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.本工作预言了一类具有呼吸模式（breathing mode）的新型笼目（kagome）材料Zr₃X₈（X=Cl、Br、I），并揭示了呼吸模式在能带拓扑（band topology）、电子性质、铁电性与磁性中的关键作用。尽管呼吸模式仅能在狄拉克点（Dirac point）处打开拓扑平庸能带隙，但随着其强度逐渐增强，可引发拓扑相变：由于呼吸模式与自旋轨道耦合（spin-orbit coupling）在调控能带隙过程中存在竞争效应，体系会从非平庸绝缘体转变为平庸绝缘体。呼吸模式可通过与极化位移模式的线性耦合效应诱导出面外铁电极化，而铁电翻转过程则通过两种模式的同时反转得以实现。随着阴离子半径的增大，材料的磁基态会从条纹反铁磁相转变为铁磁相。