A Z2 invariant for chiral and particle–hole symmetric topological chains.

We define a Z 2 -valued topological and gauge invariant associated with any one-dimensional, translation-invariant topological insulator that satisfies either particle–hole symmetry or chiral symmetry. The invariant can be computed from the Berry phase associated with a suitable basis of Bloch functions that is compatible with the symmetries. We compute the invariant in the Su–Schrieffer–Heeger model for chiral symmetric insulators and in the Kitaev model for particle–hole symmetric insulators. We show that in both cases, the Z 2 invariant predicts the existence of zero-energy boundary states for the corresponding truncated models. [ABSTRACT FROM AUTHOR]