We present an ab initio method for electronic structure calculations of materials at finite temperature (FT) based on the all-electron quasiparticle self-consistent $\mathit{GW}$ $\left(\mathrm{QPSC}\mathit{GW}\right)$ approximation and Keldysh time-loop Green’s function approach. We apply the method to Si, Ge, GaAs, InSb, and diamond and show that the band gaps of these materials universally decrease with increasing temperature in contrast with results of the local density approximation (LDA) of density functional theory where the band gaps universally increase. At temperatures of a few eV the difference between quasiparticle energies obtained in FT $\mathrm{QPSC}\mathit{GW}$ and FT LDA approaches is significantly reduced. This result suggests that existing simulations of very high-temperature materials based on the FT LDA are more justified than it might appear from the well-known LDA band gap errors at zero temperature.

• Received 26 April 2006

DOI:https://doi.org/10.1103/PhysRevB.74.033101