This paper studies how uneven distributions of Berry curvature in an electronic band can change the nature of chiral superconductivity. Berry curvature is a property of electronic bands that acts like a magnetic field in momentum space. The authors show that when Berry curvature is non-uniform, the superconducting gap can develop vortex‑like phase windings in momentum space away from the usual high‑symmetry points.

To explore this, the researchers use a controllable continuum model called the λN‑model. This model represents an isolated, spinless electronic band whose Berry curvature profile and total Berry flux (the Chern number) can be tuned independently. Instead of using a weak‑coupling approximation that only pairs electrons near the Fermi surface, they solve the full nonlinear Bardeen–Cooper–Schrieffer (BCS) gap equation on the whole band. That allows pairing across a large patch of momentum space and lets electrons probe the full Berry curvature landscape.

They find that non‑uniform Berry curvature enriches the superconducting order parameter by nucleating momentum‑space vortices in the gap function. Vortices tend to appear near regions of large Berry curvature and their formation can lower the condensation energy, so stronger interactions and sharply peaked Berry curvature make vortex nucleation more likely. By tuning the model parameters, the authors identify regimes of vortex nucleation and regimes where the number of vortices saturates. They also report that vortices can appear along rings of maximal Berry curvature in some geometries relevant to rhombohedral graphene multilayers.

The paper connects these vortices to topology. The total vorticity in the projected gap is constrained by the parent‑band Chern number: the total gap vorticity equals twice the Chern number of the normal‑state band. However, the topological invariant of the Bogoliubov–de Gennes (BdG) quasiparticles—the BdG Chern number—is determined only by the vortices that lie inside the occupied region of momentum space. In their formulation, the BdG Berry curvature is set by a momentum‑space phase current (an analogue of a supercurrent), and under mild assumptions the BdG Chern number equals Q, the signed sum of vortex windings enclosed by the occupied states. These relations give a clear link between parent‑band topology and superconducting topology.