Hedin equations in resonant microcavities

Abstract

With the improvement of the experimental techniques, many new phenomena in which the photon degrees of freedom are involved have been discovered. Typical examples are the exciton-polariton quasi-particles, excitons strongly coupled to photons. A correct description of these systems requires a full account of the photon's dynamics, including the vector gauge degrees of freedom. In order to include this contribution in ab initio many-body perturbation theories, here we present a generalization of the Hedin equations, originally derived for a many electron system with Coulomb interaction. These equations are now derived to take into account the strong coupling physics of the electrons and the transverse photon's degrees of freedom.

Nonlocal kinetic energy functional from the jellium-with-gap model: Applications to orbital-free density functional theory

“…(7), (10), (16)- (18), depends on the energy-gap E g . Previous investigation on exchange-correlation kernel indicated that E g can be fixed to the experimental fundamental gap of semiconductors and insulators 109 . In this subsection we will verify if this can be considered a good approximation also for the kinetic energy.…”

Jellium-with-gap model applied to semilocal kinetic functionals

“…This term is correct (see Eq. (4)) and it has been also used in the jellium-with-gap XC kernel 35 , which gives accurate optical absorption spectra of semiconductors and insulators. On the other hand, if we first perform a series expansion for ∆ → 0, and then a series expansion for η → 0 we obtain:…”

“…The jellium-with-gap model 29 , was developed outside the KS framework, using perturbation theory to take into account the band gap energy. This model was used to have qualitative and quantitative insight for semiconductors [30][31][32][33][34] , to develop an XC kernel for the optical properties of materials 35 , and to construct accurate correlation energy functionals for the ground-state DFT 29,[36][37][38][39][40] . We will show that the Lindhard function for the jellium-with-gap model (F GAP ), previously introduced by Levine and Louie 33 in a different context (dielectric constant and XC potential), may be seen as a sophisticated analytical form suitable for KE approximations.…”

Conserving approximations in cavity quantum electrodynamics: Implications for density functional theory of electron-photon systems

“…In the recent years both frameworks have be generalized to include photonic degrees of freedom. A QED extension of the non-relativistic MBPT and the Hedin equations approach to describe many-electron systems in microcavities have been proposed in 36,37 . The generalization of TDDFT, known as QED-TDDFT or QEDFT, was developed in Refs.…”