Electron-phonon coupling in half-Heusler compounds: A comparative study of TiCoSb and TiNiSn

Electron-phonon coupling has inspired broad research because of the dominant role in electron and phonon transport properties, whereas how to control the coupling strength through band-structure engineering is a widely debated issue in solid-state physics. Here, we establish a general relationship between valence-band shape and electron-phonon coupling by conducting a comparative study of typical half-Heusler compounds TiCoSb and TiNiSn. The competition between symmetry-allowed $d\text{\ensuremath{-}}d$ and $p\text{\ensuremath{-}}d$ orbital couplings eventually determines the valence-band-edge shape. The $d\text{\ensuremath{-}}d$ coupling between Co/Ni and Ti atoms favors a unique wavelike valence band with multiple nearly equal-energy valleys in TiCoSb and the $p\text{\ensuremath{-}}d$ coupling between Sb/Sn and Ti atoms prefers a single parabolic valence band in TiNiSn. More importantly, the wavelike band effectively strengthens the electron-phonon coupling by introducing the intervalley scattering that remains stronger than the intravalley scattering. In contrast, the single parabolic band seriously suppresses the scattering process because the intravalley scattering dominates the electron-phonon coupling. The different scattering mechanism results in a series of anomalous electron and phonon transport properties, for example, in sharp contrast to TiNiSn, TiCoSb has a more pronounced decrease in band gap with temperature and a weaker temperature dependence of lattice thermal conductivity. Our findings provide universal insights into the effects of complex band structure on electron-phonon coupling and help to develop different strategies to improve and design better thermoelectric materials.