Gauge invariance and Hall terms in the quasiclassical equations of superconductivity

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 5, 2001, Pages

  Kita, Takafumi ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CONDUCTANCE; CONDUCTOR; ENERGY; MATERIAL STATE; MATHEMATICAL ANALYSIS; TIME;

EID: 0035424013     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.054503     Document Type: Article

References (23)

1. J. Bardeen and M. J. Stephen, Phys. Rev. 140, A1197 (1965).
2. P. Nozíeres and W. F. Vinen, Philos. Mag. 14, 667 (1966).
3. For an overview and references, see, e.g., S. J. Hagen, A. W. Smith, M. Rajeswari, J. L. Peng, Z. Y. Li, R. L. Greene, S. N. Mao, X. X. Xi, S. Bhattacharya, Q. Li, and C. J. Lobb, Phys. Rev. B 47, 1064 (1993).
4. T. Nagaoka, Y. Matsuda, H. Obara, A. Sawa, T. Terashima, I. Chong, M. Takano, and M. Suzuki, Phys. Rev. Lett. 80, 3594 (1998).
5. For an overview and references, see, e.g., E. B. Sonin, Phys. Rev. B 55, 485 (1997);
6. M. Stone, cond-mat/9708017 (unpublished).
7. For a review, see e.g., J. W. Serene and D. Rainer, Phys. Rep. 101, 221 (1983);
8. A. I. Larkin and Y. N. Ovchinnikov, in Nonequilibrium Superconductivity, edited by D. N. Langenberg and A. I. Larkin (Elsevier, Amsterdam, 1986), Vol. 12, p. 493.
9. A. I. Larkin and Y. N. Ovchinnikov, Phys. Rev. B 51, 5965 (1995).
10. N. B. Kopnin, J. Low Temp. Phys. 97, 157 (1994).
11. N. B. Kopnin and A. V. Lopatin, Phys. Rev. B 51, 15 291 (1995).
12. A. Houghton and I. Vekhter, Phys. Rev. B 57, 10 831 (1998).
13. L. P. Gor’kov, Zh. Éksp. Teor. Fiz. 36, 1918 (1959) [Sov. Phys. JETP 9, 1364 (1959)].
14. G. Eilenberger, Z. Phys. 190, 142 (1966).
15. G. Eilenberger, Z. Phys. 214, 195 (1968).
16. A. I. Larkin and Y. N. Ovchinnikov, Zh. Éksp. Teor. Fiz. 55, 2262 (1968) [Sov. Phys. JETP 28, 1200 (1969)].
17. The definitions of the Nambu Green’s functions (Formula presented) (Formula presented), and (Formula presented) by Eqs. (3), (63), and (67), respectively, are the same as those of the two review articles of Ref. 6. On the other hand, the definitions of (Formula presented) (Formula presented), and (Formula presented) by Eqs. (53), (64), and (69), respectively, agree with Larkin and Ovchinnikov but differ from Serene and Rainer by a factor of (Formula presented).
18. L. D. Landau and E. M. Lifshitz, Classical Theory of Fields (Pergamon, Oxford, 1975), Sec. 6.
19. M. Levanda and V. Fleurov, J. Phys.: Condens. Matter 6, 7889 (1994); see alsoH. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, Berlin, 1996), Sec. 7.
20. See, e.g., G. D. Mahan, Many-Particle Physics (Plenum, New York, 1990), pp. 479–485.
21. It turns out eventually that the expansion in terms of (Formula presented) is not required; see the paragraph around Eq. (59). However, we here proceed with Eqs. (37) and (42), since they enable us to present a clear derivation.
22. N. R. Werthamer, in Superconductivity, edited by R. D. Parks (Marcel Dekker, New York, 1969), p. 331.
23. A. L. Schelankov, J. Low Temp. Phys. 60, 29 (1985).