Quantum geometric tensor and the topological characterization of the extended Su–Schrieffer–Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su–Schrieffer–Heeger(SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the Gauss–Bonnet theorem on the topologic...