Pressure and temperature dependence of electronic energy levels in PbSe and PbTe

Using recent highly accurate pseudopotential band structures of PbSe and PbTe, the variation of the smallest gap at $L$ with hydrostatic pressure and with temperature has been calculated. The experimental values of the pressure coefficient can well be reproduced assuming reasonable slopes of the pseudopotential-form-factor curves. Combining these values with experimental compressibility and thermal-expansion coefficients, the anharmonic part of the temperature coefficient has been evaluated and found to contribute about 50% to the total experimental temperature coefficient. The remaining contribution arising from electron-phonon interactions has been analyzed using Brooks-Yu and Fan-like scattering theory. While the inclusion of a Debye-Waller factor yields reasonable results for the $L$ gap in PbTe, it fails for the $\Sigma -L$ gap and it predicts a temperature coefficient of the opposite sign for PbSe. A detailed analysis of the PbSe discrepancy is presented. It is proposed that Fan-type intravalley and intervalley scattering can resolve the dilemma. First-order estimates for Fan-type scattering contributions are presented.