Robustness of RKKY interactions across a Weyl node-annihilation transition
Abstract
Weyl semimetals (WSMs), with their unique topological properties and distinct electronic structure, exhibit intriguing properties when either time-reversal or inversion symmetries are broken. In this work, we consider the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities in time-reversal symmetry-breaking WSMs. We derive analytical expressions for the full RKKY exchange tensor in arbitrary two-band spinful lattice systems. Our approach reveals both Heisenberg, anisotropic Ising and Dzyaloshinsky-Moriya terms, which can be calculated by energy-integrating real-space Green's functions across the entire Brillouin zone, with the band edge acting as a natural energy cutoff. We apply this framework to study a two-band tight-binding model for a time-reversal symmetry-breaking WSM that interpolates between a Weyl phase with well-separated chiral nodes and a quadratic band-touching semimetal phase. Remarkably, the spatial profile, magnitude, and anisotropic tensor structure of the exchange couplings remain persistent across the node-annihilation transition. This topological robustness reveals that short- and intermediate-range RKKY interactions are mediated by the global, Brillouin-zone-integrated quantum metric of the full valence band rather than being strictly dictated by local low-energy Berry curvature monopoles. These findings demonstrate the necessity of full-band tight-binding formulations when predicting real-space magnetic interactions, providing key insights for electric-field tuning of magnetic anisotropy and constructing realistic models of heavy-fermion and Weyl-Kondo semimetals.
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BibTeX
@misc{alves2026robustness,
title = {{Robustness of RKKY interactions across a Weyl node-annihilation transition}},
author = {João V. F. Alves and Joelson F. Silva and Luis G. G. V. Dias da Silva},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05219},
eprint = {2609.05219},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05219},
}
RIS
TY - UNPB
TI - Robustness of RKKY interactions across a Weyl node-annihilation transition
AU - João V. F. Alves
AU - Joelson F. Silva
AU - Luis G. G. V. Dias da Silva
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05219
UR - https://arxiv.org/abs/2609.05219
AB - Weyl semimetals (WSMs), with their unique topological properties and distinct electronic structure, exhibit intriguing properties when either time-reversal or inversion symmetries are broken. In this work, we consider the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities in time-reversal symmetry-breaking WSMs. We derive analytical expressions for the full RKKY exchange tensor in arbitrary two-band spinful lattice systems. Our approach reveals both Heisenberg, anisotropic Ising and Dzyaloshinsky-Moriya terms, which can be calculated by energy-integrating real-space Green's functions across the entire Brillouin zone, with the band edge acting as a natural energy cutoff. We apply this framework to study a two-band tight-binding model for a time-reversal symmetry-breaking WSM that interpolates between a Weyl phase with well-separated chiral nodes and a quadratic band-touching semimetal phase. Remarkably, the spatial profile, magnitude, and anisotropic tensor structure of the exchange couplings remain persistent across the node-annihilation transition. This topological robustness reveals that short- and intermediate-range RKKY interactions are mediated by the global, Brillouin-zone-integrated quantum metric of the full valence band rather than being strictly dictated by local low-energy Berry curvature monopoles. These findings demonstrate the necessity of full-band tight-binding formulations when predicting real-space magnetic interactions, providing key insights for electric-field tuning of magnetic anisotropy and constructing realistic models of heavy-fermion and Weyl-Kondo semimetals.
ER -