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More than 40 years after the discovery of the quantum Hall effect, the investigation of new variants of this phenomenon and of the exotic physics they represent is still a lively research topic. In this Viewpoint, five scientists involved in the very recent discovery of a new type of Hall effect — the fractional quantum anomalous Hall effect — discuss their results and their implications.

Topological Kondo insulators have been suggested in three-dimensional bulk materials like SmB₆, but they have not been observed in two-dimensional materials. Now, this is achieved in a transition metal dichalcogenide moiré bilayer.

Tunable moiré WSe₂ bilayers realize Hubbard-model physics, exhibiting antiferromagnetism, strange metals and superconducting domes, offering a controllable platform to study high-transition-temperature superconductivity.

Moiré systems formed by 2D atomic layers have widely tunable electrical and optical properties and host exotic, strongly correlated and topological phenomena, including superconductivity, correlated insulator states and orbital magnetism. In this Viewpoint, researchers studying different aspects of moiré materials discuss the most exciting directions in this rapidly expanding field.

Quantum emitters in atomically thin materials host optically addressable single spins. Here, the authors demonstrate spin selectivity in the preparation of the spin-valley state of site-controlled localized single holes in CrI3/WSe2 heterostructures.

A tunnel field-effect transistor with spin-dependent outputs that are voltage controllable and reversible can be created using a dual-gated graphene/CrI₃/graphene tunnel junction.

The valley degree of freedom in monolayer transition metal dichalcogenides can be addressed by optical means. Here, the authors develop a waveguide-based method to detect emission from dark excitons in single-layer WSe2, access the valley degree of freedom through the Zeeman effect, and demonstrate long valley lifetime of charged dark excitons.

The fabrication of high-quality WSe₂ monolayers makes it possible to access the fully valley- and spin-polarized structure of Landau levels theoretically predicted for transition metal dichalcogenides.

Circularly polarized light has been used to confine charge carriers in single-layer molybdenum disulphide entirely to a single energy-band valley, representing full valley polarization.

The authors present magnetotransport measurements of tetralayer WSe₂, which serves as a simulator for correlated Dirac fermion physics. They tune the interactions using the twist angle and electric field, resulting in a semimetal–Mott insulator transition.

Quantum oscillations are reported in Coulomb-coupled electron–hole double layers that originate from recurring transitions between competing excitonic insulator and layer-decoupled quantum Hall states.

Researchers have demonstrated that atomically thin materials can be highly reflective, contrary to general thinking. This finding could have technological implications for nanophotonics, optoelectronics and quantum optics.

Twisted transition metal dichalcogenide bilayers exhibit several emerging physical properties, but the connection to the underlying band structure singularities remains difficult to determine experimentally. Here, the authors characterize the influence of an electrically tunable van Hove singularity in twisted bilayer WSe₂ on its ferromagnetic and topological phases.

A new class of moiré materials based on monolayers with triangular lattices and low-energy states at the M points of the Brillouin zone is introduced, demonstrating emergent momentum-space non-symmorphic symmetries, a kagome plane-wave lattice structure, and potential quasi-one-dimensionality.

The authors imprint a moiré potential on a remote monolayer semiconductor through the moiré potential created in a remote MoSe₂/WS₂ moiré bilayer. The imprinted moiré potential enables gate-controlled generation of flat bands and correlated insulating states in the targeted monolayer.

Robust superconductivity is observed in twisted bilayer tungsten diselenide (WSe₂) on the verge of Coulomb-induced charge localization around half-band filling and zero external displacement fields.

Kondo physics has been observed in moiré bilayers, but the expected magnetic transitions have not been reported. Now, a metal–insulator transition with ferromagnetic order that develops at nearly the same time is reported in a moiré bilayer.

Twisted WSe₂ AB-homobilayers enable the realization of bilayer Hubbard models in the weak interlayer hopping limit.

A nonlinear anomalous Hall effect, allowed for certain point group symmetries, is observed in metallic WTe₂.

The superconducting properties of NbSe₂ as it approaches the monolayer limit are investigated by means of magnetotransport measurements, uncovering evidence of spin–momentum locking.

The application of electric fields enables reversible switching of the magnetic order of CrI₃ bilayers between antiferromagnetic and ferromagnetic states.

A new chemical vapour deposition method enables transition-metal dichalcogenide (TMD) monolayers to be grown directly on insulating silicon dioxide wafers, demonstrating the possibility of wafer-scale batch fabrication of high-performance devices with TMD monolayers.

The valley Hall effect in bilayer MoS₂ transistors can be controlled using a gate voltage and the induced valley polarization imaged with Kerr microscopy.

Electrostatic doping in vertical van der Waals CrI₃–graphene heterostructures provides means to control the magnetic properties of monolayer and bilayer CrI₃.

