  Recently published discoveries of acoustic and optical mode inversion in the
phonon spectrum of certain metals became the first realistic example of
non-interacting topological bosonic excitations in existing materials. However,
the observable physical and technological use of such topological phonon phases
remained unclear. In this work we provide a strong theoretical and numerical
evidence that for a class of metallic compounds (known as triple point
topological metals), the points in the phonon spectrum, at which three (two
optical and one acoustic) phonon modes (bands) cross, represent a well-defined
topological material phase, in which the hosting metals have very strong
thermoelectric response. The triple point bosonic collective excitations
appearing due to these topological phonon band-crossing points significantly
suppress the lattice thermal conductivity, making such metals phonon-glass
like. At the same time, the topological triple-point and Weyl fermionic
quasiparticle excitations present in these metals yield good electrical
transport (electron-crystal) and cause a local enhancement in the electronic
density of states near the Fermi level, which considerably improves the
thermopower. This combination of "phonon-glass" and "electron-crystal" is the
key for high thermoelectric performance in metals. We call these materials
topological thermoelectric metals and propose several newly predicted compounds
for this phase (TaSb and TaBi). We hope that this work will lead researchers in
physics and materials science to the detailed study of topological phonon
phases in electronic materials, and the possibility of these phases to
introduce novel and more efficient use of thermoelectric materials in many
everyday technological applications.
