OBSERVED AND PREDICTED MANY-BODY EFFECTS IN THERMOELECTRICITY IN METALS

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OBSERVED AND PREDICTED MANY-BODY

EFFECTS IN THERMOELECTRICITY IN METALS

J. Opsal, J. Bass

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 8 , Tome 39, aotit 1978, page _C6-1031

J.L. Opsal and J. Bass

P h y s i c s Department, Michigan S t a t e U n i v e r s i t y , E a s t L a n s i n g , Michigan 48824, U.S.A.

RBsum6.- On fait une revue des effets N corps qui sont observes et prBdits pour l'effet thermo6lec- trique des mdtaux. On considsre la possibilitd d'indentifier les termes qui ne sont pas encore bien compris.

Abstract.- A review is given of observed and predicted many-body effects in thermoelectricity in metals. The possibility of isolating terms which are not yet well understood is discussed.

We and others have recently shown that, contra- ry to previous belief, the thermoelectricity coefficients of a metal are enhanced at low temperatures by large many-body effects which must be taken into account in any quantitative calculation of thermopower/l/. These enhancements set the thenno- electric coefficients apart from the electrical and thermal conductivities, neither of which shown any such enhancement. In this paper we briefly review what is known and what is not yet known about many- body effects in thermoelectricity.

First, we note that thermoelectric coefficients consist of two components ; electron diffusion, and phonon-drag. Many-body effects appear only in the electron-diffusion component. This component is determined by energy derivatives of quasi-particle properties and, as discussed elsewhere, it is these derivatives which bring forth many-body effects 11,2/.

It is convenient to distinguish two categories of predicted many-body effects, one of which has to do only with intrinsic properties of the quasi-par- ticles, such as mass and velocity, and the other of which is associated with quasi-particle scattering.

The first category contains two effects : (1) Enhancement of the bare particle mass by a factor 1 +

X,

which appears in the thermoelectric coefficients as an enhancement in-the density of states at the Fermi energy by this same factor/l/. (2) Small, but strongly energy dependent corrections to the quasi-particle velocity, over and above the 1 + h correction, which can also produce a significant contribution to some thermoelectric coeffi-

+

Work supported in part by the United States NSF under grants DMR-77-04680 and DMR-75-01584

cientsl31.

The second category contains several effects: (3) virtual recoil, a many-body correction to the scattering of electrons by impurities121 ; (4) phony- phonon-drag, a many-body correction to the scattering of electrons by phonons/4/ ; (5) and (6) vertex renormalization of electron-impurity and electron- phonon scattermg/5,6/ ; (7) recently suggested additional contributions, which as yet cannot be easi- ly categorized/7/.

The only one of these seven (or more ?) predicted many-body effects which has been definitely established experimentally is the mass-enhancement correction. By measuring selected thermoelectric effects, it has been shown that all of the thermo electric coefficients are enhanced by the factor 1 +

X

/l/, with this enhancement being confirmed for one of the coefficients to within a few percent of h 18,9/. This coefficient is the off-diagonal component of the thermoelectric tensor in the pre- sence of a magnetic field. It was extracted by measuring the high field limit of the Nernst-Ettingshau- sen effect in both A1191 and Moly/8/. As described elsewhere, in high magnetic field this off-diagonal component is independent of scattering, contains only this one many-body effect, and appears to be iden- tical to the electronic specific heat to within a constant multiplying factor /10/. Figure 1 shows the Nernst-Ettingshausen coefficient for A1 over the temperature range 1.8 K to 5 K. The intercept with the T = 0 axis is required diffusion component and the horizontal dashed line is the value predicted with no adjustable parameters for an enhancement of 1 + h determined from the measured electronic specific heat. With no enhancement, the value would have been about 4.0 in the units given, which falls well below the bottom of the graph. We nob that the

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Fig. 1 : The Nernst-Ettingshausen -pa divided by the magnetic field B, as a function of the temperature squared, for aluminum. The different symbols indica- te magnetic fields of 1.5 tesla

(A),

1.8 tesla

m),

2.0 tesla (o), and 2.1 tesla ( 0 ) . The broken line indicates the value predicted from the known electronic specific heat, which contains the enhancement factor 1 +

X.

enhancement in A1 is large, exceeding 40 %. It can be even larger in other metals, a value of 180 %

being expected for Pb/ll/.

