We theoretically show that in the presence of conventional or higher order van Hove singularities(VHS), the bare finite momentum pairing, also known as the pair density wave (PDW), susceptibility can be promoted to the same order of the most divergent bare BCS susceptibility through a valley-contrasting flux 3$ϕ$ in each triangular plaquette at $ϕ=\fracπ{3}$ and $ϕ=\fracπ{6}$ in moiré systems. This makes the PDW order a possible leading instability for an electronic system with repulsive interactions. We confirm that it indeed wins over all other instabilities and becomes the ground state under certain conditions through the renormalization group calculation and a flux insertion argument. Moreover, we also find that a topological nontrivial loop current order becomes the leading instability if the Fermi surface with conventional VHS is perfectly nested at $ϕ=\fracπ{3}$. Similar to the Haldane model, this loop current state has the quantum anomalous Hall effect. If we dope this loop current state or introduce a finite next-nearest neighbour hopping $t^{\prime}$, the chiral $d$-wave PDW becomes the dominant instability. Experimentally, the flux can be effectively tuned by an out-of-plane electric field in moiré systems based on graphene and transition metal dichalcogenides.
Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials
Relativistic Mott transition and high-order van Hove singularity in twisted double bilayer WSe${}_2$: mean-field and functional renormalization group study
Van Hove Singularity-Driven Topological Magnetism in Twisted MoTe2
University of Washington（华盛顿大学）；Harvard University（哈佛大学）；Massachusetts Institute of Technology（麻省理工学院）；University of California - Santa Barbara（加利福尼亚大学圣巴巴拉分校）；National Institute for Materials Science（国立材料研究所）
