to be an efficient trap for electrons, displaying two states that are deeply confined within the semiconductor gap and have a spatial extent of 2 nm. Soliton networks thus provide a path to engineer deeply confined states with a strain-dependent tunable spatial separation, without the necessity of introducing chemical defects into the host materials. By sliding one layer with respect to the other in a van der Waals heterostructure, Edelberg et al. create a honeycomb network of solitons. Vertices of the network trap electrons, allowing strain-tunable control of confined states.

HighlightsThis article presents an overview of twisted bilayer graphene (tBLG) on their fabrication techniques and twisting angle-dependent properties.The properties of tBLG can be controlled by controlling the twisting angle between two graphene sheets.Two-dimensional (2D) materials exhibit enhanced physical, chemical, electronic, and optical properties when compared to those of bulk materials. Graphene demands significant attention due to its superior physical and electronic characteristics among different types of 2D materials. The bilayer graphene is fabricated by the stacking of the two monolayers of graphene. The twisted bilayer graphene (tBLG) superlattice is formed when these layers are twisted at a small angle. The presence of disorders and interlayer interactions in tBLG enhances several characteristics, including the optical and electrical properties. The studies on twisted bilayer graphene have been exciting and challenging thus far, especially after superconductivity was reported in tBLG at the magic angle. This article reviews the current progress in the fabrication techniques of twisted bilayer graphene and its twisting angle-dependent properties.

The ability to manipulate the twisting topology of van der Waals structures offers a new degree of freedom through which to tailor their electrical and optical properties. The twist angle strongly affects the electronic states, excitons and phonons of the twisted structures through interlayer coupling, giving rise to exotic optical, electric and spintronic behaviours 1 – 5 . In twisted bilayer graphene, at certain twist angles, long-range periodicity associated with moiré patterns introduces flat electronic bands and highly localized electronic states, resulting in Mott insulating behaviour and superconductivity 3 , 4 . Theoretical studies suggest that these twist-induced phenomena are common to layered materials such as transition-metal dichalcogenides and black phosphorus 6 , 7 . Twisted van der Waals structures are usually created using a transfer-stacking method, but this method cannot be used for materials with relatively strong interlayer binding. Facile bottom-up growth methods could provide an alternative means to create twisted van der Waals structures. Here we demonstrate that the Eshelby twist, which is associated with a screw dislocation (a chiral topological defect), can drive the formation of such structures on scales ranging from the nanoscale to the mesoscale. In the synthesis, axial screw dislocations are first introduced into nanowires growing along the stacking direction, yielding van der Waals nanostructures with continuous twisting in which the total twist rates are defined by the radii of the nanowires. Further radial growth of those twisted nanowires that are attached to the substrate leads to an increase in elastic energy, as the total twist rate is fixed by the substrate. The stored elastic energy can be reduced by accommodating the fixed twist rate in a series of discrete jumps. This yields mesoscale twisting structures consisting of a helical assembly of nanoplates demarcated by atomically sharp interfaces with a range of twist angles. We further show that the twisting topology can be tailored by controlling the radial size of the structure. Experiments demonstrate a class of van der Waals nanowires, made from layered crystals of the semiconductor germanium sulfide, in which a tunable interlayer twist evolves naturally during synthesis.

Interfaces between twisted 2D materials host a wealth of physical phenomena originating from the long-scale periodicity associated with the resulting moiré structure. Besides twisting, an alternative route to create structures with comparably long—or even longer—periodicities is inducing a differential strain between adjacent layers in a van der Waals (vdW) material. Despite recent theoretical efforts analyzing its benefits, this route has not yet been implemented experimentally. Here we report evidence for the simultaneous presence of ferromagnetic and antiferromagnetic regions in CrBr 3 —a hallmark of moiré magnetism—from the observation of an unexpected magnetoconductance in CrBr 3 tunnel barriers with ferromagnetic Fe 3 GeTe 2 and graphene electrodes. The observed magnetoconductance evolves with temperature and magnetic field as the magnetoconductance measured in small-angle CrBr 3 twisted junctions, in which moiré magnetism occurs. Consistent with Raman measurements and theoretical modeling, we attribute the phenomenon to the presence of a differential strain in the CrBr 3 multilayer, which locally modifies the stacking and the interlayer exchange between adjacent CrBr 3 layers, resulting in spatially modulated spin textures. Our conclusions indicate that inducing differential strain in vdW multilayers is a viable strategy to create moiré-like superlattices, which in the future may offer in-situ continuous tunability even at low temperatures. The overlap of different crystal lattices can give rise to a Moire structure with long range periodicity. While this feature has been heavily exploited in twisted van der Waals heterostructures, here, Yao et al find the telltale signatures of Moire magnetism in CrBr3 multilayers induced by differential strain, in the absence of twisting.

The moiré superlattice formed by van der Waals (vdW) stacking of two-dimensional (2D) monolayers with a twist angle can give rise to a variety of novel correlated physical phenomena. In this study, we propose that a 2D semiconductor composed of vdW layers with band edge states extended into the interlayer region can host time-reversal-invariant topological states, as demonstrated by density functional theory and tight-binding calculations. This emergent physics in moiré superlattices is experimentally verified in a twisted bilayer InSe with a twisting angle of θ  = 7.34°. Using scanning tunneling microscopy/spectroscopy (STM/STS), we observed topological edge modes associated with the Z 2 topological metal state at the moiré domain boundary, while these states are absent in the bilayer without twisting. Our theoretical predictions and experimental discoveries advance the field of moiré physics and twistronics, offering a promising strategy for the creation of moiré topological devices. Time-reversal invariant topological states in twisted 2D semiconductors have been previously reported, but their direct visualization in real space has remained elusive. Here, the authors report scanning tunnelling microscopy/spectroscopy measurements of twisted bilayer InSe, showing the formation of magnetic-field sensitive topological edge modes at the moiré domain boundary.