Field theory of mesoscopic fluctuations in superconductor/normal-metal systems

JETP Letters

Volumn 67, Issue 1, 1998, Pages 22-27

  Altland, A ^a   Simons, B D ^a   Taras Semchuk, D ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001914433     PISSN: 00213640     EISSN: None     Source Type: Journal    
DOI: 10.1134/1.567622     Document Type: Article

References (27)

1. C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).
2. G. Eilenberger, Z. Phys. 182, 427 (1965);
3. 214, 195 (1968).
4. K. D. Usadel, Phys. Rev. Lett. 25, 507 (1970).
5. B. L. Altshuler and B. Z. Spivak, Zh. Éksp. Teor Fiz. 92, 609 (1987) [Sov. Phys. JETP 65, 343 (1987)].
6. M. L. Mehta, Random Matrices, New York: Academic Press, 1991.
7. For a review, see Nonequilibrium Superconductivity, Ed. V. L. Ginzburg, Nova Science Publications, 1988.
8. c) case has been analyzed previously in A. Altland and M. R. Zirnbauer, Phys. Rev. Lett. 76, 3420 (1996);
9. K. M. Frahm, P. W. Brouwer, J. A. Melsen, and C. W. J. Beenakker, Phys. Rev. Lett. 76, 2981 (1996).
10. In general, the proximity of an N metal leads to a renormalization of the superconducting order parameter in the boundary region. However, we do not expect this phenomenon to have an essential impact on our results.
11. R. Oppermann, Nucl. Phys. B 280, 753 (1987).
12. K. B. Efetov, Supersymmetry in Disorder and Chaos, New York: Cambridge University Press, 1997.
13. W in powers of W leads to contributions that are linear in W. These linear vertices generally have to be summed up to infinite order, which is difficult if not impossible.
14. M. Yu. Kupriyanov and V. F. Lukichev, Zh. Éksp. Teor. Fiz. 94, 139 (1988) [Sov. Phys. JETP 67, 1163 (1988)].
15. B. A. Muzykantskii and D. E. Khmel'nitskii, Phys. Rev. B 51, 5840 (1995).
16. W. Belzig, C. Bruder, and G. Schoen, Phys. Rev. B 54, 9443 (1996).
17. F. Zhou, P. Charlat, B. Spivak, and B. Pannetier, http://xxx.lanl.gov/abs/ cond-mat/9707056.
18. Note that the solution of Eq. (4) does not in general belong to the standard saddle-point manifold of the σ model. It can, however, be accessed by a deformation of the integration contour. 17
19. A. Altland, B. D. Simons, and D. Taras-Semchuk, to be published.
20. V. I. Fal'ko and K. B. Efetov, Europhys. Lett. 32, 627 (1995);
21. A. D. Mirlin, Phys. Rev. B 53, 1186 (1996).
22. A〉, allowing such terms to be neglected.
23. V. E. Kravtsov and A. D. Mirlin, JETP Lett. 60, 656 (1994).
24. B. D. Simons and B. L. Altshuler, Phys. Rev. Lett. 70, 4063 (1993).
25. B. L. Altshuler and B. I. Shklovskii, Zh. Éksp. Teor. Fiz. 91, 220 (1986) [Sov. Phys. JETP 64, 127 (1986)].
26. B. A. Muzykantskii and D. E. Khmel'nitskii, JETP Lett. 62, 76 (1995);
27. A. V. Andreev, O. Agam, B. D. Simons, and B. L. Altshuler, Phys. Rev. Lett. 76, 3947 (1996).