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Bethe-Salpeter Equation and Excitonic effects: a short introduction Valerio Olevano Laboratoire des Solides Irradiés École Polytechnique, Palaiseau.

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Presentation on theme: "Bethe-Salpeter Equation and Excitonic effects: a short introduction Valerio Olevano Laboratoire des Solides Irradiés École Polytechnique, Palaiseau."— Presentation transcript:

1 Bethe-Salpeter Equation and Excitonic effects: a short introduction Valerio Olevano Laboratoire des Solides Irradiés École Polytechnique, Palaiseau

2 Exciton and Bethe-Salpeter equation c v cv h c v h c v h W EXC P = ++ O(2) + RPAGWBSE Polarisation e-e- h+h+

3 Definitions L = 2-particles Correlation Function Polarization Dielectric Function (observables) G = Green Function 2-particles Green Function

4 Bethe-Salpeter Equation Bethe-Salpeter Equation Interaction Kernel = Self-Energy W =Screened Interaction

5 Resolution of the BSE: Excitonic Hamiltonian Overlap Matrix Excitonic Eigenfunctions Excitonic Eigenvalues Excitonic Hamiltonian

6 Excitonic Macroscopic Dielectric Function

7 Excitonic Hamiltonian: Resonant and Coupling terms Hermitean Symmetric full diago of a Non-Hermitean matrix or diagonalization of an Hermitean matrix (R) plus (eventually) Perturbation Theory


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