Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators

We investigate a second-order topological quantum transition of a modified Kane-Mele model driven by an electron-phonon interaction. The results show that the system parameters of the bare modified Kane-Mele model are renormalized by the electron-phonon interaction. Starting from the second-order topological phase for the bare model, the increasing electron-phonon coupling strength can drive the second-order topological insulator into a semimetal phase. Such a second-order topological phase transition is characterized by the band-gap closing, discontinuity of the averaged ferminoic number, and the topological invariant.