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Study of WSe2/WS2 moire 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.

The Hubbard model, formulated by physicist John Hubbard in the 1960s(1), is a simple theoretical model of interacting quantum particles in a lattice. The model is thought to capture the essential physics of high-temperature superconductors, magnetic insulators and other complex quantum many-body ground states(2,3). Although the Hubbard model provides a greatly simplified representation of most real materials, it is nevertheless difficult to solve accurately except in the one-dimensional case(2,3). Therefore, the physical realization of the Hubbard model in two or three dimensions, which can act as an analogue quantum simulator (that is, it can mimic the model and simulate its phase diagram and dynamics(4,5)), has a vital role in solving the strong-correlation puzzle, namely, revealing the physics of a large number of strongly interacting quantum particles. Here we obtain the phase diagram of the two-dimensional triangular-lattice Hubbard model by studying angle-aligned WSe2/WS2 bilayers, which form moire superlattices(6) because of the difference between the lattice constants of the two materials. We probe the charge and magnetic properties of the system by measuring the dependence of its optical response on an out-of-plane magnetic field and on the gate-tuned carrier density. At half-filling of the first hole moire superlattice band, we observe a Mott insulating state with antiferromagnetic Curie-Weiss behaviour, as expected for a Hubbard model in the strong-interaction regime(2,3,7-9). Above half-filling, our experiment suggests a possible quantum phase transition from an antiferromagnetic to a weak ferromagnetic state at filling factors near 0.6. Our results establish a new solid-state platform based on moire superlattices that can be used to simulate problems in strong-correlation physics that are described by triangular-lattice Hubbard models.

Extensive efforts have been made to harvest energy from water in the form of raindrops(1-6), river and ocean waves(7,8), tides(9) and others(10-17). However, achieving a high density of electrical power generation is challenging. Traditional hydraulic power generation mainly uses electromagnetic generators that are heavy, bulky, and become inefficient with low water supply. An alternative, the water-droplet/solid-based triboelectric nanogenerator, has so far generated peak power densities of less than one watt per square metre, owing to the limitations imposed by interfacial effects-as seen in characterizations of the charge generation and transfer that occur at solid-liquid(1-4) or liquid-liquid(5,18) interfaces. Here we develop a device to harvest energy from impinging water droplets by using an architecture that comprises a polytetrafluoroethylene film on an indium tin oxide substrate plus an aluminium electrode. We show that spreading of an impinged water droplet on the device bridges the originally disconnected components into a closed-loop electrical system, transforming the conventional interfacial effect into a bulk effect, and so enhancing the instantaneous power density by several orders of magnitude over equivalent devices that are limited by interfacial effects.

A device involving a polytetrafluoroethylene film, an indium tin oxide substrate and an aluminium electrode allows improved electricity generation from water droplets, which bridge the previously disconnected circuit components.