Topology of Bloch Bands from Cauchy Data (opens in new tab)

In a previous work, the topology of inversion-symmetric one-dimensional periodic media was characterized through the pole-zero pattern of an impedance-like function associated with Bloch waves. This construction reproduces the Berry--Zak invariant and provides a criterion for topological interface states. In the present work, we give a geometric interpretation of this formalism. We show that poles and zeros arise naturally from the action of i...