Andersen Group El.-Phon. QMC C60 Resistivity saturation

Resistivity saturation

In a semiclassical theory, the resistivity in a metal can be interpreted in terms of the mean free path l, the average distance an electron travels before it is scattered. For a good metal, i.e., Cu, l is typically very much larger than the distance d between two atoms. For several systems, e.g., many transition metal compounds, the resistivity becomes very large and the apparent l can become comparable to d. It is then typically found that the resitivity saturates, i.e,. grows much slower with the temperature T. In the figure, we compare the resistivity of Cu and Nb3Sb as well as the Ioffe-Regel resistivity, corresponding to l=d. In the 1970's and 1980's many examples like this were found, and this kind of behaviour was considered universal. In a semiclassical picture this makes sense, since one would expect that l could not be much smaller than d. However, the semiclassical theory breaks down when l~d, and the semiclassical argument is therefore not convincing.

More recently, a number of metals have been found where the Ioffe-Regel condition ( l > d ) is violated, so-called bad metals. This is in particular true for the high-Tc superconductors (e.g., La2-xSrxCuO4) and the alkali-doped fullerenes (A3C60) (see figure). This illustrates that the semiclassical argument (predicting l>d) is incorrect for these systems, emphasizing the need for a better theory for explaining resistivty saturation. The figure also emphasize the need for an explanation of the violation of the Ioffe-Regel condition for La2-xSrxCuO4 and A3C60.

We have developed a theory for describing these systems using the optical conductivity σ(w) as a function of the frequency w. We consider large values of T and use the f-sum rule. This allows us to obtain an approximate upper limit for the resistivity in terms of the kinetic energy and the effective band width. This upper limit typically has a weak T dependence. For for some metals, the resistivity grows so rapidly that the upper limit is approached for values of T that can be reached experimentally. Then saturation happens. After "saturation" the resistivity typically grows slowly. For some systems, however, the upper limit has a strong T dependence. Then the resistivity may grow so rapidly after "saturation" (where the upper limit for this T is approximately reached) that the concept of "saturation" becomes meaningless. We find that the systems may be grouped in three classes
1) Nb3Sb, representing a system with resistivity saturation according to the Ioffe-Regel criterion, i.e., for l~d.
2) La2-xSrxCuO4, consistent with resistivity saturation but at values much larger than predicted by the Ioffe-Regel criterion, i.e., l << d
3) A3C60, probably lacking resistivity saturation.
We find that the Ioffe-Regel condition can be derived quantum-mechanically by assuming that
i) the electrons are noninteracting,
ii) T<<W, where W is the band width, and
iii) there is no strong downturn in σ(w) at small w.
For the high-Tc superconductors and several other strongly correlated systems, condition i) is violated and for the alkali-doped fullerides condition ii) is violated.

Recent experimental work suggests that for the organic compound Θ-BEDT-TTF the Ioffe-Regel condition may be strongly violated due to a strong downturn in σ(w) at small w. This would then put Θ-BEDT-TTF in a fourth class, which violates condition iii).

We have extended these considerations to the electronic thermal conductivity κ of metals. For Nb we show that the saturation of the mean-free path approximately leads to κ=a+bT, where a and b are constants. In the large T limit we derive the Wiedemann-Franz law. For A3C60 we find a surprising drop in κ at very large T and strong violation of the Wiedemann-Franz law. We show that this is related to an unusal behavior of the specific heat at very large T.


O. Gunnarsson and K. Vafayi:
Comment on ``Collapse of Coherent Quasiparticle States in $\Theta$-(BEDT-TTF)$_2$I$_3$ Observed by Optical Spectroscopy''
Phys. Rev. Lett. 98, 219802 (2007), (pdf-file)

K. Vafayi, M. Calandra, and O. Gunnarsson:
Electronic thermal conductivity at high temperatures: Violation of the Wiedemann-Franz law in narrow band metals
Phys. Rev. B 74, 235116 (2006) .

O. Gunnarsson, M. Calandra, and J.E. Han:
Saturation of electrical resistivity
Rev. Mod. Phys. 75 , 1085 (2003).

M. Calandra and O. Gunnarsson:
Violation of Ioffe-Regel condition but saturation of resistivity of the high Tc cuprates.
Europhys. Lett. 61, 88 (2003).

M. Calandra and O. Gunnarsson:
Electrical resistivity at large temperatures: Saturation and lack thereof
Phys. Rev. B 66 , 205105 (2002)..

M. Calandra and O. Gunnarsson:
Saturation of electrical resistivity in metals at large temperatures
Phys. Rev. Lett. 87, 266601 (2001).

O. Gunnarsson and J.E. Han:
The mean free path for electron conduction in metallic fullerenes
Nature 405 , 1027 (2000).

For further information contact Olle Gunnarsson (

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Last Update: September 2012
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