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Bloch electrons in multiorbital systems carry quantum geometric informationcharacteristic of their wavevector-dependent interorbital mixing. The geometricnature impacts electromagnetic responses, and this effect carries over to thesuperconducting state, which receives a geometric contribution to thesuperfluid weight. In this paper, we show that this contribution could becomenegative under certain appropriate circumstances. This may facilitate thestabilization of Cooper pairings with real space phase modulation, i.e. thepair density wave order, as we demonstrate through two-orbital model Bogoliubovde-Gennes mean-field calculations. The quantum geometric effect thereforeconstitutes an intrinsic mechanism for the formation of such a novel phase ofmatter in the absence of external magnetic field.

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