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Electron-Phonon Coupling: Band Gap Renormalization

In the previous exercises, we have used Phonopy to compute the (harmonic and quasi-harmonic) vibrational properties of silicon from the first principles. In turn, we will now use the results achieved in previous exercises to investigate how the vibrational effects influence the electronic properties of silicon, and in particular, the temperature dependence of its electronic band gap. To allow for qualitative insights into the role of electron-phonon coupling, we will perform calculations that explicitly account for thermodynamic changes in the lattice (Ex. 6) and atomic (Ex. 7) degrees of freedom along the lines of Ref. 1 and 2, respectively. As it was the case for the harmonic phonons, such real space approaches are not the only option available to date to account for these effects: in recent years, DFPT based methods have been applied successfully for these purposes as well 34.

  1. J. M. Skelton, et al., Phys. Rev. B 89, 205203 (2014). ↩

  2. R. Ramirez, C. Herrero, and E. Hernandez, Phys. Rev. B 73, 245202 (2006). ↩

  3. M. Cardona, Solid State Comm. 133, 3 (2005). ↩

  4. F. Giustino, S. G. Louie, and M. L. Cohen, Phys. Rev. Lett. 105, 265501 (2010). ↩