Altermagnetism-induced topological phase transitions in the Kane-Mele model

We theoretically demonstrate that the Chern number tunable quantum anomalous Hall effect (QAHE) and second-order topological insulators can be induced in a two-dimensional ${\mathbb{Z}}_{2}$ topological insulator (TI), i.e., the Kane-Mele model, by applying $d$-wave altermagnetism. When the N\'eel vector of altermagnetism lies in the $x\text{\ensuremath{-}}y$ plane, the ${\mathbb{Z}}_{2}$ TI is broken and driven into a second-order topological insulator phase, exhibiting the representative corner states at nanoflakes. When the intrinsic Rashba spin-orbit coupling is further included, the second-order TI is further driven into the QAHE phase with various Chern numbers (e.g., $\mathcal{C}=\ifmmode\pm\else\textpm\fi{}1$ or $\ifmmode\pm\else\textpm\fi{}3$). When the N\'eel vector is along the $z$ direction, the intrinsic Rashba spin-orbit coupling is necessary to break the mirror symmetry to allow a sequential emergence of second-order TI and QAHE along with the increase of altermagnetism strength. We also observe the QAHE with mixed chirality, i.e., there exist counterpropagating edge modes but net chiral current at the ribbon boundary. Our work shows that altermagnetism can play a crucial role in exploring a rich variety of topological phases, just like its counterparts of ferromagnetism and antiferromagnetism.