Pair density wave and loop current promoted by van Hove singularities in moir\'e systems

TL;DR

This paper demonstrates that van Hove singularities in moiré systems can promote pair density wave and loop current orders, with potential tunability via electric fields, revealing new possible ground states in these materials.

Contribution

It shows that van Hove singularities can enhance pair density wave and loop current instabilities in moiré systems, with detailed analysis of conditions and topological properties.

Findings

PDW susceptibility can be promoted to leading order at specific flux values.

Loop current order with quantum anomalous Hall effect can become the ground state.

Chiral d-wave PDW can dominate upon doping or finite next-nearest neighbor hopping.

Abstract

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$\phi$ in each triangular plaquette at $\phi=\frac{\pi}{3}$ and $\phi=\frac{\pi}{6}$ in moir\'e 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 $\phi=\frac{\pi}{3}$. 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 moir\'e systems based on graphene and transition metal dichalcogenides.