The role of breathing mode in band topology and multiferroics in two-dimensional kagome magnets

Here, we predict a new family of kagome materials with breathing mode, Zr$_3X_8$ (\emph{X} = Cl, Br, I), and reveal the role of breathing mode in band topology, electronic property, ferroelectricity, and magnetism. Although the breathing mode can only open a topologically trivial band gap at the Dirac point, its gradual enhancement can induce a topological phase transition from a non-trivial to a trivial insulator due to the competitive effect between the breathing mode and spin-orbit coupling in modulating the band gap. The breathing mode induces out-of-plane ferroelectric polarization through a linear coupling effect with the polar displacement mode, and the ferroelectric switching is accomplished by the simultaneous reversal of the two modes. The magnetic ground states change from stripe antiferromagnetic to ferromagnetic phase with increasing anion radius.