Non-Abelian Gauge-Coupled Superconducting Pairs: A Yang–Mills Framework for Multicomponent and Topological Superconductivity

This theoretical study develops an effective framework for superconducting Cooper pairs interacting with both the electromagnetic U(1) gauge field and an emergent non-Abelian SU(2) Yang–Mills gauge field. The central assumption is that the internal spin, orbital, band, valley, sublattice, or pseudospin degrees of freedom of a multicomponent superconducting order parameter can be represented by a non-Abelian matter field rather than by a single complex scalar field.The conventional Ginzburg–Landau theory describes superconductivity throughan Abelian complex order parameter and consequently explains the Meissner effect,electromagnetic flux quantization, and Abrikosov vortices. However, it is not sufficientto describe superconductors whose order parameter contains dynamically coupledinternal components. In the present model, the scalar order parameter is replacedby a multiplet transforming under an internal SU(2) representation, while the electromagnetic U(1) symmetry is retained. The resulting gauge structure isG = U(1)em × SU(2)int.The effective theory contains the kinetic energy of the superconducting multiplet,the Maxwell field, the Yang–Mills field, a symmetry-breaking potential, and possiblegauge-mixing and topological terms. The framework predicts non-Abelian flux tubes,hybrid vortices, modified penetration depths, internal-state-dependent Josephsoneffects, monopole-like defects, and noncommuting vortex holonomies.The proposed theory is particularly relevant to multiband superconductors, spin–orbit-coupled materials, spin-triplet superconductors, magnetic superconductors,1 topological heterostructures, moiré systems, and quantum platforms with syntheticgauge fields. In condensed-matter applications, the non-Abelian gauge field should generally be interpreted as an emergent or effective connection generated by internal quantum degrees of freedom.