Acoustic Deformation Potentials of $n$-Type PbTe from First Principles

We calculate the uniaxial and dilatation acoustic deformation potentials, ${\mathrm{\Xi }}_u^{\text{L}}$ and ${\mathrm{\Xi }}_d^{\text{L}}$, 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 ${\mathrm{\Xi }}_u^{\text{L}}=7.0$~eV and ${\mathrm{\Xi }}_d^{\text{L}}=0.4$~eV. Computing the relative shifts of the L valleys induced by strain with the HSE03 functional including SOI gives ${\mathrm{\Xi }}_u^{\text{L}}=5.5$~eV and $\Xi^{$\text{L}$}_d = 0.8$eV,ingoodagreementwiththeDFPTvalues\mathrm{.}Ourcalculatedvaluesof$\Xi^{$\text{L}$}_u$agreefairlywellwithexperiment($\sim 3-4.5$~eV). The computed values of ${\mathrm{\Xi }}_d^{\text{L}}$ 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.