Extended Data Table 1 Possible invariants for space group 227

From: Catalogue of topological electronic materials

  1. Z2,2,2,4 are the four symmetry-based indicators. The remainder of the labels in the top row refer to topological invariants protected by various lattice symmetries as defined in ref. 27, in which: ‘weak’ denotes weak topological indices; \({m}_{(2)}^{010}\) shows the mirror Chern number which takes a value between −1 and +2, protected by the (010)-mirror plane; \({{\boldsymbol{G}}}_{abc}^{mnl}\) denotes the Z2 invariant protected by a glide plane perpendicular to the mnl direction with glide vector abc; i is the Z2 invariant protected by inversion symmetry about the origin; and \({n}_{{\boldsymbol{k}}}^{mnl}\) is the Z2 invariant protected by an n-fold rotation about the mnl direction followed by a translation along the same direction through the k/n lattice vector.
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