Acoustic Deformation Potentials of n-type PbTe from First Principles

We calculate the uniaxial and dilatation acoustic deformation potentials, $\Xi_{u}$ and $\Xi_{d}$, of the conduction band L valleys of PbTe from first principles, using the local density approximation (LDA) and hybrid functional (HSE03) exchange-correlation functionals. We find that the choice of a functional does not substantially affect the effective band masses and deformation potentials as long as a physically correct representation of the conduction band states near the band gap has been obtained. Fitting of the electron-phonon matrix elements obtained in density functional perturbation theory (DFPT) with the LDA excluding spin orbit interaction (SOI) gives $\Xi^{\text{L}}_u = 7.0$ eV and $\Xi^{\text{L}}_d = 0.4$ eV. Computing the relative shifts of the L valleys induced by strain with the HSE03 functional including SOI gives $\Xi^{\text{L}}_u = 5.5$ eV and $\Xi^{\text{L}}_d = 0.8$ eV, in good agreement with the DFPT values. Our calculated values of $\Xi^{\text{L}}_u$ agree fairly well with experiment ($\sim 3-4.5$ eV). The computed values of $\Xi^{\text{L}}_d$ are substantially smaller than those obtained by fitting electronic transport measurements ($\sim 17-22$ eV), indicating that intravalley acoustic phonon scattering in PbTe is much weaker than previously thought.