Manipulating corner states without topological phase transition in two-dimensional intrinsic triferroic materials

Engineering topological boundary states have attracted enormous interest with great insight into both the fundamental understanding and future applications of topological states. Despite the fact that several proposals have been made to achieve the second-order corner states from the first-order helical and/or chiral edge states, manipulation of corner states without topological phase transition remain elusive. Here, taking $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{FeO}}_{2}\mathrm{H}$ monolayer and $1{\mathrm{T}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{CrCoS}}_{4}$ monolayer as the material candidates, we propose a general mechanism for manipulating corner states without topological phase transition in two-dimensional intrinsic triferroics. Under in-plane spontaneous polarization, electrons acquire a transverse velocity, leading to the emergence of nontrivial corner states located at the mirror-symmetric corners perpendicular to the polarization direction. Remarkably, in contrast to previously reported proposals with topological phase transition, we put forward that the spatial distribution of the corner states can be effectively engineered by a ferroelastic switching with the second-order topological insulator remaining intact, thereby driving the advancement of multiferroics in topological spintronics.