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Graphene on boron nitride gives rise to a moiré superlattice displaying the Hofstadter butterfly: a fractal dependence of energy bands on external magnetic fields. Now, by means of capacitance spectroscopy, further aspects of this system are revealed—most notably, suppression of quantum Hall antiferromagnetism at particular commensurate magnetic fluxes.

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.

Chern numbers characterize the quantum Hall effect conductance—non-zero values are associated with topological phases. Previously only spotted in electronic systems, they have now been measured in ultracold atoms subject to artificial gauge fields.

Moiré superlattices arising in bilayer graphene coupled to hexagonal boron nitride provide a periodic potential modulation on a length scale ideally suited to studying the fractal features of the Hofstadter energy spectrum in large magnetic fields.

The combination of interparticle interactions and a synthetic gauge field leads to chirality in the propagation dynamics of particles in a ladder-like lattice.

The robustness of edge states against external influence is a phenomenon that has been successfully applied to electron transport. A study now predicts that the same concept can also lead to improved optical devices. Topological protection might, for example, reduce the deleterious influence of disorder on coupled-resonator optical waveguides.

Here, the authors show that Brown-Zak fermions in graphene-on-boron-nitride superlattices exhibit mobilities above 10⁶ cm²/V s and micrometer scale ballistic transport.

An atomic single electron transistor, which utilizes a single atomic defect in a van der Waals material as an ultrasensitive, high-resolution potential sensor, is used to image the electrostatic potential within a moiré unit cell.

Placing graphene on a boron nitride substrate and accurately aligning their crystallographic axes, to form a moiré superlattice, leads to profound changes in the graphene’s electronic spectrum.

Mobile impurities can be useful probes of quantum states. Here, the authors theoretically identify polarons formed on the edge of topological insulating states, termed chiral polarons, that can be used to probe topological matter.

The reliable fabrication of 2D heterostructures with controllable moiré patterns is important for the investigation of their emergent physical properties. Here, the authors report an alignment technique enabling the fabrication of double-aligned hBN/graphene/hBN supermoiré lattice structures with a yield close to 100%.

Probing topological orders in many-body systems remains a major challenge, which requires bulk-edge correspondence. Here, Grusdt et al.present an approach to show that fractional charges can be directly probed in the bulk of fractional quantum Hall systems using mobile impurities through interferometric measurements.

The authors report an experimental study of the Hall effect measuring electrical quantities in ultracold fermionic quantum simulators. This provides a way forward in measuring transport properties in these platforms and verifying long-standing theoretical predictions.

Precise control of the relative orientation of two two-dimensional layers enables reproducible fabrication of heterostructure devices. Here, the authors show that graphene rotates towards the crystallographic direction of a boron-nitride substrate due to the interplay between van der Waals and elastic energies.

Synthetic dimensions provide a way to artificially engineer extra spatial dimensions through other degrees of freedom. We review how synthetic dimensions have emerged as a promising tool for quantum simulations of topological lattice models in atomic, molecular and optical systems.

Thouless introduced the idea of a topological charge pump: the quantized motion of charge due to the slow cyclic variation of a periodic potential. This topologically protected transport has now been realized with ultracold bosonic atoms.

Topological states that are created from strong electron–electron interactions at half-integer superlattice fillings are observed at zero magnetic field.

By implementing a 2D topological charge pump using ultracold bosonic atoms, the theoretically predicted 4D integer quantum Hall effect is confirmed experimentally.

Scaling theory governs much of the physics around us. Here, the authors present experimental evidence showcasing the breakdown of logarithmic scaling in electric circuits and the emergence of fractal-like patterns in impedance scaling relationships.

Arrays of superconducting transmon qubits can be used to study the Bose–Hubbard model. Synthetic electromagnetic fields have now been added to this analogue quantum simulation platform.

Spin–orbit coupling is implemented in an optical lattice clock using a narrow optical transition in fermionic 87Sr atoms, thus mitigating the heating problems of previous experiments with alkali atoms and offering new prospects for future investigations.

