Magnetic and charge instabilities in vanadium-based topological kagome metals

Abstract

Vanadium-based topological kagome metals ${\mathrm{AV}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, Cs) have drawn great attention recently due to the discoveries of charge order, nematic phase, time-reversal symmetry breaking, and superconductivity. In this work, we study the Fermi-surface instabilities of topological kagome metals ${\mathrm{AV}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, Cs) in all the charge-orbital-spin channels based on first principles calculations, and provide a first principles theory for the current-loop state in this class of materials. After comprehensive analysis of the interaction-renormalized generalized susceptibility tensor combined with unrestricted Hartree-Fock calculations, we find that the leading instability modes at the Fermi surface are three spin magnetic modes at $\mathrm{\ensuremath{\Gamma}}$ point, giving rise to ferromagnetism within the kagome plane with small magnetization on the V atoms. We further show that counter-propagating current loops within the kagome plane can be generated due to the interplay between spin magnetism and spin-orbit coupling, and the current pattern is consistent with recent muon spin spectroscopy measurements. Moreover, some other puzzling experiments in this system such as the giant anomalous Hall effect and nematicity can also be explained from our results.