Quantum Geometry And Off-Diagonal Long-Range Order In Multi-band Superconductor

In addition to a conventional contribution, the superfluid density in mutli-band superconductors, has a geometric contribution associated with the inter-band matrix element of the current operator. In the weakly dispersing or flat-band limit, this geometric contribution, which is proportional to the quantum metric of the band, dominates and determines the superfluid weight. In this talk, we will discuss the geometric contribution to the off-diagonal long-range order in multi-band superconductors. Off-diagonal long-range order of the density correlation functions is a characteristic property of superfluidity of helium-3 and superconductivity of BCS wavefunctions. We calculate the density correlation function and the large eigenvalue of density matrix of multiband systems, and isolate the geometric contribution to the off-diagonal long-range order.