Entangled electron current through finite size normal-superconductor tunneling structures

European Physical Journal B

Volumn 40, Issue 4, 2004, Pages 379-396

  Prada, E ^a   Sols, F ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC CURRENTS; ELECTRIC POTENTIAL; HAMILTONIANS; INTERFACES (MATERIALS); LOW TEMPERATURE EFFECTS; MATRIX ALGEBRA; QUANTUM THEORY; THERMODYNAMICS;

ELECTRON CURRENT; NORMAL-SUPERCONDUCTORS (NS); QUANTUM INFORMATION DEVICES;

SUPERCONDUCTING MATERIALS;

EID: 6344294230     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1140/epjb/e2004-00284-8     Document Type: Article

References (61)

1. A.F. Andreev, Zh. Ekps. Teor. Fiz. 46, 1823 (1964) [Sov. Phys. JETP 19, 1228 (1964)]; A.F. Andreev, Zh. Ekps. Teor. Fiz. 49, 655 (1966) [22, 455 (1966)]
2. A.F. Andreev, Zh. Ekps. Teor. Fiz. 46, 1823 (1964) [Sov. Phys. JETP 19, 1228 (1964)]; A.F. Andreev, Zh. Ekps. Teor. Fiz. 49, 655 (1966) [22, 455 (1966)]
3. A.F. Andreev, Zh. Ekps. Teor. Fiz. 46, 1823 (1964) [Sov. Phys. JETP 19, 1228 (1964)]; A.F. Andreev, Zh. Ekps. Teor. Fiz. 49, 655 (1966) [22, 455 (1966)]
4. A.F. Andreev, Zh. Ekps. Teor. Fiz. 46, 1823 (1964) [Sov. Phys. JETP 19, 1228 (1964)]; A.F. Andreev, Zh. Ekps. Teor. Fiz. 49, 655 (1966) [22, 455 (1966)]
5. J. Demers, A. Griffin, Can. J. Phys. 49, 285 (1970)
6. G.E. Blonder, M. Tinkham, T.M. Klapwijk, Phys. Rev. B 25, 4515 (1982)
7. M. Tinkham, Introduction to Superconductivity, 2nd edn. (McGraw-Hill, New York, 1996)
8. J.M. Byers, M.E Flatté, Phys. Rev. Lett. 74, 306 (1995)
9. J. Torres, T. Martin, Eur. Phys. J. B 12, 319 (1999)
10. G. Deutscher, D. Feinberg, Appl. Phys. Lett. 76, 487 (2000)
11. P. Recher, E.V. Sukhorukov, D. Loss, Phys. Rev. B 63, 165314 (2001)
12. G. Falci, D. Feinberg, F.W.J. Hekking. Europhys. Lett. 54, 255 (2001)
13. R. Mélin, J. Phys.: Condens. Matter 13, 6445 (2001)
14. G.B. Lesovik, T. Martin, G. Blatter, Eur. Phys. J. B 24, 287 (2001)
15. V. Apinyan, R. Mélin, Eur. Phys. J. B 25, 373 (2002)
16. R. Mélin, D. Feinberg, Eur. Phys. J. B 26, 101 (2002)
17. D. Feinberg, G. Deutscher, Physica E 15, 88 (2002)
18. P. Recher, D. Loss, Phys. Rev. B 65, 165327 (2002)
19. N.M. Chtchelkatchev, G. Blatter, G.B. Lesovik, T. Martin, Phys. Rev. B 66, 161320 (2002)
20. D. Feinberg, Eur. Phys. J. B 36, 419 (2003)
21. P. Recher, D. Loss, Phys. Rev. Lett. 91, 267003 (2003)
22. P. Samuelsson, E.V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 91, 157002 (2003)
23. M. Kupka, Phys. C 221, 346 (1994)
24. M. Kupka, Phys. C 281, 91 (1997)
25. P.G. de Gennes, Superconductivity of Metals and Alloys, (Addison-Wesley, Reading, 1989)
26. C.W.J. Beenakker, in Mesoscopic Quantum Physics, edited by E. Akkermans, G. Montamboux, J.L. Pichard (North-Holland, Amsterdam, 1995)
27. J. Sánchez-Cañizares, F. Sols, J. Phys.: Condens. Matter 7, L317 (1995)
28. J. Sánchez-Cañizares, F. Sols, Phys. Rev. B 55, 531 (1997)
29. R. Kümmel, Z. Physik 218, 472 (1969)
30. F. Sols, J. Sánchez-Cañizares, Superlatt. and Microstruct. 25, 627 (1999)
31. C.J. Lambert, J. Phys.: Condens. Matter 3, 6579 (1991)
32. C.W.J. Beenakker, Phys. Rev. B 46, 12841 (1992)
33. H. Nakano, H. Takayanagi, Phys. Rev. B 50, 3139 (1994)
