Mechanisms of Pair Density Wave Order from Electron Repulsion*

Pair-density-wave (PDW) is an exotic superconducting state in which two fermions with finite center-of-mass momentum form Cooper pair and condense, breaking the translation symmetry. Although the earliest proposal for realising this state in a strong magnetic field, also know as Fulde-Ferrell-Larkin-Ovchinnikov state, has been more or less well understood, an increasing number of experiments on different correlated materials in recent years have claimed to discover various kinds of PDW state without magnetic field. This, from a theoretical point of view, calls for a timely study of the mechanism behind the zero-field PDW state. In this talk, I will discuss several examples where PDW can be realized as the leading instability of an itinerant fermion system as a result of electron interaction. Usually, the PDW is not a weak coupling instability. I will first show, based on a pair-hopping Hamiltonian, that the onset of PDW from electron repulsion requires the suppression of on-site Hubbard interaction, and the pairing strength has to surpass some threshold value. Then, turning to physical systems, I will discuss how the PDW can be possibly realized in kagome metals, due to a special reason known as sublattice interference which emerges when the system is doped to the p-type Van Hove singularity (interestingly the same reason can also induce time-reversal symmetry broken density waves). Complementary to the strong coupling analysis, I will also show that, under certain circumstances such as Fermi surface nesting in particle-particle channel or the presence of higher order Van Hove singularity, the PDW can be promoted as a weak coupling competing order. For physical systems, the twisted bilayer transition-metal-dichalcogenides and doped Haldane-Hubbard model will be discussed. Lastly, the multiband systems as promising platforms for PDW will be discussed, where the fermion interactions projected to certain band are accompanied by form factors which can carry nontrivial momentum dependence and realize finite momentum pairing.