Electron-Phonon Coupling in Superconducting Alkali-Metal Doped Fullerenes
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ELECTRON-PHONON COUPLING IN SUPERCONDUCTING ALKALI-METAL DOPED FULLERENES R.A. JISIlIt and M.S. DRESSELIIAUSt t Department of Physics, California State University at Los Angeles, Los Angeles, CA 90032 t Department of Electrical Engineering and Computer Science and Department of Physics, MIT, Cambridge MA 02139
Abstract The dimensionless electron-phonon coupling parameter in alkali metal-doped fullerenes is evaluated in a model whereby the electrons are treated within a tight binding formalism. The phonon mode frequencies and eigenvectors are obtained from a lattice dynamical model which accurately fits all available experimental data on these modes. It is shown that the electrormphonon interaction can account for the relatively high values of the superconducting transition temperatures in alkali-metal fullerenes.
1
Introduction
Shortly after the synthesis of solid C 60 [1], superconductivity was discovered in potassium-doped C 6 o, namely K3 C 60 , with a transition temperature T. = 18 K [2]. This was followed by the synthesis of other superconducting compounds such as Rb3 C 60 , RbCs 2 C 6 0, and Rb 2 CsC 6 0, with values of T. exceeding 30 K [3, 4, 5]. Except for the copper-oxide ceramics, these compounds have the highest reported values of the superconducting transition temperature. Understanding the mechanism of superconductivity in these materials is thus of great importance. In this work we consider the influence of curvature of the C60 molecule on the strength of the electron-phonon coupling. The phonon frequencies and eigenvectors are calculated within a force-constant model which accurately fits all available experimental data obtained from Raman [6, 7, 8, 9], infrared [1, 10], inelastic neutron scattering [11, 12, 13], and high resolution electron energy loss [14] spectroscopies. The electron-phonon coupling in M 3 C 60 is described in terms of a tight binding Hamiltonian [15] which is believed to be appropriate for the 7r-bonds in carbon systems [16]. In this work we shall consider coupling between electrons and on-ball phonons, which will be assumed to be dispersionless in the Brillouin zone.
2
Tight Binding Hamiltonian
The tight binding Hamiltonian, based on the assumption that the orbital on a carbon atom in C 60 follows the displaced ion without any appreciable deformation [17], can be written as 'h
J(?1, s; "S', )at a~~
=
(1)
n,n1,3,,a#
where (n, s) represents the atomic site, n denotes the unit cell, and s denotes the basis atom within the unit cell, at,.(a,,) is the creation (annihilation) operator for one electron in the orbital W•(fi-Rno,ii,,s), R/, being the equilibrium position of the atom at site (n,s) and if,, is its displacement from equilibrium. The matrix element J(n, s; n', s') in Eq. 1 is given by J(n, s; n'Ws') =
J
•'(
- fn,,' - i-n,,., 5 +
and represents the matrix element of the atomic potential nearest neighboring atoms.
+ i•,,,)V(rF(r)dF
(2)
'(rj between orbitals belonging to
Mat. Res. Soc. Symp. Proc. Vol. 270. @1992 Materials Research Society
162
Upon expan
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