Density-matrix quantum kinetics of spin-mode crossover and ac Edelstein response in spin--orbit-coupled chiral metals

Abstract

To clarify spin relaxation and precession across the weak-to-strong SOC crossover in chiral conductors, we formulate a density-matrix quantum kinetic theory for a three-dimensional isotropic chiral metal with hedgehog SOC and nonmagnetic impurity scattering. The formulation retains interband coherence, and its collision integral conserves charge, energy, and spin during impurity scattering. We identify three spin modes that evolve continuously from a long-lived D'yakonov--Perel'relaxation mode and two strongly damped precessional modes at weak SOC to one relaxational and two coherent precessional modes at strong SOC. A closed multipole decomposition maps the spin dynamics onto an effective Bloch equation, providing a unified interpretation of relaxation and precession across the crossover. We further derive the ac Edelstein susceptibility and the reciprocal current response to a time-dependent Zeeman field, show that their poles coincide with the spin modes, and verify Onsager reciprocity. The theory thus provides a unified analytic description of spin relaxation, precession, and spin--charge conversion across the weak-to-strong SOC crossover.