An effective medium theory for studying the electronic structure of the orientationally disordered M3C60 fullerides is developed and applied to study various normal state properties. The theory is based on a cluster-Bethe-lattice method in which the disordered medium is modeled by a threeband Bethe lattice, into which we embed a molecular cluster whose scattering properties are treated exactly. Various single-particle properties and the frequency-dependent conductivity are calculated in this model, and comparison is made with numerical calculations for disordered lattices, and with experiment.PACS numbers: 71.25. Pi, 71.25.Tn, 74.70.Wz In the metallic fullerides M3C60 doped with the large alkali metals, the fullerene molecules are quenched into an orientationally disordered state [1]. In this state, each of the Ceo molecules is centered on the sites of an fee Bravais lattice and adopts a high symmetry setting, with the twofold symmetry axes aligned along [001] crystal directions. There are two inequivalent ways of achieving this orientation on each lattice site, and the intensities of x-ray reflections measured for these solids are well described by a merohedrally disordered structural model in which the choice of setting varies randomly from site to site in the solid [1]. It is now widely accepted that merohedral disorder is either a dominant or a contributing factor to a number of the observed electronic properties of these doped systems [2]. In this paper we apply an effective medium theory to study the conduction-electron states in these disordered solids.The amplitude for electronic hopping across bond r between neighboring fullerene sites in these systems can be represented by a real 3x3 matrix, TJ^r), in which each of the matrix elements corresponds to a possible choice of orbital polarization JJL(V) = x,y,z in the t\ u manifold on the initial and final sites [3][4][5][6]. Orientational disorder on the fullerene sites leads to a model with offdiagonal disorder in a Hamiltonian for an electron which carries with it an internal "orbital" degree of freedom, represented by a three component field. Gelfand and Lu [3] made the interesting observation that the sizes and signs of the various matrix elements in T can be changed by changing the relative molecular orientations on the terminal sites. This is a representation-dependent statement, since the signs and sizes of the various elements in T are also changed by any local rotation of the internal ti u orbital bases on either of the terminal sites. Of course, physically measurable quantities in this problem can always be expressed in a representation-independent (gauge invariant) manner that does not refer to a specific convention for defining the orbital polarizations on the various molecular sites. For example, the total density of states is obtained from a trace over the single-particle Green's function, N(E) --(l/7r)ImtrG+(i£), where the trace requires a sum over both sites and over the orbital degrees of freedom on a single site. If one considers a momen...
The coupling between the intramolecular vibrational modes and the doped conduction electrons in M 3 C 60 is studied by a calculation of the electronic contributions to the phonon self energies. The calculations are carried out for an orientationally ordered reference solid with symmetry F m3m and for a model with quenched orientational disorder on the fullerene sites. In both cases, the dispersion and symmetry of the renormalized modes is governed by the electronic contributions. The current current correlation functions and frequency dependent conductivity through the midinfrared are calculated for both models. In the disordered structures, the renormalized modes derived
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