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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.

Single-cell RNA sequencing and spatial transcriptomics reveal that the somitogenesis clock is active in mouse gastruloids, which can be induced to generate somites with the correct rostral-caudal patterning.

Gastruloids are three-dimensional aggregates of embryonic stem cells that display key features of mammalian development after implantation, including germ-layer specification and axial organization(1-3). To date, the expression pattern of only a small number of genes in gastruloids has been explored with microscopy, and the extent to which genome-wide expression patterns in gastruloids mimic those in embryos is unclear. Here we compare mouse gastruloids with mouse embryos using single-cell RNA sequencing and spatial transcriptomics. We identify various embryonic cell types that were not previously known to be present in gastruloids, and show that key regulators of somitogenesis are expressed similarly between embryos and gastruloids. Using live imaging, we show that the somitogenesis clock is active in gastruloids and has dynamics that resemble those in vivo. Because gastruloids can be grown in large quantities, we performed a small screen that revealed how reduced FGF signalling induces a short-tail phenotype in embryos. Finally, we demonstrate that embedding in Matrigel induces gastruloids to generate somites with the correct rostral-caudal patterning, which appear sequentially in an anterior-to-posterior direction over time. This study thus shows the power of gastruloids as a model system for exploring development and somitogenesis in vitro in a high-throughput manner.