Berry Curvature and Spin-One Color Superconductivity

Abstract

We explore the interplay between Berry curvature and topological properties in single-flavor color superconductors, where quarks form spin-one Cooper pairs. By deriving a new relation, we connect the topological nodal structure of the gap function in momentum space to the (nonabelian) Berry flux associated with paired quarks. This generalizes the early work by Li and Haldane [Phys. Rev. Lett. 120, 067003 (2018)] to systems with additional internal quantum numbers, such as color. In the ultrarelativistic limit, we uncover rich topological structures driven by the interplay of spin, chirality, and color. Specifically, we identify chirality-induced topological nodes in the transverse (opposite chirality pairing) polar and A phases. In contrast, the color-spin-locking phase lacks these nodes due to a nontrivial color Berry flux, which in turn induces gapless excitations with total Berry monopole charges of $\pm 3/2-$differing from conventional Weyl fermions. Our findings can be potentially extended to other fermionic systems carrying additional internal degrees of freedom.