Beyond spin-1/2: Multipolar spin-orbit coupling in noncentrosymmetric crystals with time-reversal symmetry

We develop a symmetry-adapted multipolar mathbf{k}cdotmathbf{p} theory close to the bulk Γ point for time-reversal-symmetric, noncentrosymmetric C_3v crystals in the strong atomic spin-orbit-coupling (jj-coupling) limit. Using a jin\{1/2,3/2,5/2\} multiplet basis appropriate for heavy-element p- and d-bands, we systematically construct all symmetry-allowed spin-orbit coupling terms up to fifth order in momentum and generalize the usual spin texture to a total-angular-momentum texture. For j>1/2, multipolar spin-orbit coupling qualitatively reshapes Fermi surfaces and makes the topology of Bloch states band dependent. This leads to anisotropic high-j textures that go beyond a single Rashba helix. We classify these textures by their total-angular-momentum vorticity W_n for every energy band and identify distinct |W_n|=1,2,5 phases. We show that their crossovers generate enhanced and nonmonotonic current-induced spin-polarization responses, namely the Edelstein effect, upon tuning the chemical potential. Our results provide a symmetry-based framework for analyzing and predicting multipolar spin-orbit coupling, total-angular-momentum textures, and spintronic responses in heavy-element materials without an inversion center.