Enhanced electron–phonon interactions in mono- and few-layer NbSe₂ result in a significantly increased transition temperature of charge density waves compared with values in the bulk.

Monolayer graphene has no electronic band gap. Bilayer graphene does, and can be controlled by an electric field. And for trilayer graphene, infrared transmission measurements indicate both situations are possible depending on the stacking of the layers.

The appealing electronic properties of the monolayer semiconductor molybdenum disulphide make it a candidate material for electronic devices. The observation of tightly bound trions in this system—which have no analogue in conventional semiconductors—opens up possibilities for controlling these quasiparticles in future optoelectronic applications.

Graphene, an atom-thin carbon sheet is interesting for its fundamental properties as well as for its possible applications in electronics, is not strictly two-dimensional. Microscopic corrugations, or ripples, have been observed in all graphene sheets so far. Direct experimental study of the physics of such ripples has been hindered by the lack of flat graphene layers. Ultraflat graphene is now achieved through its deposition on the atomically flat terraces of cleaved mica surfaces.

Valley magnetization in single-layer MoS₂ is demonstrated by breaking the three-fold rotational symmetry via uniaxial stress. The results are consistent with a theoretical model of valley magnetoelectricity driven by Berry curvature effects.

Tunnelling spectroscopy reveals a continuous closing of the superconducting gap at low temperature and high in-plane magnetic field in few-layer NbSe₂, due to the Ising spin–orbit coupling of these materials.

An optical readout technique for the chemical potential of an arbitrary two-dimensional material is realized using a monolayer transition metal dichalcogenide semiconductor sensor whose optical response sharply depends on the chemical potential.

The Haldane model is a paradigmatic example of topological behaviour but has not previously been implemented in condensed-matter experiments. Now a moiré bilayer is shown to realize this model with the accompanying quantized transport response.

Transport evidence of a fractional quantum spin Hall insulator is reported in 2.1°-twisted bilayer MoTe₂, which supports spin-S_z conservation and flat spin-contrasting Chern bands.

Spin polarons, bound states of a doped carrier and a spin flip excitation, are observed in a transition metal moiré bilayer.

Thermodynamic evidence of both integer and fractional Chern insulators at zero magnetic field is reported in small-angle twisted bilayer MoTe₂ by combining the local electronic compressibility and magneto-optical measurements.

Intrinsic ferroelectricity in bilayer WTe₂ can be used for electrical switching of the centred-rectangular moiré potential in WTe₂/WSe₂ heterostructures.

A giant spin Hall effect with long spin diffusion length and coexisting with ferromagnetism is observed in AB-stacked MoTe₂/WSe₂ moiré hetero-bilayers.

A Kondo lattice was realized in AB-stacked MoTe₂/WSe₂ moiré bilayers and widely and continuously gate-tunable Kondo temperatures were demonstrated.

The Wigner-Mott insulator is driven by extended Coulomb repulsion, rather than the on-site Coulomb repulsion of the Mott insulator. Here, the authors observe a continuous bandwidth-tuned transition between a metal and a Wigner-Mott insulator in a MoSe₂/WS₂ moiré superlattice at fractional lattice filling.

An electric-field-induced topological phase transition from a Mott insulator to a quantum anomalous Hall insulator in near-60-degree-twisted (or AB-stacked) MoTe₂/WSe₂ heterobilayers is reported.

So far only signatures of excitonic insulators have been reported, but here direct thermodynamic evidence is provided for a strongly correlated excitonic insulating state in transition metal dichalcogenide semiconductor double layers.

The interaction strength in moiré superlattices is tuned to drive a continuous metal-to-insulator transition at a fixed electron density.

The moiré pattern that is formed between well-aligned graphene and hexagonal boron nitride can modify the properties of WSe₂ (placed close by without intentional angle alignment), leading to the formation of a mini Brillouin zone and the folding of the bands in WSe₂.

Study of WSe₂/WS₂ moiré superlattices reveals the phase diagram of the triangular-lattice Hubbard model, including a Mott insulating state at half-filling and a possible magnetic quantum phase transition near 0.6 filling.

An optical sensing technique reveals an abundance of correlated insulating states at fractional fillings of moiré superlattices that are proposed to arise from a series of charge-ordered states.

A two-fold rotational symmetry is observed in the superconducting state of NbSe₂. This is strikingly different from the three-fold symmetry of the lattice, and suggests that a mixed conventional and unconventional order parameter exists in this material.

Switching of magnetic behaviour is one of the main ideas that drives spintronics. Now, magnetic switching via spin-orbit torque is shown in a moiré bilayer, introducing a platform for spintronic applications.

The electronic and optical properties and the recent progress in applications of 2D semiconductor transition metal dichalcogenides with emphasis on strong excitonic effects, and spin- and valley-dependent properties are reviewed.

Integration of 2D semiconductor optoelectronics with silicon photonics opens a new path for on-chip point-to-point optical communications.