  We present a theory of the superfluid weight in multiband attractive Hubbard
models within the Bardeen-Cooper-Schrieffer (BCS) mean field framework. We show
how to separate the geometric contribution to the superfluid weight from the
conventional one, and that the geometric contribution is associated with the
interband matrix elements of the current operator. Our theory can be applied to
systems with or without time reversal symmetry. In both cases the geometric
superfluid weight can be related to the quantum metric of the corresponding
noninteracting systems. This leads to a lower bound on the superfluid weight
given by the absolute value of the Berry curvature. We apply our theory to the
attractive Kane-Mele-Hubbard and Haldane-Hubbard models, which can be realized
in ultracold atom gases. Quantitative comparisons are made to state of the art
dynamical mean-field theory and exact diagonalization results.
