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A simple yet paradigmatic model for the interplay of strong electroniccorrelations and geometric frustration is the triangular lattice Hubbard model.Recently it was proposed that moir\'e structures of transition metaldichalcogenides can be used to simulate extended versions that includenon-local density-density interactions. We study competing instabilities ofinteracting electrons in such an extended Hubbard model on the triangularlattice near a filling where the density of states has a Van Hove singularity.We employ a truncated-unity functional renormalization group approach toinvestigate two cases: a paradigmatic minimally extended Hubbard model and aspecific model with parameters that are applicable to hetero-bilayers oftransition metal dichalcogenides. We unravel rich phase diagrams, includingtendencies to spin-density-wave order and unconventional pairing, which cangive rise to topological superconductivity. We classify the symmetry of thesuperconducting instabilities according to their irreducible representationsand show that higher lattice harmonics are dominant when the nearest-neighborinteraction is sizable indicating pair formation between second-nearestneighbors. The phenomenological consequences can be enhanced spin and thermalquantum Hall responses in a topological superconductor.

physical review. b./physical review. b

Competing instabilities of the extended Hubbard model on the triangular  lattice: Truncated-unity functional renormalization group and application to  moir\'e materials