A Variational Density-Functional Formulation for Emergent SU(2) Gauge Fields in Two-Dimensional Materials

This work develops a variational density-functional framework for investigatingthe influence of an emergent non-Abelian SU(2) gauge field on the magnetic andtopological properties of two-dimensional materials. The central proposal is toextend conventional spin-polarized density functional theory by treating the localspin degree of freedom as an internal gauge space and by coupling the electronicKohn–Sham spinors to an SU(2) Yang–Mills connection. Within this formulation, spin–orbit coupling, non-collinear magnetism, exchangeinteraction, Berry curvature, Dzyaloshinskii–Moriya interaction, spin-transfer torque,and topological Hall transport appear as different manifestations of a unified gaugecovariant structure. The proposed theory contains electronic kinetic energy, Hartree and exchange-correlation contributions, electromagnetic coupling, SU(2) gauge coupling, magnetic exchange, anisotropy, elastic strain, and Yang–Mills field energy. The theory is designed for two-dimensional ferromagnets, antiferromagnets, van der Waals heterostructures, transition-metal dichalcogenides, graphene-based systems, magnetic moiré structures, and interfaces with strong spin–orbit coupling.It predicts that the stabilization, deformation, and motion of magnetic skyrmionscan be controlled through local non-Abelian curvature, strain, electric fields, carrierdensity, interfacial asymmetry, and moiré modulation.