  Bloch wave functions of electrons have properties called quantum geometry,
which has recently attracted much attention as the origin of intriguing
physical phenomena. In this paper, we introduce the notion of the
quantum-geometric pair potentials (QGPP) based on the generalized band
representation and thereby clarify how the quantum geometry of electrons is
transferred to the Cooper pairs they form. QGPP quantifies the deviation of
multiband superconductors from an assembly of single-band superconductors and
has a direct connection to the quantum-geometric corrections to thermodynamic
coefficients. We also discuss their potential ability to emulate exotic pair
potentials and engineer intriguing superconducting phenomena including
topological superconductivity.