34. A. Levy Yeyati, A. Martín-Rodero, F.J. García-Vidal, Phys. Rev. B 51, 3743 (1995)
35. J. Sánchez-Cañizares, F. Sols, J. Low Temp. Phys. 122, 11 (2001)
36. J.R. Kirtley, Phys. Rev. B 47, 11379 (1992)
37. J. Bardeen, Phys. Rev. Lett. 6, 57 (1961)
38. G.D. Mahan, Many-Particle Physics, 3rd edn. (Kluwer Academic/Plenum, New York, 2000), p. 561
39. R.E. Prange, Phys. Rev. 131, 1083 (1963)
40. A. Galindo, P. Pascual, Quantum Mechanics (Springer, Berlin, 1990)
41. P.V. Gray, Phys. Rev. 140, 179 (1965)
42. z is implicit in reference [40]. We note, however, that here we find perfect agreement between Bardeen's perturbative method and the exact results in the tunneling limit
43. C.B. Duke, Tunneling in Solids (Academic Press, New York and London, 1969), p. 218
44. C.J. Chen, Phys. Rev. B 42, 8841 (1990)
45. E. Merzbacher, Quantum Mechanics, 3rd edn. (John Wiley & Sons, New York, 1998), Chap. 20
46. 2
47. A study of the angular dependence of Andreev reflection in the broad interface limit has been presented in reference [45]. However, it is restricted to a delta barrier interface and consider the case where N is a doped semiconductor
48. N.A. Mortensen, K. Flensberg, A.P. Jauho, Phys. Rev. B 59, 10176 (1999)
49. There, under the constraint of a given total current, entropy is maximized by the electron system adopting a displaced Fermi sphere configuration which exactly yields the cos θ law
50. R. Landauer, IBM J. Res. Dev. 1, 223 (1957); M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986); A. Szafer, A.D. Stone, IBM J. Res. Dev. 32, 384 (1988)
51. R. Landauer, IBM J. Res. Dev. 1, 223 (1957); M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986); A. Szafer, A.D. Stone, IBM J. Res. Dev. 32, 384 (1988)
52. R. Landauer, IBM J. Res. Dev. 1, 223 (1957); M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986); A. Szafer, A.D. Stone, IBM J. Res. Dev. 32, 384 (1988)
53. n.However, invoking trace invariance confers general validity to the argument and makes it more rigorous in the particular case of a broad interface embedded in an even broader wire
54. Together with the factor appearing in the definition (33), this factor 1/2 yields the 1/4 geometrical correction given by reference [50] and cited in reference [3]. We emphasize however that such 1/4 correction applies only to the normal conductance, as derived in reference [50], but not to the NS interface where, rather, the correct geometrical correction is 1/12, as implicitly noted in equations (33) and (41)
55. Yu.V. Sharvin, Zh. EKsp. Teor. Fiz. 48, 934 (1965) [Sov. Phys.-JETP 21, 655 (1965)]
56. Yu.V. Sharvin, Zh. EKsp. Teor. Fiz. 48, 934 (1965) [Sov. Phys.-JETP 21, 655 (1965)]
57. H.A. Bethe, Phys. Rev. 66, 163 (1944)
58. We do not rule out, however, that the errors derived from the use of equation (61) may cancel in the calculation of some physical quantities such as e.g. the ratio between the critical current and the normal conductance of a superconducting tunnel junction [53, 35]
59. V. Ambegaokar, A. Baratoff, Phys. Rev. Lett. 10, 486 (1963)
60. F.W.J. Hekking, Yu. V. Nazarov, Phys. Rev. B 49, 6847 (1994)
61. F. Sols, M. Macucci, U. Ravaioli, K. Hess, J. Appl. Phys. 66, 3892 (1989)