Abstract
We propose a superconductivity theory of two-band nonadiabatic systems with strong electron correlations in the linear approximation in nonadiabaticity. Assuming a weak electron-phonon interaction, we obtain analytic expressions for the vertex and “intersecting” functions for each of the two bands. With the diagrams involving intersections of two electron-phonon interaction lines taken into account (which means going beyond the Migdal theorem), we determine mass operators of the Green’s functions and use them to derive the basic equations of the superconductivity theory for two-band systems. We find an analytic expression for the superconducting transition temperature Tc that differs from the expression in the case of the standard two-band systems by an essential renormalization of the relevant quantities that results from the nonadiabaticity effects and strong electron correlations. We study the dependence of Tc and of the isotopic coefficient α on the Migdal parameter m = ω0/εF and show that accounting for the overlap of energy bands on the Fermi surface and for the nonadiabaticity effects at small values of the transferred momentum (q ≪ 2pF) allows obtaining high values of Tc even for the weak electron-phonon interaction.
Similar content being viewed by others
References
J. G. Berdnorz and K. A. Müller, Z. Phys. B, 64, 189 (1986).
V. A. Moskalenko, Phys. Met. Metallog., 8, 25 (1959).
H. Suhl, B. T. Matthias, and L. R. Walker, Phys. Rev. Lett., 3, 552 (1959).
M. E. Palistrant, “Comment on ‘Theory of two-band superconductors’,” cond-mat/0305496 (2003); L. Z. Kon, “Some kinetic properties of the two-band superconductors,” cond-mat/0309707 (2003).
V. A. Moskalenko, M. E. Palistrant, and V. M. Vakalyuk, Sov. Phys. Usp., 34, 717 (1991); cond-mat/0309671 (2003).
A. B. Migdal, JETP, 7, 996 (1958).
O. V. Danylenko and O. V. Dolgov, “Nonadiabatic contribution to the quasiparticle self-energy in systems with strong electron-phonon interaction,” cond-mat/0007189 (2000).
M. L. Kulic and R. Zeyher, Phys. Rev. B, 49, 4395 (1994); R. Zeyher and M. L. Kulic, Phys. Rev. B, 53, 2850 (1996).
L. Pietronero, S. Strässler, and C. Grimaldi, Phys. Rev. B, 52, 10516 (1995).
C. Grimaldi, L. Pietronero, and S. Strässler, Phys. Rev. B, 52, 10530 (1995).
M. E. Palistrant, Low Temp. Phys., 31, 738 (2005).
A. A. Abrikosov, Y. C. Campuzano, and K. Gofron, Phys. C, 214, 73 (1993).
M. E. Palistrant and F. G. Kochorbe, J. Superconductivity: Inc. Nov. Mag., 15, 113 (2002); J. Phys.: Cond. Mat., 15, 3267 (2003); M. E. Palistrant, Low Temp. Phys., 29, 889 (2003); M. E. Palistrant and F. G. Kochorbe, Internat. J. Mod. Phys. B, 17, 2545 (2003).
M. E. Palistrant, Low Temp. Phys., 26, 407 (2000); 28, 109 (2002); Theor. Math. Phys., 135, 566 (2003).
J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimistu, Nature, 463, 401 (2001).
P. C. Canfield, S. L. Bud’ko, and D. K. Finnemore, Phys. C, 385, 1 (2003).
F. Bouquet et al., Phys. C, 385, 192 (2003).
T. Mishonov, S. L. Drechsler, and E. Penev, Modern Phys. Lett. B, 17, 755 (2003); cond-mat/0209192 (2002); T. Mishonov, E. Penev, J. O. Indekeu, and V. I. Pokrovsky, Phys. Rev. B, 68, 104517 (2003); cond-mat/0209342 (2002); O. V. Dolgov, R. K. Kremer, J. Kortus, A. A. Golubov, and S. V. Shulga, Phys. Rev. B, 72, 024504 (2005).
A. S. Alexandrov, “Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime,” cond-mat/0102189 (2001).
H. Krakauer and E. Pickett, Phys. Rev. Lett., 60, 1665 (1988); J. F. Herman, R. V. Kasowski, and W. G. Hsu, Phys. Rev. B, 36, 6904 (1987); J. Kortus, I. I. Mazin, K. D. Belashchenko, V. P. Antropov, and L. L. Boyer, Phys. Rev. Lett., 86, 4656 (2001); J. M. An and W. E. Pickett, Phys. Rev. Lett., 86, 4366 (2001).
A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics [in Russian], Fizmatgiz, Moscow (1962); English transl., Dover, New York (1963).
F. G. Kochorbe and M. E. Palistrant, JETP, 77, 442 (1993); Theor. Math. Phys., 96, 1083 (1993); M. E. Palistrant, Internat. J. Mod. Phys. B, 19, 929 (2005).
W. L. McMillan, Phys. Rev., 167, 331 (1968).
V. A. Moskalenko, L. Z. Kon, and M. E. Palistrant, Low-Temperature Properties of Metals with Singularities of the Band Spectrum [in Russian], Shtiinta, Kishinev (1989).
M. E. Palistrant and F. G. Kochorbe, Phys. C, 194, 351 (1992).
R. Combescot, Phys. Rev. B, 42, 7810 (1990).
J. H. Kim and Z. Tešanović, Phys. Rev. Lett., 71, 4218 (1993); A. Lanzara et al., Nature, 412, 510 (2001); V. A. Moskalenko, P. Entel, M. Marinaro, and D. F. Digor, JETP, 97, 632 (2003).
Author information
Authors and Affiliations
Additional information
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 1, pp. 111–126, October, 2006.
An erratum to this article is available at http://dx.doi.org/10.1007/s11232-006-0155-9.
Rights and permissions
About this article
Cite this article
Palistrant, M.E., Ursu, V.A. Two-band superconductivity theory beyond the Migdal theorem. Theor Math Phys 149, 1393–1406 (2006). https://doi.org/10.1007/s11232-006-0127-0
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11232-006-0127-0