Paramagnetic contribution in superconductors with different-mass Cooper pairs

Cooper pairs formed by two electrons with different effective mass are common in multiband superconductors, pair density wave states and other superconducting systems with multi-degrees of freedom. In this work, we show that there are paramagnetic contributions to the superfluid stiffness in superconductors with different-mass Cooper pairs. This paramagnetic response is owing to the relative motion between two electrons with different mass. We investigate the paramagnetic contributions based on the linear response theory in two-band superconductors with interband pairings and in pair density wave states respectively. Our results offer a new perspective to the electromagnetic superfluid stiffness in unconventional superconductors.