Fig. 3

Two layer constructions for space group P2/m, sharing the same set of SI of (0002). a All symmetry elements of the space group in one unit cell, including eight inversion centers (red solid circles), four rotation axes (red solid lines), and two mirror planes (shaded planes). b, c LC1 and LC2 defined in the text, respectively. They have distinct topological invariants but identical indicators. d 3D Blöch wave functions in LC2 as superpositions of 2D Blöch wave functions with coefficients \(e^{ik_2x_2}\). Here we use red and blue loops to represent the 2D wave functions having mirror eigenvalues i and −i, respectively, wherein i wave functions have Chern number 1 and −i wave functions have Chern number −1. For A-eLC the 3D Blöch wave functions at k₂ = 0 and k₂ = π have the same mirror eigenvalues, leading to identical mirror Chern numbers at k₂ = 0 and k₂ = π. Although for B-eLC the Blöch wave functions at k₂ = 0 and k₂ = π have opposite mirror eigenvalues, leading to opposite mirror Chern numbers at k₂ = 0 and k₂ = π. e The two mirror-invariant planes (gray planes) in Brillouin zone