Pair density wave order in multiband systems

An indispensable ingredient for pair density wave (PDW) superconductivity is the presence of an attractive pairing interaction at finite momentum. Here, we show how this condition can be met with straightforward electron-density interactions in multiband systems. The electron-density interaction, when projected to the band basis, acquires form factors with nontrivial momentum dependence and thereby exhibits a potential tendency to a finite-momentum pairing instability. By applying a mean field analysis to two simple multiband models, the checkerboard lattice and three-band Hubbard model, we find that PDW order can indeed become the leading instability if a strong nearest-neighbor attraction is present. Moreover, the condition for the transition from a uniform superconductor to a PDW superconductor is shown via a simple quantum geometric argument.