Two-dimensional non-Abelian topological insulators and the corresponding edge/corner states from an eigenvector frame rotation perspective

We propose the concept of two-dimensional (2D) non-Abelian topological insulators which can explain the energy distributions of the edge states and corner states in systems with parity-time symmetry. From the viewpoint of non-Abelian band topology, we establish the constraints on the 2D Zak phase and polarization. We demonstrate that the corner states in some 2D systems can be explained as the boundary mode of the one-dimensional edge states arising from the multiband non-Abelian topology of the system. We also propose the use of the off-diagonal Berry phase as complementary information to assist the prediction of edge states in non-Abelian topological insulators. Our work provides an alternative approach to study edge and corner modes and this idea can be extended to three-dimensional systems.