Multipolar spin-orbit coupling in noncentrosymmetric crystals with time-reversal symmetry: Beyond spin 12

Abstract

We develop a symmetry-adapted multipolar k·p theory close to the bulk Γ point for time-reversal-symmetric, noncentrosymmetric C3v crystals in the strong atomic spin-orbit-coupling (jj-coupling) limit. Using a j∈{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 Wn for every energy band and identify distinct |Wn|=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.

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