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The frontier of moiré matter has opened up a previously inaccessible realm of emergent topological phenomena. This class of materials — formed by stacking two-dimensional layers with a small twist — provides a unique platform for investigating tailored interactions in tunable solid-state devices, where the moiré superlattice can give rise to delicate topology-driven physics. In this setting, the interplay of field-tunable correlated states, fractionalised excitations, and anomalous velocity phenomena awaits exploration and manipulation.

This cross-journal open Collection focuses on experimental and theoretical developments in the rich tapestry of topological physics in moiré matter.

We welcome the submissions of primary research papers that fall into any of the above categories, with Nature Communications and Communications Physics also considering Reviews and Perspectives that fall within the scope of the Collection. All submissions are subject to the same peer review process and editorial standards as regular Nature Communications, Communications Physics, and Scientific Reports articles.

Twisted bilayer graphene hosts a zoo of rich correlated electronic phases. Here, the authors explore the phase diagram of a twisted bilayer graphene/tungsten diselenide heterostructure and uncover a series of delicate Fermi surface reconstructions and signatures of orbital magnetism.

Moire bilayers support quantum spin Hall (QSH) and quantum anomalous Hall (QAH) states, but a unified explanation is missing. Mai et al. show that by including interactions in typical models, the QSH state shifts from 1/2 to 1/4 filling and gives way to the QAH state at low temperature.

An orbital magnetic moment emerges as a result of inversion symmetry broken at the graphene/h-BN moiré superlattice. Here, Moriya et al. report thermoelectric evidence of magnetic field induced valley splitting for a van Hove singularity in this superlattice, suggesting the emergence of an orbital magnetic moment.

Studies of twisted bilayer transition metal dichalcogenides have so far focused only on those containing group-VI metals. Here, the authors predict that twisted bilayers of ZrS_{2}, with the group-IV metal Zr, form an emergent moiré Kagome lattice with a uniquely strong spin-orbit coupling, leading to quantum-anomalous-Hall and fractional-Chern-insulating states.

Spontaneous symmetry breaking of flat bands in twisted graphene systems may lead to anomalous Hall effect with a precursor state which has not been observed. Here, the authors probe this precursor state by observing bulk valley current and large nonlocal voltage several micrometers away from the charge current path in twisted double bilayer graphene.

Here, the authors report the unexpected observation of different electronic properties of bilayer graphene/boron nitride heterostructures at 0° and 60° twist angles, showing the complex interplay between lattice relaxation and the electronic properties of moiré structures.

The broken-symmetry edge states that are the hallmark of the quantum Hall effect in graphene have eluded spatial measurements. Here, the authors spatially map the quantum Hall broken-symmetry edge states using atomic force microscopy and show a gapped ground state proceeding from the bulk through to the quantum Hall edge boundary.

The e moiré superlattice in twisted 2D structures becomes a highly tunable platform of strongly correlated electron systems. Here, the authors predict rich physics at small twist angles in twisted transition metal dichalcogenide bilayers, including a magic angle for flat band, interaction-driven Haldane insulator, fractional quantum anomalous Hall effect and quantum spin Hall insulators.

Magic-angle twisted bilayer graphene exhibits a quantum anomalous Hall effect at 3/4 filling; however, its mechanism is debated. Here, the authors show that such a phase can be realized in a lattice model of twisted bilayer graphene in the strong coupling limit, and interpret the results in terms of a topological Mott insulator phase.

Twisted monolayer-bilayer graphene is an attractive platform to study the interplay between topology, magnetism and correlations in the flat bands. Here, using electrical transport measurements, the authors uncover a rich correlated phase diagram and identify a new insulating state that can be explained by intervalley coherence with broken time reversal symmetry.

Careful measurements of the zero-field quantum anomalous Hall effect find a less-precisely-quantized Hall conductivity than the integer quantum Hall effect. Here, the authors theoretically study the effects of nonlinear corrections to the Hall conductivity in both topological and trivial magnetic insulators.

The nonlinear Hall effect describes a recently discovered phenomenon in which a time-reversal symmetric material with a Berry curvature dipole develops a transverse voltage at double the frequency of an applied current. Here, the authors theoretically explore twisted bilayer WSe2 under strain, and find that it can exhibit a large nonlinear Hall effect that is highly sensitive to the topological properties of the material.

