Effective medium theory for the normal state in orientationally disordered fullerides

Abstract

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...

Electron propagation in orientationally disordered fullerides

“…In Ref. [8], we demonstrated that this model successfully accounts for the structure of the one-electron spectrum, and for the low-frequency electronic excitations obtained from numerical work on large simulation cells.…”

“…In this section we provide a brief review of the Bethe-lattice construction which was originally reported in Ref. [8].…”

“…This fact has been emphasized by Gelfand and Lu [5], and Satpathy et al [6], who noted that because of this effect, the orientational disorder produces off-diagonal disorder in the one-electron Hamiltonian on an energy scale which corresponds approximately to the Fermi energy for the doped carriers in the t 1u conduction band. Some of the effects on this disorder on the transport properties and the frequency-dependent conductivity have since been explored [7,8].…”

“…Until quite recently, theoretical work on the electronic properties of the orientationally disordered phases has been limited to numerical simulations on supercells containing quenched orientational disorder. We recently reported a different approach to this problem, in which we developed an "effective medium" to describe the strong scattering effects in the orientationally disordered phases [8]. The theory is based on a cluster-Bethe-lattice approach in which the disordered medium is modeled by a three-band Bethe lattice, into which we embed a molecular cluster whose scattering properties are then studied.…”

Measurement of the Branching Ratio ofπ0→e+e−Alavi-Harati1, Albuquerque2, Alexopoulos3 et al. 1999Phys. Rev. Lett.14000View full textAdd to dashboardCite

“…A 1989 search by the SINDRUM collaboration [8], using stopped π − p → π 0 n, produced a 90% confidence level upper limit of 1.3 × 10 −7 , excluding the central values of both previous measurements. In 1993, BNL E851 [9] and FNAL E799-I [10] observed the decay at the (5 − 10) × 10 −8 level, near the Standard Model expectation. The BNL measurement used K + → π + π 0 decays, while the FNAL experiment used K L → 3π 0 decays.…”