Tight-Binding Formalism for Ionic Fullerides and its Application to Alkali-C 60 Polymers
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INTRODUCTION Materials consist of ionic cores and valence electrons which mutually interact to attain
the lowest free-energy state under a given external condition. To predict this microscopic optimum state, which nature automatically finds, usually requires elaborate first-principles quantum-mechanical calculations. This can be done for infinite crystalline systems as well as for finite systems having a reasonable number of independent degrees of geometrical freedom. On the other hand, the recent macroscopic production of cage-network all-carbon clusters called "fullerenes" such as C60 , C 70 , and C8 4, and also the discovery of the carbon nanotubes opened a new field in materials science and engineering. These systems have a variety of geometries with a large number of constituent atoms in a unit cell or in a molecular unit. Due to their large unit size and to experimental difficulties in determining geometries of
carbon-based complex materials because of the weak X-ray scattering ability of light elements, theoretical structure studies represent an important tool in this field. However, first-principles calculations can be computationally highly expensive, therefore, less expensive theoretical methods such as interatomic model potentials and tight-binding methods are now attracting renewed interest [1]. In particular the tight-binding model constructed so as to reproduce first-principles results for various carbon systems has been proven to be useful in studying geometries and the electronic structure of these all-carbon systems [2,3]. Among various interesting subfields of this growing field of new carbon materials, the research on the alkali-doped fullerides (ANC6O, A=Na, K, Rb, and/or Cs) have been at395 Mat. Res. Soc. Symp. Proc. Vol. 491 © 1998 Materials Research Society
tracting great interest since it has resulted in various interesting material phases including superconductivity [4]. Also recently, several A1 C60 fullerides are found to have stable polymerized phases [5], which now form another new class of carbon-based crystalline materials consisting of both sp2 and sp 3 -hybridized C atoms. Although the charge transfer from alkalimetal atoms to the fullerene units usually takes place in these fullerides, the application of the standard all-carbon tight-binding model with an additional number of electrons may not give a correct microscopic optimum state since there remain two important terms to be included for these ionic fullerides. One is the intra-C6 0 Coulomb repulsion energy, and the other is the electrostatic energy of the ionic crystalline lattice (Madelung energy). In the present work, we generalize the tight-binding model by including these two important terms for ionic fullerides. This approach is applied to the K 1 C60 polymer and these terms are found to be very important. The obtained stable state is a charge-density-wave (CDW) state with a considerably smaller amplitude than the CDW state obtained by the tight-binding model without these two additional terms. FORMALISM In the usual t
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