By interfacing graphene with other materials it is possible to break the intrinsic inversion symmetry and observe interesting quantum transport phenomena. Here, the authors conduct transport measurements of encapsulated graphene at different alignment angles and find evidence of nonlocal resistance above and below 60 K suggesting the existence of a quantum valley Hall state.

Moiré patterns have been experimentally observed in heterostructures comprised of topological insulator films. Here, the authors propose that topological insulator-based moiré heterostructures could be a host of isolated topologically non-trivial moiré minibands for the study of the interplay between topology and correlation.

The band topology of twisted 2D systems is a key factor behind their fascinating physics. Here, the authors demonstrate the role of polarization in driving the band topology evolution in twisted transition metal dichalcogenide homobilayers.

Twisted moiré heterostructures offer a highly tunable solid-state platform for exploring fundamental condensed matter physics. Here, the authors use scanning tunnelling microscopy to investigate the local electronic structure of the gate-controlled quantum anomalous Hall insulator state in twisted monolayer–bilayer graphene.

Correlated electronic states in moiré matter are of great fundamental and technological interest. Here, the authors demonstrate a Josephson junction in magic-angle twisted bilayer graphene with a correlated insulator weak link, showing magnetism and programmable superconducting diode behaviour.

Here, the authors theoretically predict the formation of synergistic correlated and topological states in Coulomb-coupled and gate-tunable graphene/insulator heterostructures, proposing a number of promising substrate candidates and a possible explanation for recent experimental observations in graphene/CrOCl heterostructures.

Moiré superlattices offer a rich platform fort the study of correlated and topological phases. Here, by using low-temperature magneto-transport measurements, the authors demonstrate electric-field induced switching between Chern states in twisted double-layer graphene in the Hofstadter regime.

Twisted double bilayer graphene hosts flat bands that can be tuned with an electric field. Here, by using gate-tuned scanning tunneling spectroscopy, the authors demonstrate the tunability of the flat band and reveal spectral signatures of correlated electron states and the topological nature of the flat band.

Twisted van der Waals structures represent a versatile platform to investigate topological and correlated electronic states. Here, the authors report the visualization of an electron crystal phase in twisted monolayer-bilayer graphene via scanning tunnelling microscopy, studying the coupling between strong electron correlation and nontrivial band topology.

The alignment of three 2D nanosheets leads to the formation of super-moiré atomic lattices, which can influence the electronic properties of van der Waals structures. Here, the authors report evidence of possible correlated insulating states in doubly-aligned hBN/graphene/hBN heterostructures, in a weak-interaction regime.

Twisted bilayer graphene hosts a sequence of electronic resets evidenced experimentally by characteristic spectroscopic cascades and sawtooth peaks in the inverse electronic compressibility. Here, the authors use combined dynamical mean-field theory and Hartree calculations to demonstrate that symmetry-breaking transitions are not necessary to observe cascades in twisted bilayer graphene.

The authors theoretically study superconductivity in twisted-bilayer and twisted-trilayer graphene, finding that flavor polarization allows for Cooper pairing in which the pairs consist of electrons in different bands. Both intervalley phonons and fluctuations of a time-reversal-symmetric intervalley coherent order can favor such pairing.

Correlation effect is essential to stabilize exotic phases such as superconductivity in twisted bilayer graphene. Here, Yuan et al. predict significantly enhanced electron correlation effects due to an emergent high-order van Hove singularity in a two dimensional moiré superlattice.

Twisted van der Waals systems are known to host flat electronic bands, originating from moire potential. Here, the authors predict from purely geometric considerations a new type of nearly dispersionless bands in twisted bilayer MoS_{2}, resulting from destructive interference between effective lattice hopping matrix elements.

Experiments on twisted bilayer graphene point to various interaction-induced phases, including the non-Fermi liquid, but its unambiguous assignment remains challenging. Here, using simultaneous transport and thermoelectric power measurements, the authors identify non-Fermi liquid signatures at low twist angle.

