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Twisted bilayer graphene (TBG) provides a unique framework to elucidate the interplay between strong correlations and topological phenomena in two-dimensional systems. The existence of multiple electronic degrees of freedom - charge, spin, and valley - gives rise to a plethora of possible ordered states and instabilities. Identifying which of them are realized in the regime of strong correlations is fundamental to shed light on the nature of the superconducting and correlated insulating states observed in the TBG experiments. Here, we use unbiased, sign-problem-free quantum Monte Carlo simulations to solve an effective interacting lattice model for TBG at charge neutrality. Besidesmore » the usual cluster Hubbard-like repulsion, this model also contains an assisted-hopping interaction that emerges due to the nontrivial topological properties of TBG. Such a nonlocal interaction fundamentally alters the phase diagram at charge neutrality, gapping the Dirac cones even for infinitesimally small interactions. As the interaction strength increases, a sequence of different correlated insulating phases emerge, including a quantum valley Hall state with topological edge states, an intervalley-coherent insulator, and a valence bond solid. The charge-neutrality correlated insulating phases discovered here provide the sought-after reference states needed for a comprehensive understanding of the insulating states at integer fillings and the proximate superconducting states of TBG.« less

The B20 chiral magnets with broken inversion symmetry and C₄ rotation symmetry have attracted much attention. The broken inversion symmetry leads to the Dzyaloshinskii–Moriya that gives rise to the helical and Skyrmion states.Wereport the unusual magnetoresistance (MR) of B20 chiral magnet Fe_0.85Co_0.15Si that directly reveals the broken C₄ rotation symmetry and shows the anisotropic scattering by Skyrmions with respect to the current directions. The intimacy between unusual MR and broken symmetry is well confirmed by theoretically studying an effective Hamiltonian with spin–orbit coupling. In conclusion, the unusual MR serves as a transport signature for the Skyrmion phase.