Temperature-dependence of electron bands in wurtzite GaN, including non-adiabatic (Polaron) contributions

We study the temperature dependence of the band gap of wurtzite structure GaN [1]. Virtual interband electron-phonon scattering is accounted properly by adiabatic (Allen-Heine-Cardona) theory. The correct way to avoid an unphysical divergence, is to use a non-adiabatic treatment for intraband scattering by small $q$ polar optical phonons [2,3]. This is equivalent to including Fr\"ohlich polaron effects. The $T=0$ zero-point weak-coupling polaron shift ($-\alpha\hbar\omega$) is well known, but finite $T$ effects are less studied. We also calculate the $T$ dependence of the band mass (both polaron and adiabatic contributions). We compare results from an {\it ab-initio} density-functional approach with those obtained starting from the traditional Fr\"ohlich Hamiltonian approach. [1] M. Cardona and … Kremer, Thin Solid Films {\bf 571}, 680 (2014). [2] S. Ponc\'e {\it et al.}, The Journal of Chemical Physics {\bf 143}, 102813 (2015) [3] C. Verdi and F. Giustino, Phys. Rev. Lett. {\bf 115}, 176401 (2015)