Pair density wave and loop current promoted by van Hove singularities in moiré systems

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$\varphi$ in each triangular plaquette at $\varphi =\frac{\pi }{3}$ and $\varphi =\frac{\pi }{6}$ 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 $\varphi =\frac{\pi }{3}$. 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 moiré systems based on graphene and transition metal dichalcogenides.

20 pages, 10 figures

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Cited by in corpus (13)

• Intravalley spin-polarized superconductivity in rhombohedral tetralayer graphene
• Weak-Coupling Theory of Pair Density-Wave Instabilities in Transition Metal Dichalcogenides
• High-order Van Hove singularities and their connection to flat bands
• Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model
• Triplet Pair-Density Wave Superconductivity on the $\pi$-flux Square Lattice
• Fractional Chern Insulators in Twisted Bilayer MoTe${}_2$: A Composite Fermion Perspective
• Singlet, Triplet and Pair Density Wave Superconductivity in the Doped Triangular-Lattice Moiré System
• Chiral and nodal superconductors in t-J model with valley contrasting flux on triangular moiré lattice
• Self-consistent theory of $2\times 2$ pair density waves in kagome superconductors
• Density matrix renormalization group study of quantum-geometry-facilitated pair density wave order
• Microscopic Mechanism of Pair-, Charge- and Spin-Density-Wave Instabilities in Interacting D-Dimensional Fermi Liquids
• In-plane magnetic field-induced orbital FFLO superconductivity in twisted WSe${}_2$ homobilayers
• Pair-density-wave phase of strongly interacting electrons on the triangular lattice: A variational Monte Carlo study