Many-Body Effects on the Zero-Point Renormalization of the Band Structure

We compute the zero-point renormalization (ZPR) of the optical band gap of diamond from many-body perturbation theory using the perturbative $G_0{W}_0$ approximation as well as quasiparticle self-consistent $GW$. The electron-phonon coupling energies are found to be more than 40% higher than standard density functional theory when many-body effects are included with the frozen-phonon calculations. A similar increase is observed for the zero-point renormalization in GaAs when $G_0{W}_0$ corrections are applied. We show that these many-body corrections are necessary to accurately predict the temperature dependence of the band gap. The frozen-phonon method also allows us to validate the rigid-ion approximation which is always present in density functional perturbation theory.

Figure 1

Electron-phonon coupling energies for the top of the valence band (lower panel) and the bottom of the conduction band at $\mathrm{\Gamma }$ (middle panel), calculated in DFPT (solid line) and with the frozen-phonon method (circles). The top panel shows the band structure with dashed lines indicating the ${{\mathrm{\Gamma }}_{25v}}^{\prime }$ and ${\mathrm{\Gamma }}_{15c}$ energies.

Figure 2

Electron-phonon coupling energies for the top of the valence band (lower panel) and the bottom of the conduction band at $\mathrm{\Gamma }$ (top panel), in DFT (squares), in $G_0{W}_0$ (circles) and in $GW$ (stars).

Figure 3

Temperature dependence of the direct band gap computed in DFPT (squares) and with $GW$ corrections (discs). The band gap (7.732 eV) is computed in $G_0{W}_0$, and the two experimental data sets (upper and lower triangles) are from Ref. [42].