Although the mass enhancement just described is the only many-body contribution to thermoelectricity which has been definitively established experimentally, we believe that its existence provides strong support for the existence of all the other predicted many-body effects, since they arise from many-body terms of similar structure. It is there- fore of interest to examine how they might be iso- lated and studied.

The problems are that they all appear together and that all but one of them are associated with quasi-particle scattering, which so far has not been accurately calculated for real metals.

Terms (2),(3) and (5) are all expected to vary linearly with temperature at the lowest temperatures, with more complex variations appearing as the temperature increases. Observed changes in the thermopo- wers of A1/12/ and Pb/13/ have been attributed to term (3), virtual recoil. However it has not yet been possible to w l e out alternative interpretations of the same data, primarily interpretations based upon anisotropic elbctron-impurity scattering. New information about anisotropic impurity scattering in A1 now becoming available from the Haas-van Alphen mea3urements may allow resolution of these conflic-

ting interpretations and establishment of the size of this effect.

Terms (4) and (6) are expected to vary as T~ at very low temperatures. They thus mimic the beha-

viour expected from phonon-drag. It has recently been suggested/l4/ that the magnitude of these effects might be established by first understanding

the behaviour of phonon-drag in the high field Nernst-Ettingshausen effect, where the only many- body effect is the well understood mass-enhancement. Oncephonon-drag is understood in the high field li-

mit, it should be possible to calculate its value accurately in zero field. Any significant differen- ces between these calculated values and experiment would then be attributed to terms (4) and (6), and possibly also (7).

To sum up, one many-body effect has been shown experimentally to exist in thermoelectricity and to be large. Additional effects have been predicted, and there is reason to believe that they exist too, and could be large. From the above ana- lysis, we conclude that there is a good possibility of substancial progress in the near future in understanding the role of many-body effects in thermoelectricity, the only transport coefficient which mani- fests such effects.

References

/l/ Opsal,J.L., Thaler,B.J. and Bass,J., Phys. Rev. Lett.

2

(1976) 1211

/2/ Nielsen,P.E. and Taylor,P.L., Phys. Rev. Lett. 21 (1968) 893

-

/3/ Lyo,S.K., Phys. Rev. Lett.

39

(1977) 363 ; Phys. Rev.

1

(1978) (In press)

141 Nielsen,P.E. and Taylor,P.L., Phys. Rev. Lett. 25 (1970) 371 ; Phys. Rev.

B10

(1974) 4061

-

/5/ Hasegawa,A., Solid St. Commun.

15

(1974) 1361 161 Hasegawa,A., J. Phys. F : Metal Phys. A(1974)

2164

/7/ Vilenkin,A. and Taylor,P.L., Bull. Am. Phys. Soc. 23 (1978) 428

181 Fletcher,R., Phys. Rev.

B14

(1976) 4329

191 Thaler,B.J., Fletcher,R., and Bass,J., J. Phys.

F : Metal Phys.

8

(1978) 131

/l01 Bass,J.,Fletcher,R.,Opsal,J.L. and Thaler,B.J., Proceedings of the Intll.Conf.on Thermoelectri- city in Metallic Conductors, F.J. Blatt and P.A. Schroeder Eds.Plenum PressYl978,(In press) /11/ Grimvall, G., Physica Scripta

2

(1976) 63 1121 Dudenhoffer,A.W. and Boarassa,R.R., Phys.Rev.

B5 (1972) 1651

-

/13/ Bourassa,R.R. and Dudenhoffer, A.W., Phys.Rev. B7 (1973) 1270