Exceptionally high carrier mobility in hexagonal diamond

Hexagonal diamond (h-diamond), or Lonsdaleite, is a promising wide-bandgap semiconductor known for its high thermal conductivity and hardness. Based on \textit{ab initio} calculations, we demonstrate its exceptionally high carrier mobilities. At room temperature, the hole mobilities along the $\perp c$ and $\parallel c$ directions are 6000 and 6024 cm$^{2}$V$^{-1}$s$^{-1}$, respectively, while the corresponding electron mobilities reach 12339 and 28473 cm$^{2}$V$^{-1}$s$^{-1}$. These values are significantly superior to those of most known semiconductors, including cubic diamond. The small effective masses in h-diamond are comparable to those in the cubic phase, which cannot explain its substantially higher mobilities. Instead, two underlying mechanisms are uncovered. First, selection rules enforced by the symmetry of h-diamond significantly suppress scattering, particularly for transverse acoustic phonons, which predominate in the cubic phase around room temperature. Secondly, the spatial mismatch between the electronic wavefunctions and phonon-induced scattering potentials leads to real-space electron-phonon decoupling, which manifests as the suppression of out-of-plane polarised longitudinal acoustic scattering for holes, and a systematic weakening of acoustic scattering for electrons.