Exchange — Correlation Potential for the Quasi-Particle Bloch States of a Semiconductor

  • W. Hanke
  • N. Meskini
  • H. Weiler


A summary is given of recent investigations we have performed on a) the interrelation of many-body perturbation theory for the non-local and energy-dependent self-energy and the density-functional theory, b) the single-particle-like excitations in Si which are calculated within the time-dependent screened Hartree-Fock (TDSHF) approximation, and c) an analytical energy- and local-density (ρ1/3-) dependent model for the self-energy of nonmetallic systems in general.

We elaborate on recent attempts to derive the local and energy-dependent density-functional potential vxc from the diagrammatic structure of many-body perturbation theory for the exact exchange-correlation energy, without explicit recourse to an extremal principle. The local vxc can be related to the nonlocal and dynamic self-energy Σ obtained from perturbation theory.

We summarize our recent calculations of quasiparticle states in silicon which aim at a first-principle understanding of the self-energy corrections in a prototype semiconductor. TDSHF is used by replacing the exchange operator by a dynamically screened interaction. In contrast to previous calculations in semiconductors the wave-vector and frequency-dependent two-particle propagator is calculated from first principles and includes local-field and particle-hole (excitonic) effects. The band gap, the valence-band width and the general features of quasiparticle decay are in good accord with experiment, though our construction of bare HF states via a density matrix built from pseudopotential eigenstates puts limits on this comparison.

On the basis of these numerical results, we outline the construction of an analytic, energy-dependent and local density-dependent model for the self-energy operator. This tight-binding model reproduces the computational results for dynamical self-energies in both the insulator C and semiconductor Si within a few percent across valence and conduction bands. The strength of the self-energy scales with ρ1/3. In particular, it is shown how the intrinsi- cally non-local (due to long-range electron-hole polarizations) potential can still approximately be converted via a Lorentz-sphere construction into a local potential. Together with the perturbation-theoretical expression for the “exact” vxc of density-functional theory this tight-binding model is finalY used to derive a model expression for vxc of a non-metal.


Dyson Equation Quasiparticle State Plasmon Pole Bare Coulomb Interaction Quasiparticle Decay 
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • W. Hanke
    • 1
  • N. Meskini
    • 1
    • 2
  • H. Weiler
    • 1
  1. 1.Max-Planck-Institut für FestkörperforschungStuttgart 80The Federal Republic of Germany
  2. 2.Faculté des Sciences, Departement de PhysiqueCampus UniversitaireBelvédère, TunisTunisia

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