Anisotropic RKKY interactions in nodal-line semimetals

Abstract

Nodal-line semimetals (NLSMs) are typically characterized by a nodal ring, a closed line of Dirac points in the Brillouin zone, which features a torus-shaped Fermi surface, as well as a quantized Berry phase $\ensuremath{\pi}$. By investigating the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in NLSMs, a close relationship between the magnetic interaction and the radius ${k}_{0}$ of the nodal ring is revealed. For impurities deposited in the direction normal to the nodal-ring plane, when the long-range interaction at half-band filling follows the decaying law ${R}^{\ensuremath{-}3}$ with impurity distance, which is a result of anisotropic dispersion of semi-Dirac semimetal, the decaying rate for the relatively short-range impurity distance would be prolonged by nodal-ring radius ${k}_{0}$, which is prominent for the intermediate radius. This phenomenon originates from the competition between the contribution from the electron states inside and outside the nodal ring. In contrast, for impurities distributed in the nodal-ring plane, the RKKY interaction $J\ensuremath{\propto}{k}_{0}^{2}\mathrm{cos}(2{k}_{0}R){R}^{\ensuremath{-}4}$ shows an oscillation, from whose period one can easily determine the parameter ${k}_{0}$ of the nodal ring. Furthermore, at finite Fermi energy, we find a distinct signature of the RKKY interaction to characterize the topological trivial and topological nontrivial phases in NLSMs.