3D chiral higher order topological insulators in altermagnets

Altermagnets are characterized by a distinctive mechanism of time-reversal symmetry breaking where the product of time-reversal and rotation symmetry is preserved, while neither symmetry exists independently. This feature has launched a search for higher-order topological phases in altermagnets, in which edge modes are protected by the composite symmetry rather than conventional time-reversal symmetry. While much work has focused on 2D higher order topology in TI-altermagnet heterostructures, less attention has been devoted to realizing intrinsic 3D higher order topology hosting chiral edge modes. In this talk, we outline progress toward achieving such a state in altermagnetic systems. We present realistic tight-binding models alongside potential material realizations, highlighting that this long-sought phase of matter may naturally emerge within altermagnets.