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Spin currents in crystals with spin-orbit coupling: Multiband effects in an effective Hamiltonian formalism

Kirill V. Samokhin1,*, Manfred Sigrist2, and Mark H. Fischer3

  • *Contact author: kirill.samokhin@brocku.ca
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Phys. Rev. Research 8, 013216 – Published 26 February, 2026

DOI: https://doi.org/10.1103/2nmp-8gdx

Abstract

When focusing on a few essential bands in an effective description of a material to calculate observable quantities, the respective operators have to be adjusted accordingly. Ignoring contributions arising from integrating out remote bands can lead to qualitatively wrong results. We present a detailed analysis of the interband mixing effects on spin currents. Specifically, we calculate the intrinsic spin current in a time-reversal invariant noncentrosymmetric crystal in the presence of electron-lattice spin-orbit coupling. Starting from formally exact microscopic expressions, we derive the spin-current operator restricted to one or more essential bands by iterative elimination of the contributions from distant bands. We show that the standard definition of the spin-current operator in terms of the group velocity obtained from an effective band Hamiltonian cannot be justified using a microscopic theory. The modified expression for the spin-current operator contains additional terms, which dominate the equilibrium spin current in a uniform crystal. We show that the magnitude of these additional terms can considerably exceed the spin current obtained using the standard definition.

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Phys. Rev. Research 8, 013216– Published 26 February, 2026
  • Received 25 September 2025
  • Accepted 28 January 2026
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