Pair density wave facilitated by Bloch quantum geometry in nearly flat band multiorbital superconductors

Bloch electrons in multiorbital systems carry quantum geometric information characteristic of their wavevector-dependent interorbital mixing. The geometric nature impacts electromagnetic responses, and this effect carries over to the superconducting state, which receives a geometric contribution to the superfluid weight. In this paper, we show that this contribution could become negative under certain appropriate circumstances. This may facilitate the stabilization of Cooper pairings with real space phase modulation, i.e., the pair density wave order, as we demonstrate through two-orbital model Bogoliubov de-Gennes mean-field calculations. The quantum geometric effect therefore constitutes an intrinsic mechanism for the formation of such a novel phase of matter in the absence of external magnetic field.