Second-order topological insulator induced by compensated altermagnetism without bulk spin splitting

We theoretically demonstrate a second-order topological insulating phase induced by compensated altermagnetism, while keeping the bulk gap unchanged, in a two-dimensional topological insulator film. By introducing a layer-resolved out-of-plane $d$-wave altermagnetic term with opposite signs on the top and bottom layers, the system preserves $\mathcal{PT}$ symmetry and maintains spin degeneracy in the bulk bands, while simultaneously gapping the helical edge states and generating localized corner states. The resulting higher-order phase is characterized by nonzero mirror-graded winding numbers, and an effective edge theory shows that the corner states arise from Dirac mass domain walls. We further determine the phase boundaries analytically and construct the corresponding topological phase diagram, establishing a robust route to higher-order topology without bulk spin splitting.