By Henry Ehrenreich, Frans Spaepen
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Extra resources for Solid State Physics: Advances in Research and Applications, Vol. 54
Subtracting the HartreeFock exchange potential from the self-energy operator and using Eq. 25) The expectation value of Cc with respect to single-particle orbitals Ok= I k ) and 0,= Il) equals Energy-dependent correlations decrease the Hartree-Fock band gap by raising the valence-band energy and lowering the conduction-band energy, 25 QUASIPARTICLE CALCULATIONS IN SOLIDS as can be seen by considering the above equations. For a valence electron in the highest occupied state, Iub), the largest contribution to (ublCC(E = E J u b ) comes from the sum over the occupied states.
Lett. 80, 2389 (1998), and references therein. 72 L. Hedin, B. I. Lundqvist, and S. Lundqvist, J . Res. Natl. Bur. Stand. Sect. A 74A, 417 (1970). 7 3 L. Hedin, Phys. Scripta 21, 477 (1980). 7 4 D. C. Langreth, Phys. Rev. E l , 471 (1970). 7 5 P. Minnhagen, J . Phys. C: Sol. State Phys. 8, 1535 (1975). 76 The term shake-up spectra corresponds to excitations created by a sudden change in a quantum-mechanical system. Consider, for example, the creation of a core hole in a solid via a photoemission process.
The quasiparticle equation can be derived by inserting the spectral representation of the interacting Green function into Dyson’s equation and is given in Eq. 3). It is formally similar to the single-particle equation of Kohn-Sham theory (Eq. 9)), but the solutions of the quasiparticle equation, that is, the quasiparticle energy Ei and wave function Y i ,are physically meaningful rather than mere mathematical tools as is the case in DFT. Whenever possible one chooses as a starting point a suitable independentparticle Hamiltonian whose wave functions mi(r) are nearly identical with the quasiparticle wave functions Yi(r), which choice allows the determination of quasiparticle energies via first-order perturbation theory.