<i>GW</i>approach to the calculation of electron self-energies in semiconductors

Abstract

Various approximation schemes concerning the calculation of the electron self-energy M for a semiconductor in the (bubble) GW scheme of Hedin [Phys. Rev. 139, A796 (1965)] are discussed. It is shown by using a contour-deformation procedure in the complex energy plane that M, as obtained in the first iteration cycle of the GW scheme, is Hermitian for real energies \ensuremath{\Vert}\ensuremath{\varepsilon}\ensuremath{\Vert}3${\ensuremath{\varepsilon}}_{g}$/2, where ${\ensuremath{\varepsilon}}_{g}$ is the unperturbed energy gap, and non-Hermitian for \ensuremath{\Vert}\ensuremath{\varepsilon}\ensuremath{\Vert}&gt;3${\ensuremath{\varepsilon}}_{g}$/2. The Taylor expansion for M around the midgap energy value \ensuremath{\varepsilon}=0 has a convergence radius of 3${\ensuremath{\varepsilon}}_{g}$/2. Extended use of a (truncated) Taylor series at \ensuremath{\Vert}\ensuremath{\varepsilon}\ensuremath{\Vert}&gt;3${\ensuremath{\varepsilon}}_{g}$/2 is not capable of giving the non-Hermitian part of M, while there is also no guarantee that the Hermitian part is correctly obtained in this way.