Electrical resistivity in metallic fullerenes

June 29, 2000

The electrical resistivity of metals is usually related to the average distance, l, electrons travel without being scattered. This semi-classical approach puts constraints on l, which were considered universal. Scientists at the Max-Planck Institute for Solid State Research, Stuttgart, report strong violations of these constraints for metallic fullerenes (Nature, June 29) [1].

In a perfect crystalline array of atoms, an electron can travel without being scattered. This can be understood within quantum mechanics, which explains how an electron can diffract around the atoms [2]. An electron is scattered, however, when it encounters an impurity or a thermally displaced atom. As the temperature is raised, the thermal displacements of the atoms increase and the electrons are scattered more frequently. This leads to a larger resistivity, which is interpreted in terms of a smaller l (called mean free path). In this semi-classical picture, however, one would expect that l cannot become smaller than the distance, d, between two atoms. Indeed during the 70's and 80's, many metals were observed for which the resistivity saturated when l became comparable to d. The expected constraint, l = d, was therefore considered to be universally satisfied. Recently, apparent exceptions have been found for some high temperature superconductors and for the alkali-doped fullerenes, A3C60 (A = K, Rb). In the latter case, l was expected to be larger than the separation d = 10Å between two fullerene molecules, while the measured resistivity at high temperatures is interpreted in terms of l ~ 1-2Å.

The mean free path is not measured directly but is determined indirectly from the experimental resistivity. It is assumed that all conduction electrons (three for A3C60) contribute to the conductivity and the value of l required to reproduce the experimental resistivity is then calculated. The metal could, however, be in an exotic state, where only a small fraction of the conduction electrons contribute to the conductivity. One would then have to conclude that l is correspondingly larger, perhaps larger than d.

This raises the question of whether l « d is in principle possible and whether l = d is violated for A3C60. In a paper in Nature [1], scientists at the Max-Planck Institute for Solid State Research, Stuttgart, address these questions. A simple model of A3C60 was constructed, where the scattering of the three conduction electrons against thermal, intramolecular vibrations is included. The resistivity of the model was calculated essentially exactly. The resistivity as a function of temperature is shown in Fig. 1. The model shows metallic behavior and there is no sign of the system being in an exotic state. The calculation was also performed for unrealistically high temperatures to look for a saturation in the resistivity. However, the resistivity of the model grows without any apparent limit, and the corresponding mean free path, l, is less than 1 Å at the largest temperatures considered. This demonstrates that a saturation in resistivity when l ~ d is not a universal behavior, since the model of A3C60 would then also have to show such a saturation. The model calculation furthermore makes suggestions about what special features of A3C60 lead to this very unusual behavior of the resistivity. The small value of l in A3C60 illustrates that the semi-classical picture breaks down for these systems. In metals, the electrons are usually described as quasi-particles with long life times. For the fullerenes the life time becomes extremely short at large temperatures and the quasi-particle concept makes little sense.
[1] O. Gunnarsson and J.E. Han
"The mean free path for electron conduction in metallic fullerenes"
Nature, June 29 (2000)

[2] P.B. Allen
in News and Views: "Misbehavior in metals: Non-gas states"
Nature, June 29 (2000)

Dr. Olle Gunnarsson
Max-Planck-Institut für Festkörperforschung
Heisenbergstrabe 1
D-70506 Stuttgart, Germany
Phone: +49-(0)711 - 6891669
Fax: +49-(0)711 - 6891632
E-mail: gunnar@anp.mpi-stuttgart.mpg.de


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