Investigating the inner structure of baryons is important to further our understanding of the strong interaction. Here, the BESIII Collaboration extracts the absolute value of the ratio of the electric to magnetic form factors and its relative phase for e + e − → J/ψ → ΛΣ decays, enhancing the signal thanks to the vacuum polarisation effect at the J/ψ peak.

Efficient manipulation of quantum states is a key step towards applications in quantum information, quantum metrology, and nonlinear optics. In this paper, the authors show that 1D atomic arrays in a periodic magnetic field can realize an effective 2D Hofstadter-butterfly-like model with synthetic dimensions exhibiting super- and sub-radiant topological edge states despite featuring long-range interactions.

In addition to its low-field superconducting state, UTe₂ features a re-entrant superconducting state when high magnetic fields are applied at a particular range of angles. Here, the authors demonstrate that the high-field re-entrant superconducting state survives even when the low-field superconducting state is destroyed by disorder.

Phases of matter can host different transport behaviours, ranging from diffusion to localization. Anomalous transport has now been observed in an interacting Bose gas in a one-dimensional lattice subject to a pulsed incommensurate potential.

Standard topological invariants commonly used in static systems are not enough to fully capture the topological properties of Floquet systems. In a periodically driven quantum gas, chiral edge modes emerge despite all Chern numbers being equal to zero.

Non-volatile electrical switching of magnetic order in an orbital Chern insulator is experimentally demonstrated using a moiré heterostructure and analysis shows that the effect is driven by topological edge states.

Here, the authors show that the interatomic coupling between two layers of a 2D crystal can be determined by studying the angle-resolved photoemission spectra of a trilayer structure with one aligned and one twisted interface, and obtain the inter-atomic coupling for carbon atoms in twisted trilayer graphene.

This study explores reentrant topological behaviors in a 1D system of interacting fermionic atoms trapped in an optical lattice obtained by overlapping two commensurable superlattices. It reveals a series of trivial-topological transitions and a spin-density wave pattern influenced by the lattice’s structure and atomic interactions, which could be observed in cold-atom experiments in future experimental setups.

During HCMV infection, mitochondrial progenies derived from peripheral fragmentation can be protected from mitophagy and result in elevated respiration through a mechanism leveraging ER-mitochondria and inter-mitochondria membrane contacts.

Electrons are confined to an artificial Sierpiński triangle. Microscopy measurements show that their wavefunctions become self-similar and their quantum properties inherit a non-integer dimension between 1 and 2.

Individual carbon monoxide molecules on a copper surface can be manipulated with scanning tunnelling microscopy to realize an electronic Lieb lattice.

Moiré superlattice exciton states are observed in WSe₂/WS₂ heterostructures with closely aligned layers.

Visible light can induce writing and erasing of charge doping in graphene/boron nitride heterostructures while maintaining high carrier mobility.

Diurnal and seasonal temperature variations of comet 67P’s nucleus are monitored by Rosetta’s imaging spectrometer VIRTIS during two months in 2014. The nucleus appears thermally homogeneous, with the temperature fluctuations mainly controlled by self-heating and heliocentric distance.

In social insect colonies, workers perform a variety of tasks, such as foraging, brood care and nest construction. As the needs of the colony change, and as resources become available, colonies adjust the numbers of workers engaged in each task. Task allocation is the process that results in specific workers being engaged in specific tasks, in numbers appropriate to the current situation.

Global energy budgets of planets are important to understand their climate system. Here, the authors show long-term multi-instrument observations from Cassini spacecraft, which reveals dynamical imbalances of Saturn’s global energy budget.

Boundary-localized bulk eigenstates given by the non-Hermitian skin effect are observed in a non-reciprocal topological circuit. A fundamental revision of the bulk–boundary correspondence in an open system is required to understand the underlying physics.

Artificial structures with novel thermal properties are promising for heat-transfer applications. This Review provides an overview of thermal metamaterials and devices, discussing the working principles underlying the manipulation of thermal conduction and radiation at different length scales.