Moiré engineering1–3 of van der Waals magnetic materials4–9 can yield new magnetic ground states via competing interactions in moiré superlattices10–13. Theory predicts a suite of interesting phenomena, including multiflavour magnetic states10, non-collinear magnetic states10–13, moiré magnon bands and magnon networks14 in twisted bilayer magnetic crystals, but so far such non-trivial magnetic ground states have not emerged experimentally.

Moiré heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moiré bands in heterobilayer TMDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling ν=2 (two holes per moiré unit cell) and a valley-polarized quantum anomalous Hall state at filling ν=1 were observed in AB stacked moiré MoTe2/WSe2 heterobilayers.

Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moiré materials provide a highly tuneable platform for studies of electron correlation1–12. Correlation-driven phenomena, including the Mott insulator2–5, generalized Wigner crystals2,6,9, stripe phases10 and continuous Mott transition11,12, have been demonstrated. However, non-trivial band topology has remained unclear. Here we report the observation of a quantum anomalous Hall effect in AB-stacked MoTe2 /WSe2 moiré heterobilayers.

We demonstrate a mechanism for magnetoresistance oscillations in insulating states of two-dimensional (2D) materials arising from the interaction of the 2D layer and proximal graphite gates. We study a series of devices based on different 2D systems, including mono- and bilayer Td-WTe2, MoTe2/WSe2 moiré heterobilayers, and Bernal-stacked bilayer graphene, which all share a similar graphite-gated geometry.

Excitonic insulators (EIs) arise from the formation of bound electron–hole pairs (excitons)1,2 in semiconductors and provide a solid-state platform for quantum many-boson physics3–8. Strong exciton–exciton repulsion is expected to stabilize condensed superfluid and crystalline phases by suppressing both density and phase fluctuations8–11. Although spectroscopic signatures of EIs have been reported6,12–14, conclusive evidence for strongly correlated EI states has remained elusive.

Ferromagnetism in two-dimensional materials presents a promising platform for the development of ultrathin spintronic devices with advanced functionalities. Recently discovered ferromagnetic van der Waals crystals such as CrI3, readily isolated two-dimensional crystals, are highly tunable through external fields or structural modifications. However, there remains a challenge because of material instability under air exposure. Here, we report the observation of an air-stable and layer-dependent ferromagnetic (FM) van der Waals crystal, CrPS4, using magneto-optic Kerr effect microscopy.

Van der Waals moiré materials have emerged as a highly controllable platform to study electronic correlation phenomena1–17. Robust correlated insulating states have recently been discovered at both integer and fractional filling factors of semiconductor moiré systems10–17. In this study we explored the thermodynamic properties of these states by measuring the gate capacitance of MoSe2/WS2 moiré superlattices. We observed a series of incompressible states for filling factors 0–8 and anomalously large capacitance in the intervening compressible regions.

The evolution of a Landau Fermi liquid into a non-magnetic Mott insulator with increasing electronic interactions is one of the most puzzling quantum phase transitions in physics1–6. The vicinity of the transition is believed to host exotic states of matter such as quantum spin liquids4–7, exciton condensates8 and unconventional superconductivity1. Semiconductor moiré materials realize a highly controllable Hubbard model simulator on a triangular lattice9–22, providing a unique opportunity to drive a metal–insulator transition (MIT) via continuous tuning of the electronic interactions.

The strong Ising spin–orbit coupling in certain two-dimensional transition metal dichalcogenides can profoundly affect the superconducting state in few-layer samples. For example, in NbSe2, this effect combines with the reduced dimensionality to stabilize the superconducting state against magnetic fields up to 35 T, and could lead to topological superconductivity. Here we report a two-fold rotational symmetry of the superconducting state in few-layer NbSe2 under in-plane external magnetic fields, in contrast to the three-fold symmetry of the lattice.

Stripe phases, in which the rotational symmetry of charge density is spontaneously broken, occur in many strongly correlated systems with competing interactions1–11. However, identifying and studying such stripe phases remains challenging. Here we uncover stripe phases in WSe2/WS2 moiré superlattices by combining optical anisotropy and electronic compressibility measurements. We find strong electronic anisotropy over a large doping range peaked at 1/2 filling of the moiré superlattice. The 1/2 state is incompressible and assigned to an insulating stripe crystal phase.