Excitonic insulator theory

In contrast, Kulikov (1982) calculates the band structures of LaHj and LaHj, using self-consistent local-density functional theory. He stresses the importance and sensitivity of the choice for the crystal potential, finding incipient overlap between the conduction and valence bands for LaHj. The concept leads to an excitonic insulator phase at low temperatures. The low-temperature phase is semiconducting, and the higher-temperature phase is metallic i.e., the interpretation is opposite from that of Fujimori and Tsuda (1981). 

The bandlike aspects of the excitonic insulator model can be replaced by a more localized description developed from liquid-state theory (Hall and Wolynes, 1986 Lx>gan and Edwards, 1986 Xu and Stratt, 1989). In essence, the delocalized Wannier) exciton is replaced by a localized Frenkel) exciton. Such calculations exhibit a sharp transition in the degree of hybridization as the density of the system is varied. When the mercury density reaches a critical value, the degree of -character in the ground state drops sharply from the 100% (pure s-) atomic value. In common with other exciton models, the electronic transitions associated with electric dipole interactions in the localized limit are strongly enhanced by clustering. 

Both CIS and TDHF have the correct size dependence and can be applied to large molecules and solids (we will shortly substantiate what is meant by the correct size dependence ) [42-51], It is this property and their relatively low computer cost that render these methods unique significance in the subject area of this book despite their obvious weaknesses as quantitative excited-state theories. They can usually provide an adequate zeroth-order description of excitons in solids [50], Adapting the TDHF or CIS equations (or any methods with correct size dependence, for that matter) to infinitely extended, periodic insulators is rather straightforward. First, we recognize that a canonical HF orbital of a periodic system is characterized by a quantum number k (wave vector), which is proportional to the electron s linear momentum kh. In a one-dimensional extended system, the orbital is... 

However, in insulator solids or long linear chains possessing a band structure with delocalized electrons, a new physical phenomenon must be taken into account, namely, interaction between the excited electron and the remaining, positive hole in the valence band. This interaction in molecular crystals in usually described with the help of the simplest form of exciton theory, so-called Frenkel exciton theory (see, e.g., Knox< >) which assumes that the excited electron and the remaining positive hole can be found in the same unit cell. 

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