korn-luttinger superconductivity in skyrmion lattice model

The Kohn–Luttinger mechanism provides a theoretical route to superconductivity driven purely by repulsive electron–electron interactions. In this framework, effective attractive interactions can emerge in certain angular momentum channels, leading to unconventional pairing even in the absence of phonon mediation. We find that the skyrmion lattice model serves as a new platform for studying Kohn–Luttinger–like superconductivity. In this system, the coexistence of a flat band and nontrivial quantum geometry gives rise to a variety of unconventional superconducting behaviors, such as a pronounced peak in the superconducting transition temperature near the band edge and an order parameter that remains nearly invariant with respect to changes in the chemical potential. Remarkably, the pairing channels are no longer labeled by angular momentum but instead by translational quantum numbers in momentum space. Within this novel pairing channel, the interaction under the random phase approximation exhibits a strong effective attraction, providing a microscopic origin for the emergence of such unconventional superconductivity.