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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.

Hydrogen peroxide (H2O2) is a major reactive oxygen species in unicellular and multicellular organisms, and is produced extracellularly in response to external stresses and internal cues(1-4). H2O2 enters cells through aquaporin membrane proteins and covalently modifies cytoplasmic proteins to regulate signalling and cellular processes. However, whether sensors for H2O2 also exist on the cell surface remains unknown. In plant cells, H2O2 triggers an influx of Ca2+ ions, which is thought to be involved in H2O2 sensing and signalling. Here, by using forward genetic screens based on Ca2+ imaging, we isolated hydrogen-peroxide-induced Ca(2+)increases (hpca) mutants in Arabidopsis, and identified HPCA1 as a leucine-rich-repeat receptor kinase belonging to a previously uncharacterized subfamily that features two extra pairs of cysteine residues in the extracellular domain. HPCA1 is localized to the plasma membrane and is activated by H2O2 via covalent modification of extracellular cysteine residues, which leads to autophosphorylation of HPCA1. HPCA1 mediates H2O2-induced activation of Ca2+ channels in guard cells and is required for stomatal closure. Our findings help to identify how the perception of extracellular H2O2 is integrated with responses to various external stresses and internal cues in plants, and have implications for the design of crops with enhanced fitness.

HPCA1, a member of a previously uncharacterized subfamily of leucine-rich-repeat receptor-like kinases, is the hydrogen-peroxide sensor at the plasma membrane in Arabidopsis.