Twist-angle disorder is considered a major source of sample-to-sample variation in magic-angle twisted bilayer graphene. By using scanning tunnelling spectroscopy, the authors demonstrate that a small doping inhomogeneity, present in typical samples, is amplified near the flat band edges and can be another source of disturbance for the flat band physics.

The superposition of two layers of graphene or hBN at an angle gives rise to interesting geometrical structures, named Moiré superlattice, that has been intensively studied recently. The authors report on experimental data and simulations for twisted h-BN/AB-stacked tetralayer graphene heterostructures, finding that band gaps appear because of Fermi surface nesting due to the specific angle used.

Scanning tunneling microscopy (STM) is a powerful tool that can be used to both investigate and manipulate surfaces at the atomic scale. Here, using epitaxial graphene layers on a SiC substrate, the authors show that STM can be used to manipulate the covalent bonding between a graphitic buffer layer-substrate interface, and in turn modify the charge state of the epitaxial graphene.

Twisted double bilayer graphene has recently become a popular system to investigate strongly correlated phenomenon where the twist angle is a key degree of freedom. Here, the authors investigate thermopower in twisted double bilayer graphene finding a large enhancement of thermopower and magnetoresistance within a small magnetic field near the charge neutrality point, indicating a compensated semimetallic state.

The authors present a series of correlated insulating states of twisted bilayer graphene that is detected using an atomic force microscope tip. An additional experiment demonstrates the coupling of a mechanical oscillator to a quantum device.

The electronic structure of graphene can be modified by applying the so-called superlattice potential, arising either from interfacing with hexagonal boron nitride lattices or gate capacitance with spatially periodic modulation, giving rise to a range of unusual transport behavior. Here, the authors report a simulation method to reproduce transport experiments, showing consistent transmission spectra and mini-band structures for graphene superlattices.

Twisted bilayer systems can be used as a platform to engineer new correlated states, with most focus being placed on integer fillings. Here the authors consider fractional filling and the influence this has on the configuration of Wannier orbitals in the strong coupling limit, realising a state they term a fractional correlated insulator.

In moiré superlattices, a multitude of higher order Bragg gaps and van Hove singularities emerges as the band structure renormalizes. Here, the authors map these gaps uniquely to the recently predicted topological Bragg indices of the underlying supermoiré lattice.

In conventional materials, charge carriers are electron-like quasiparticles, but topological bands allow for more exotic possibilities. Here, the authors predict that in the Chern-ferromagnet phase of twisted bilayer graphene charge is carried by spin polarons, bound states of an electron and a spin flip.

Gate-defined superconducting moiré devices offer high tunability for probing the nature of superconducting and correlated insulating states. Here, the authors report the Little–Parks and Aharonov–Bohm effects in a single gate-defined magic-angle twisted bilayer graphene device.

Sliding and twisting of van der Waals layers can produce fascinating physical phenomena. Here, authors show that moiré polar domains in bilayer hBN give rise to a topologically non-trivial winding of the polarization field, forming networks of merons and antimerons.

Interfacial ferroelectricity may emerge in moiré superlattices. Here, the authors find that the polarized charge is much larger than the capacity of the moiré miniband and the associated anomalous screening exists outside the band.

Twisted 2D materials have recently emerged as a controllable quantum simulator platform. Here, the authors apply the same approach to tune the edge states of zigzag graphene nanoribbons, showing a unique degree of freedom represented by the lateral stacking offset of the 1D nanostructures.

The mechanism of current-driven magnetization switching in twisted bilayer graphene (TBG) is poorly understood. Here, He et al. show that a small current can generate a large orbital magnetization due to symmetry breaking by the twisting and substrate in TBG, leading to a giant orbital magnetoelectric effect.

Spin-based electronics offers significantly improved efficiency, but a major challenge is the electric manipulation of spin. Here, Powalla et al find a large gate induced spinpolarization in graphene/WTe2 heterostructures, illustrating the potential of such heterostructures for spintronics.

The reduced dimensions of 2D magnets expose their magnetic anisotropy, adding a twist into the system provides another degree of freedom to explore. Here, the authors use stochastic Landau–Lifshitz-Gilbert simulations to investigate ground-state topological spin textures induced by interlayer fields in twisted bilayer CrI3.