Particle-hole attraction

Eq.(2.27) together with the Dyson equation (2.1 ) (with t defines so-called "0-derivable" approximations. 0 derivability guarantees then a self-consistent approximation in many-body perturbation theory which, for a given order of approximation, satisfies various conservation laws. For example the particle-hole attraction in eq.(2.9) is given by (Ward identity) 6 0/6g6g. 

The second requirement for a model to posses particle-hole symmetry is that the electron-electron interactions must be balanced - on average - by electron-nuclear interactions. For a chain with translational symmetry every site is equivalent with the same potential energy. For a linear chain, with open boundary conditions, however, the sites are not equivalent. The electrons on sites in the middle of a chain experience a larger potential energy from the nuclei than electrons on sites towards the ends of the chain. This potential energy, Vj = is shown in Fig. 2.9. Correspondingly, the electrons on sites in the middle of the chain experience a larger electron-electron repulsion than electrons towards the end of the chain. When this repulsion is equal and opposite to the electron-nuclei attraction, there is particle-hole symmetry, and every site is essentially equivalent. 

In this section we derive an effective Hamiltonian that describes the high energy physics associated with particle-hole (or ionic) excitations across the charge gap. The Hamiltonian will describe a hole in the lower Hubbard band and a particle in the upper Hubbard band, interacting with an attractive potential. This attractive potential leads to bound, excitonic states. In the next chapter we derive an effective-particle model for these excitons. A real-space representation of an ionic state is illustrated in Fig. 5.5(b). 

The study of excitons in conjugated polymers has often been inspired by the treatment of excitons in bulk three-dimensional semiconductors (as described in Knox (1963)). A particle-hole excitation from the valence band to the conduction band in a semiconductor leaves a positively charged hole in the valence band and a negatively charged electron in the conduction band. The Coulomb attraction between these particles results in bound states, or excitons. In three-dimensional semiconductors the excitons are usually weakly bound, with large particle-hole separations, and are well described by a hydrogenic model. Excitons in this limit are known as Mott- Wannier excitons. 

This is the lowest pseudomomentum branch of the family of n = 1 Mott-Wannier singlet excitons resulting from the Coulomb attraction between the particle-hole excitation from the valence (di) to the conduction d ) bands. 

In some semiconductor polymer blends the excited electron becomes a free particle in the conduction band and, similarly, the hole left in the valance band also becomes free [69]. This leaves behind a localized positively charged hole. The electron and hole attract each other by electrostatic coulombic forces, however, and may possibly form a bound state in which the two particles revolve together around their center of mass such a state is referred to as an exciton. The exciton level is in the same neighborhood as the donor level. The energy of the photon involved in exciton absorption is given by ... 

Mobile H centres in alkali halides are known to aggregate in a form of complex hole centres [64] this process is stimulated by elastic attraction. It was estimated [65, 66] that for such similar defect attraction the elastic constant A is larger for a factor of 5 than that for dissimilar defects - F, H centres. Therefore, elastic interaction has to play a considerable role in the colloid formation in alkali halides observed at high temperatures [67]. In this Section following [68] we study effects of the elastic interaction in the kinetics of concentration decay whereas in Chapter 7 the concentration accumulation kinetics under permanent particle source will be discussed in detail. 

The interpretation of the interband transition is based on a single particle model, although in the final state two particles, an electron and a hole, exist. In some semiconductors, however, a quasi one-particle state, an exciton, is formed upon excitation [23,24]. Such an exciton represents a bound state, formed by an electron and a hole, as a result of their Coulomb attraction, i.e. it is a neutral quasi-particle, which can move through the crystal. Its energy state is close to the conduction band (transition 3 in Fig. 2), and it can be split into an independent electron and a hole by thermal excitation. Therefore, usually... 

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