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Prog. Theor. Phys. Vol. 46 No. 3 (1971) pp. 757-775

Microscopic Theory of Thermal Conductivity in an Electron-Phonon System

Yoshiyuki Ono

Department of Physics, University of Tokyo, Tokyo

(Received April 6, 1971)

Abstract:

Using the Kubo formula and thermal Green function technique, we formulate a microscopic method for calculating the thermal conductivity of an electron-phonon system. First, we derive generalized Ward idetities (GWI) for the heat current vertices, and calculate the Green functions and current vertices in an approximation consistent with the GWI. Thermal conductivity becomes divergent in this calculation in the same sense that electrical conductivity is divergent as was shown by Holstein. The additivity of electron and phonon contributions to thermal conductivity is shown to be approximately valid.

URL : http://ptp.ipap.jp/link?PTP/46/757/
DOI : 10.1143/PTP.46.757

[ Full Text PDF : FREE ACCESS (981K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. R. E. Peierls, Ann. of Phys. 4 (1930), 121; ibid. 5 (1930), 244; ibid. 12 (1932), 154; Quantum Theory of Solid (Oxford Univ. Press, 1955).
2. M. S. Green, J. Chem. Phys. 20 (1952), 1281[CrossRef]; ibid. 22 (1954), 398[CrossRef].
   H. Mori, J. Phys. Soc. Jpn. 11 (1956), 1029[JPSJ].
   R. Kubo, M. Yokota and S. Nakajima, J. Phys. Soc. Jpn. 12 (1957), 1203[JPSJ].
   S. Nakajima, Prog. Theor. Phys. 20 (1958), 948[PTP].
   J. A. McLennan, Jr., Phys. Rev. 115 (1959), 1405[APS].
   D. N. Zubarev, Doklady Akad. Nauk SSSR 140 (1961), 92 [English translation: Sov. Phys. Doklady 6 (1962), 776].
   J. M. Luttinger, Phys. Rev. 135 (1964), A1505[APS].
3. T. Holstein, Ann. of Phys. 29 (1964), 410[CrossRef].
4. O. V. Konstantinov and V. I. Perel', Zh. Exp. i Teor. Fiz. 39 (1960), 197 [English translation: Sov. Phys. -JETP 12 (1961), 142].
5. T. Matsubara, Prog. Theor. Phys. 14 (1955), 351[PTP].
6. A. A. Abrikosov, L. P. Gor'kov and I. Ye. Dzyaloshinskii, Zh. Exp. i Teor. Fiz. 36 (1959), 900 [English translation: Sov. Phys. -JETP 9 (1959), 636].
7. A. B. Migdal, Zh. Exp. i Teor. Fiz. 34 (1958), 1438 [English translation: Sov. Phys. -JETP 7 (1958), 996].
8. A. A. Abrikosov, L. P. Gor'kov and I. Ye. Dzyaloshinskii, Quantum Field Theoretical Methods in Statistical Physics (Pergamon Press, 1965), 2nd ed.
9. Y. Nambu, Phys. Rev. 117 (1960), 648[APS].
10. J. R. Schrieffer, Theory of Superconductivity (Benjamin, 1964).
11. H. Fukuyama, H. Ebisawa and Y. Wada, Prog. Theor. Phys. 42 (1969), 494[PTP].
12. L. P. Kadanoff and P. C. Martin, Phys. Rev. 124 (1961), 670[APS].
13. K. Maki, Prog. Theor. Phys. 31 (1964), 378[PTP].
14. V. Ambegaokar and A. Griffin, Phys. Rev. 137 (1965), A1151[APS].
15. K. Baumann, Ann. of Phys. 23 (1963), 221[CrossRef].
16. J. Zittartz, Phys. Rev. 165 (1968), 612[APS].
17. Ph. Choquard, Helv. Phys. Acta 36 (1963), 415.
18. For example, S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Colonial Press Inc., 1961).
19. Y. Ono, unpublished material, 1971.
20. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, 1952).
21. For example, P. G. Klemens, Handbuch der Physik 14 (1956), 198.
22. A. Sommerfeld and H. Bethe, Handbuch der Physik 24-2 (Springer, Berlin, 1933), p. 333.
23. A. H. Wilson, The Theory of Metals (Cambridge Univ. Press, 1953) 2nd ed.
24. D. K. C. MacDonald, Thermoelectricity-An Introduction to the Principles (John Wiley and Sons Inc., New York, 1962).

Citing Article(s) :

1. Journal of the Physical Society of Japan 81 (2012) 113602 (3 pages) :

   Microscopic Theory of Magnon-Drag Thermoelectric Transport in Ferromagnetic Metals

   Daisuke Miura and Akimasa Sakuma

2. Progress of Theoretical Physics Supplement No.69 (1980) pp. 365-375 :

   Theory of Phonon Drag in a Strong Magnetic Field

   Yoshiyuki Ono

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