Type-II Dirac semimetal stabilized by electron-phonon coupling.

There is major interest, in condensed matter physics, in understanding the role of topology: remarkable progress has been made in classifying topological properties of non-interacting electrons, and on understanding the interplay between topology and electron-electron interactions. We extend such studies to interactions with the lattice, and predict non-trivial topological effects in infinitely long-lived polaron bands. Specifically, for a two-dimensional many-band model with realistic electron-phonon coupling, we verify that sharp level crossings are possible for polaron eigenstates, and prove that they are responsible for a novel type of sharp transition in the ground state of the polaron that can occur at a fixed momentum. Furthermore, they result in the appearance of Dirac cones stabilized by electron-phonon coupling. Thus, electron-phonon coupling opens an avenue to create and control Dirac and Weyl semimetals.