Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap like an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities. To date, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G0=e^2/h. Here we report transport evidence of a fractional QSH insulator in 2.1-degree-twisted bilayer MoTe2, which supports spin-Sz conservation and flat spin-contrasting Chern bands.

The electron’s kinetic energy plays a pivotal role in magnetism. While virtual electron hopping promotes antiferromagnetism in an insulator, real hopping processes usually favour ferromagnetism. However, in kinetically frustrated systems such as hole-doped triangular lattice Mott insulators, real hopping has instead been shown to favour antiferromagnetism. Kinetic frustration has also been predicted to induce a new quasiparticle, a bound state of the doped hole and a spin flip called a spin polaron, at intermediate magnetic fields, which could form an unusual metallic state.

The spin Hall effect (SHE), in which an electrical current generates a transverse spin current, plays an important role in spintronics for the generation and manipulation of spin-polarized electrons. The phenomenon originates from spin–orbit coupling. In general, stronger spin–orbit coupling favours larger SHEs but shorter spin relaxation times and diffusion lengths. However, correlated magnetic materials often do not support large SHEs.

Two-dimensional moiré materials are formed by overlaying two layered crystals with small differences in orientation or/and lattice constant, where their direct coupling generates moiré potentials. Moiré materials have emerged as a platform for the discovery of new physics and device concepts, but while moiré materials are highly tunable, once formed, moiré lattices cannot be easily altered. Here we demonstrate the electrostatic imprinting of moiré lattices onto a target monolayer semiconductor.

Moiré materials provide fertile ground for the correlated and topological quantum phenomena. Among them, the quantum anomalous Hall (QAH) effect, in which the Hall resistance is quantized even under zero magnetic field, is a direct manifestation of the intrinsic topological properties of a material and an appealing attribute for low-power electronics applications. The QAH effect has been observed in both graphene and transition metal dichalcogenide (TMD) moiré materials. It is thought to arise from the interaction-driven valley polarization of the narrow moiré bands.

The Chern insulator displays a quantized Hall effect without Landau levels. Theoretically, this state can be realized by engineering complex next-nearest-neighbour hopping in a honeycomb lattice—the so-called Haldane model. Despite its profound effect on the field of topological physics and recent implementation in cold-atom experiments, the Haldane model has not yet been realized in solid-state materials.

Moiré materials with superlattice periodicity many times the atomic length scale have shown strong electronic correlations and band topology with unprecedented tunability. Non-volatile control of the moiré potentials could allow on-demand switching of superlattice effects but has remained challenging to achieve. Here we demonstrate the switching of the correlated and moiré band insulating states, and the associated nonlinear anomalous Hall effect, by the ferroelectric effect.

The Kondo lattice—a matrix of local magnetic moments coupled through spin-exchange interactions to itinerant conduction electrons—is a prototype of strongly correlated quantum matter1–4. Usually, Kondo lattices are realized in intermetallic compounds containing lanthanide or actinide1,2. The complex electronic structure and limited tunability of both the electron density and exchange interactions in these bulk materials pose considerable challenges to studying Kondo lattice physics.

In spin torque magnetic memories, electrically actuated spin currents are used to switch a magnetic bit. Typically, these require a multilayer geometry including both a free ferromagnetic layer and a second layer providing spin injection. For example, spin may be injected by a non-magnetic layer exhibiting a large spin Hall effect, a phenomenon known as spin–orbit torque. Here we demonstrate a spin–orbit torque magnetic bit in a single two-dimensional system with intrinsic magnetism and strong Berry curvature.