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Control of the interlayer twist angle in two-dimensional van der Waals (vdW) heterostructures enables one to engineer a quasiperiodic moiré superlattice of tunable length scale1–8. In twisted bilayer graphene, the simple moiré superlattice band description suggests that the electronic bandwidth can be tuned to be comparable to the vdW interlayer interaction at a ‘magic angle’9, exhibiting strongly correlated behaviour. However, the vdW interlayer interaction can also cause significant structural reconstruction at the interface by favouring interlayer commensurability, which competes with the intralayer lattice distortion10–16. Here we report atomic-scale reconstruction in twisted bilayer graphene and its effect on the electronic structure. We find a gradual transition from an incommensurate moiré structure to an array of commensurate domains with soliton boundaries as we decrease the twist angle across the characteristic crossover angle, θc ≈ 1°. In the solitonic regime (θ < θc) where the atomic and electronic reconstruction become significant, a simple moiré band description breaks down and the secondary Dirac bands appear. On applying a transverse electric field, we observe electronic transport along the network of one-dimensional topological channels that surround the alternating triangular gapped domains. Atomic and electronic reconstruction at the vdW interface provide a new pathway to engineer the system with continuous tunability.An investigation of the structural and transport properties of bilayer graphene as a function of the twist angle between the layers reveals atomic-scale reconstruction for twist angles smaller than a critical value.

Van der Waals (vdW) solids can be engineered with atomically precise vertical composition through the assembly of layered two-dimensional materials 1 , 2 . However, the artisanal assembly of structures from micromechanically exfoliated flakes 3 , 4 is not compatible with scalable and rapid manufacturing. Further engineering of vdW solids requires precisely designed and controlled composition over all three spatial dimensions and interlayer rotation. Here, we report a robotic four-dimensional pixel assembly method for manufacturing vdW solids with unprecedented speed, deliberate design, large area and angle control. We used the robotic assembly of prepatterned ‘pixels’ made from atomically thin two-dimensional components. Wafer-scale two-dimensional material films were grown, patterned through a clean, contact-free process and assembled using engineered adhesive stamps actuated by a high-vacuum robot. We fabricated vdW solids with up to 80 individual layers, consisting of 100 × 100 μm 2 areas with predesigned patterned shapes, laterally/vertically programmed composition and controlled interlayer angle. This enabled efficient optical spectroscopic assays of the vdW solids, revealing new excitonic and absorbance layer dependencies in MoS 2 . Furthermore, we fabricated twisted N -layer assemblies, where we observed atomic reconstruction of twisted four-layer WS 2 at high interlayer twist angles of ≥4°. Our method enables the rapid manufacturing of atomically resolved quantum materials, which could help realize the full potential of vdW heterostructures as a platform for novel physics 2 , 5 , 6 and advanced electronic technologies 7 , 8 . A robotic method enables rapid manufacturing of complex van der Waals solids.

Compelling evidence suggests distinct correlated electron behavior may exist only in clean 2D materials such as 1T-TaS 2 . Unfortunately, experiment and theory suggest that extrinsic disorder in free standing 2D layers disrupts correlation-driven quantum behavior. Here we demonstrate a route to realizing fragile 2D quantum states through endotaxial polytype engineering of van der Waals materials. The true isolation of 2D charge density waves (CDWs) between metallic layers stabilizes commensurate long-range order and lifts the coupling between neighboring CDW layers to restore mirror symmetries via interlayer CDW twinning. The twinned-commensurate charge density wave (tC-CDW) reported herein has a single metal–insulator phase transition at ~350 K as measured structurally and electronically. Fast in-situ transmission electron microscopy and scanned nanobeam diffraction map the formation of tC-CDWs. This work introduces endotaxial polytype engineering of van der Waals materials to access latent 2D ground states distinct from conventional 2D fabrication. Correlated quantum states in free-standing two-dimensional materials are susceptible to defects and thermal disorder. Here, the authors demonstrate two-dimensional ordered charge density wave states above room temperature in clean interleaved polytype heterostructures of a van der Waals material.

