Non-Hermitian higher-order topological insulators enabled by altermagnet engineering

We show that proximity to an altermagnet provides an efficient route to engineering non-Hermitian higher-order topological phases. The proximity-induced altermagnetic order gaps the edge states of a topological insulator, thereby driving a transition from a first-order to a second-order topological phase. When combined with nonreciprocal hopping, the system exhibits both the non-Hermitian skin effect and a hybrid skin-topological effect, whereby first-order edge states and second-order corner states accumulate at selected corners of the lattice. We demonstrate that the spectral winding number of the edge states under cylindrical geometry dictates this corner localization and can be reversed by tuning the altermagnetic order. Consequently, both edge and corner states become directionally controllable. Our results establish altermagnets as a versatile platform for realizing and tuning skin-topological phenomena in non-Hermitian higher-order topological systems.