  The nonreciprocal critical supercurrents endow the superconducting diode
effect (SDE) in noncentrosymmetric superconductors with time-reversal symmetry
breaking. Recently, it was reported that the SDE has been observed in
narrow-band superconductors such as twisted trilayer graphene with zero
magnetic field. In this work, we unveil the SDE in superconductors that host
narrow bands near Fermi energy, where the supercurrent has a significant
contribution from the wave-function quantum geometry. By establishing the
phenomenological Ginzburg-Landau theory, we show that besides the conventional
band dispersion effect arising from the Fermi surface asymmetry, the
microscopic origin of SDE from quantum geometry is the quantum metric dipole.
Importantly, in the flat-band limit where the attractive interaction strength
is much larger than the bandwidth, the supercurrent and diode effect
contributed from quantum geometry becomes the leading order. The
interaction-driven valley polarization which lifts the valley degeneracy is
also necessary. Our work reveals a band-geometric origin of nonreciprocity in
narrow-band superconductors.
