Quasiparticle correction

More advanced teclmiques take into account quasiparticle corrections to the DFT-LDA eigenvalues. Quasiparticles are a way of conceptualizing the elementary excitations in electronic systems. They can be detennined in band stmcture calculations that properly include the effects of exchange and correlation. In the... 

Bechstedt F 1992 Quasiparticle corrections for energy gaps in semiconductors Adv. Solid State Phys. 32 161... 

Figure B3.2.1. The band structure of hexagonal GaN, calculated using EHT-TB parameters detemiined by a genetic algorithm [23]. The target energies are indicated by crosses. The target band structure has been calculated with an ab initio pseudopotential method using a quasiparticle approach to include many-particle corrections [194].

The absorption spectrum is proportional to the imaginary part of the macroscopic dielectric function. Adopting the same level of approximation that we have introduced to obtain GW quasiparticle energies, i.e. neglecting the vertex correction by putting T = 55, we get the so called random phase approximation (RPA) for the dielectric matrix. Within this approximation, neglecting local field effects, the response to a longitudinal field, for q 0, is ... 

Neglecting off-diagonal elements of the self-energy matrix in the canonical Hartree-Fock basis in (1.15) constitutes the quasiparticle approximation. With this approximation, the calculation of EADEs is simplified, for each KT result may be improved with many-body corrections that reside in a diagonal element of the self-energy matrix. 

A corollary of the above results is that one should expect isotope effects in the quasiparticle spectrum measured in the pseudogap state, since once localized, the hot quasiparticles can become strongly coupled to the lattice. (When not localized, the coupling of the hot quasiparticles to phonons is markedly reduced by vertex corrections associated with their magnetic coupling.) Any coupling of cold quasiparticles to the lattice would be very much smaller. These conclusions appear consistent with the ARPES results reported by Lanzara at this workshop, ft leads me to predict that no isotope effect will be found for hot quasiparticles in overdoped materials. 

The formal expressions for higher-order MBPT corrections for both the total energy and band energy are the same as those for the total energy and quasiparticle energy, respectively, in finite systems. By substituting Eq. (15) and... 

Approximate propagators may be designed to provide perturbative corrections to Koopmans results or may have the flexibility to account for correlation states where Ih or Ip descriptions of final states are qualitatively invalid. For the first case, in which the one-electron picture of electron detachment or attachment is adequate, quasiparticle self-energy approximations are suitable. In other cases, nondiagonal self-energy approximations are necessary. 

Having been derived on the basis of purely qualitative considerations, the Hamiltonian (6.6) naturally requires some substantiation. It can be shown (see (10) and references therein) that when the cubic terms of the intramolecular anharmonicity, which do not conserve the number of quasiparticles, are taken into account, as well as anharmonicity of the fourth order, we obtain a Hamiltonian of the form (6.6), provided that the natural frequencies of the intramolecular vibrations appearing in the Hamiltonian Ho are considered to have been found taking anharmonicity into account. This provides a correction of the order of A/nn. 

Thus, strictly speaking, the operator (6.6) can be employed for investigating the states of a crystal with two vibration quanta only when the intramolecular anharmonicity of the form given in (6.5) dominates, and the part of the anhar-monicity that is associated with the presence of intermolecular interaction can be neglected.47 Since, by assumption, A/Ml -C 1 and A/Ml -C 1, the total Hamiltonian (6.6) also neglects terms that do not conserve the number of quasiparticles (inessential corrections are introduced if they are taken into account). 

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