AlterSeeK-Path: Systematic construction of generalized band-structure paths for displaying altermagnetic spin splitting

Abstract

Altermagnetic materials exhibit spin splitting in their electronic band structures while maintaining zero net magnetization. However, conventional high-symmetry k-paths generally hide this splitting because they follow symmetry lines that in most cases enforce spin degeneracy. We present AlterSeeK-Path, an open-source Python tool that systematically constructs generalized band-structure paths for collinear altermagnets. The method selects the centroid of the conventional irreducible wedge used in routine band-structure calculations as the representative general k-point, maps it to a spin-flip-related partner, and inserts paired segments through these points into the standard high-symmetry path; these segments systematically sample the interior of the irreducible wedge. We demonstrate the construction for all 54 three-dimensional combinations of extended Bravais lattice type and spin Laue group across the six crystal systems that support collinear altermagnetism, and for the 12 two-dimensional cases spanning the four compatible two-dimensional Bravais lattices. Representative band structures are shown for the distinct lattice/path cases. With AlterSeeK-Path, these band structures can be constructed with essentially the same effort as conventional band structures.