Chiral excitonic order from twofold van Hove singularities in kagome metals.

Recent experiments on kagome metals AV3Sb5 (A=K,Rb,Cs) identify twofold van Hove singularities (TvHS) with opposite concavity near the Fermi energy, generating two approximately hexagonal Fermi surfaces - one electron-like and the other hole-like. Here we propose that a TvHS generates a novel time-reversal symmetry breaking excitonic order - arising due to bound pairs of electrons and holes located at opposite concavity van Hove singularities. We introduce a minimal model for the TvHS and investigate interaction induced many-body instabilities via the perturbative renormalisation group technique and a free energy analysis. Specialising to parameters appropriate for the kagome metals AV3Sb5, we construct a phase diagram comprising chiral excitons, charge density wave and a region of coexistence. We propose this as an explanation of a diverse range of experimental observations in AV3Sb5. Notably, the chiral excitonic state gives rise to a quantum anomalous Hall conductance, providing an appealing interpretation of the observed anomalous Hall effect in kagome metals. Possible alternative realisations of the TvHS mechanism in bilayer materials are also discussed. We suggest that TvHS open up interesting possibilities for correlated phases, enriching the set of competing ground states to include excitonic order.

Tunable Superconductivity and Möbius Fermi Surfaces in an Inversion-Symmetric Twisted van der Waals Heterostructure.

We theoretically study a moiré superlattice geometry consisting of mirror-symmetric twisted trilayer graphene surrounded by identical transition metal dichalcogenide layers. We show that this setup allows us to switch on or off and control the spin-orbit splitting of the Fermi surfaces via application of a perpendicular displacement field D_{0} and explore two manifestations of this control: first, we compute the evolution of superconducting pairing with D_{0}; this features a complex admixture of singlet and triplet pairing and, depending on the pairing state in the parent trilayer system, phase transitions between competing superconducting phases. Second, we reveal that, with application of D_{0}, the spin-orbit-induced spin textures exhibit vortices which lead to "Möbius fermi surfaces" in the interior of the Brillouin zone: diabatic electron trajectories, which are predicted to dominate quantum oscillation experiments, require encircling the Γ point twice, making their Möbius nature directly observable. Further, we show that the superconducting order parameter inherits the unconventional, Möbius spin textures. Our findings suggest that this system provides a promising experimental avenue for systematically studying the impact of spin-orbit coupling on the multitude of topological and correlated phases in near-magic-angle twisted trilayer graphene.