  We investigate a second-order topological quantum transition of a modified
Kane-Mele model driven by 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
secondorder topological phase transition is characterized by the band-gap
closing, discontinuity of averaged ferminoic number and topological invariant.
