Quantum Kinetic Anatomy of Electron Angular Momenta Edge Accumulation

Abstract

Controlling electron's spin and orbital degrees of freedom has been a major research focus over the past two decades, as it underpins the electrical manipulation of magnetization. Leveraging a recently introduced quantum kinetic theory of multiband systems [T. Valet and R. Raimondi, Phys. Rev. B 111, L041118 (2025)], we outline how the intrinsic angular momenta linear response is partitioned into intraband and interband contributions. Focusing on time reversal and inversion symmetric metals, we show that the spin and orbital Hall currents are purely intraband. We also reveal that the intrinsic edge densities originate partially, and in the orbital case probably mostly, from a new interband mechanism. We discuss how this profoundly impacts the interpretation of orbital edge accumulation observations, and has broader implications for current induced torques.

Figures (2)

• Figure 1: Near a boundary $\Sigma$ of a (TR+I) symmetric metal conductor, a tangential electric field $E^x$ is inducing a density of X, with X standing for either spin (S) or orbital (L) angular momentum. (a) The band projected part $X^{j}_{(bp)}$, is confined within a few angular momentum diffusion lengths $l_{Xdl}$, resulting from the detailed balance between the intrinsic angular momentum Hall current with vertex correction $\mathcal{\bm J}^{y j}_{XHE} + \mathcal{\bm J}^{y j}_{X (vc)}$, the backflow current $\mathcal{\bm J}^{y j}_{X (back)}$ and the angular momemtum relaxation. (b) The interband part $X^{j}_{(ib)}$, is confined within a few electron mean free paths $\lambda$. It results from quantum coherences induced by the transverse gradient in the longitudinal response, which also manifests itself by a decreased charge current density $\mathcal{J}_c^x$ near the edge.
• Figure 2: (a) Schematic band structure of the R-T Hamiltonian model of two-dimensional (TR+I) symmetric metal considered in this work, for a concrete calculation of the interband effect. A positive Fermi level intersects only the electron like band, but virtual interband transition may occurs, see the text. (b) P-orbital composition textures of the eigenstates on the Fermi "surface" in momentum space, for both bands.