Twist engineering—the alignment of two-dimensional (2D) crystalline layers with a specific orientation—has led to tremendous success in controlling the charge degree of freedom, particularly in producing correlated and topological electronic phases in moiré crystals 1 , 2 . However, although pioneering theoretical efforts have predicted that non-trivial magnetism 3 – 5 and magnons 6 , 7 can be made by twisting 2D magnets, the experimental realization of engineering the spin degree of freedom by twisting remains elusive. Here we fabricate twisted double bilayers of a 2D magnet, namely, chromium triiodide (CrI 3 ), and demonstrate the successful twist engineering of 2D magnetism in them. We identify signatures of a new magnetic ground state that is distinct from those in natural two-layer (2L) and four-layer (4L) CrI 3 . We show that for a very small twist angle, this emergent magnetism can be well approximated by a weighted linear superposition of those of 2L and 4L CrI 3 , whereas for a large twist angle, it mostly resembles that of isolated 2L CrI 3 . However, at an intermediate twist angle, there is a finite net magnetization that cannot be simply inferred from any homogeneous stacking configuration, but emerges because spin frustrations are introduced by competition between ferromagnetic and antiferromagnetic exchange coupling within individual moiré supercells. Stacking and twisting two-dimensional materials has led to the observation of a variety of electronic phenomena. Now, magnetic behaviour that is distinct from anything seen in individual layers is induced by a moiré pattern in double bilayer chromium triiodide.

Moiré magnetism is emerging as a platform to design and control exotic magnetic phases in twisted magnetic two-dimensional crystals. Non-collinear spin texture emerging from twisted two-dimensional magnets with collinear spins is one of the most profound consequences of moiré magnetism and forms the basis for realizing non-trivial magnetic orders and excitations. However, no direct experimental observations of non-collinear spins in moiré magnets have been made, despite recent theoretical and experimental efforts. Here, we report evidence of non-collinear spin texture in two-dimensional twisted double bilayer CrI3. We distinguish the non-collinear spins with a gradual spin flop process from the collinear spins with sudden spin flip transitions and identify a net magnetization emerging from the collinear spins. We also demonstrate that both non-collinear spins and net magnetization are present at twist angles from 0.5° to 5° but are most prominent for 1.1°. We resolve a critical temperature of 25 K for the onset of the net magnetization and the softening of the non-collinear spins in the 1.1° samples. This is substantially lower than the Néel temperature of 45 K for natural few layers. Our results provide a platform to explore non-trivial magnetism with non-collinear spins.A moiré potential may play a role in determining the magnetic properties of a two-dimensional homo or heterostructure. Now, non-collinear spin structures are observed in twisted double bilayer CrI3, providing a platform to engineer unusual magnetic textures.

Moiré magnetism featured by stacking engineered atomic registry and lattice interactions has recently emerged as an appealing quantum state of matter at the forefront of condensed matter physics research. Nanoscale imaging of moiré magnets is highly desirable and serves as a prerequisite to investigate a broad range of intriguing physics underlying the interplay between topology, electronic correlations, and unconventional nanomagnetism. Here we report spin defect-based wide-field imaging of magnetic domains and spin fluctuations in twisted double trilayer (tDT) chromium triiodide CrI 3 . We explicitly show that intrinsic moiré domains of opposite magnetizations appear over arrays of moiré supercells in low-twist-angle tDT CrI 3 . In contrast, spin fluctuations measured in tDT CrI 3 manifest little spatial variations on the same mesoscopic length scale due to the dominant driving force of intralayer exchange interaction. Our results enrich the current understanding of exotic magnetic phases sustained by moiré magnetism and highlight the opportunities provided by quantum spin sensors in probing microscopic spin related phenomena on two-dimensional flatland. By carefully inducing twists or lattice stacking offsets between two adjacent van der Waals crystals, a superlattice potential can be introduced. This Moire lattice offers an incredibly rich physics, ranging from superconductivity to exotic magnetism, depending on van der Waals materials in question. Here, Du et al. study the magnetic domains in twisted CrI 3 , and show that despite this domain structure, spin fluctuations are spatially homogenous.

Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89° and the amplitude reaches 8 pm around the magic angle of 1. 1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS 2 , CrI 3 , and WSe 2 /MoSe 2 . In twisted 2D materials, spontaneous lattice reconstructions mean that twist angle alone provides an incomplete description. Here, using electron diffraction, the authors show that the displacement field in twisted bilayer graphene can be described as a superposition of three periodic lattice distortion (PLD) waves with wavevectors oriented at 120° from each other, forming a “torsional\" PLD.

Recent demonstrations of moiré magnetism, featuring exotic phases with noncollinear spin order in the twisted van der Waals (vdW) magnet chromium triiodide CrI 3 , have highlighted the potential of twist engineering of magnetic (vdW) materials. However, the local magnetic interactions, spin dynamics, and magnetic phase transitions within and across individual moiré supercells remain elusive. Taking advantage of a scanning single-spin magnetometry platform, here we report observation of two distinct magnetic phase transitions with separate critical temperatures within a moiré supercell of small-angle twisted double trilayer CrI 3 . By measuring temperature-dependent spin fluctuations at the coexisting ferromagnetic and antiferromagnetic regions in twisted CrI 3 , we explicitly show that the Curie temperature of the ferromagnetic state is higher than the Néel temperature of the antiferromagnetic one by ~10 K. Our mean-field calculations attribute such a spatial and thermodynamic phase separation to the stacking order modulated interlayer exchange coupling at the twisted interface of moiré superlattices. van der Waals magnets can be arranged into twisted heterostructures, with the twisting leading to the formation of new magnetic phases. Here, Li, Sun, and coauthors show via NVcentre based magnetometry small angle twisted double trilayer CrI 3 exhibits a co-existing, hybrid magnetic phase with distinct phase transition temperatures.

Charge density waves are emergent quantum states that spontaneously reduce crystal symmetry, drive metal-insulator transitions, and precede superconductivity. In low-dimensions, distinct quantum states arise, however, thermal fluctuations and external disorder destroy long-range order. Here we stabilize ordered two-dimensional (2D) charge density waves through endotaxial synthesis of confined monolayers of 1T-TaS 2 . Specifically, an ordered incommensurate charge density wave (oIC-CDW) is realized in 2D with dramatically enhanced amplitude and resistivity. By enhancing CDW order, the hexatic nature of charge density waves becomes observable. Upon heating via in-situ TEM, the CDW continuously melts in a reversible hexatic process wherein topological defects form in the charge density wave. From these results, new regimes of the CDW phase diagram for 1T-TaS 2 are derived and consistent with the predicted emergence of vestigial quantum order. Stabilizing charge density wave states in low-dimensional systems is challenging. Here, the authors stabilize an ordered incommensurate charge density wave at elevated temperatures via endotaxial synthesis of TaS 2 polytype heterostructures, where charge density wave layers are encapsulated within metallic layers.

While the surface-bulk correspondence has been ubiquitously shown in topological phases, the relationship between surface and bulk in Landau-like phases is much less explored. Theoretical investigations since 1970s for semi-infinite systems have predicted the possibility of the surface order emerging at a higher temperature than the bulk, clearly illustrating a counterintuitive situation and greatly enriching phase transitions. But experimental realizations of this prediction remain missing. Here, we demonstrate the higher-temperature surface and lower-temperature bulk phase transitions in CrSBr, a van der Waals (vdW) layered antiferromagnet. We leverage the surface sensitivity of electric dipole second harmonic generation (SHG) to resolve surface magnetism, the bulk nature of electric quadrupole SHG to probe bulk spin correlations, and their interference to capture the two magnetic domain states. Our density functional theory calculations show the suppression of ferromagnetic-antiferromagnetic competition at the surface is responsible for this enhanced surface magnetism. Our results not only show counterintuitive, richer phase transitions in vdW magnets, but also provide viable ways to enhance magnetism in their 2D form. Surface magnetic order could precede bulk order, but detecting such a separation necessitates experimental probes sensitive to both surface and bulk phase transitions. Here, using second harmonic generation, the authors propose that this situation is realized in a van der Waals antiferromagnet CrSBr.