Kondo effect under arbitrary spin-momentum locking

TL;DR

The paper addresses how spin-momentum locking in Weyl-type electrons influences the Kondo effect for a localized impurity. It develops a model with isotropic linear dispersion and arbitrary spin locking, diagonalizes the spin structure, and analyzes the Kondo problem using second-order perturbation theory to obtain the T-matrix and scattering rate. The central result is a simple Kondo temperature formula that depends only on the spin average on the Fermi surface, $T_K(\bar{\mathbf{s}}) \propto \exp\left(- \frac{3-\bar{\mathbf{s}}^2}{3-3\bar{\mathbf{s}}^2} \frac{1}{J\nu_F}\right)$, recovering the conventional $T_K \,\propto \,\exp(-1/(J\nu_F))$ at $|\bar{\mathbf{s}}|=0$ and predicting $T_K=0$ for $|\bar{\mathbf{s}}|=1$. The work highlights that Kondo screening is controlled by the Fermi-surface spin average rather than the detailed locking, with spin polarization progressively suppressing the effect; the authors also discuss extensions to more general dispersions and strong-coupling regimes.

Abstract

The Kondo effect originates from the spin exchange scattering of itinerant electrons with a localized magnetic impurity. Here, we consider generalization of Weyl-type electrons with their spin locked on a spherical Fermi surface in an arbitrary way and study how such spin-momentum locking affects the Kondo effect. After introducing a suitable model Hamiltonian, a simple formula for the Kondo temperature is derived with the second-order perturbation theory, which proves to depend only on the spin averaged over the Fermi surface. In particular, the Kondo temperature is unaffected as long as the average spin vanishes, but decreases as the average spin increases in its magnitude, and eventually vanishes when the spin is completely polarized on the Fermi surface, illuminating the role of spin-momentum locking in the Kondo effect.

Figures (2)

• Figure 1: Feynman diagrams for the $T$ matrix to the second order in perturbation. Solid curves, dashed lines, and dots represent itinerant electrons, localized magnetic impurity, and spin exchange interaction, respectively.
• Figure 2: Normalized Kondo temperature $T_K(\bar{{\bm{s}}})/T_K({\bm{0}})$ from Eq. (\ref{['eq:temperature']}) as a function of $|\bar{{\bm{s}}}|$ for $J\nu_F=1/100$, $1/10$, $1$, and $10$ from the leftmost curve to the rightmost one.