Real-time diagrammatic approach to transport through interacting quantum dots with normal and superconducting leads

Physical Review B - Condensed Matter and Materials Physics

Volumn 77, Issue 13, 2008, Pages

  Governale, Michele ^a   Pala, Marco G ^b   König, Jürgen ^a,c  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b IMEP LAHC   (France)

^c UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 42449151657     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.77.134513     Document Type: Article

References (48)

1. M. R. Buitelaar, T. Nussbaumer, and C. Schönenberger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.256801 89, 256801 (2002)
2. J.-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, T. Ondarçuhu, and M. Monthioux, Nat. Nanotechnol. NNAABX 1748-3387 10.1038/nnano.2006.54 1, 53 (2006)
3. P. Jarillo-Herrero, J. A. van Dam, and L. P. Kouwenhoven, Nature (London) NATUAS 0028-0836 10.1038/nature04550 439, 953 (2006)
4. H. I. Jørgensen, K. Grove-Rasmussen, T. Novotný, K. Flensbert, and P. E. Lindelof, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.207003 96, 207003 (2006).
5. J. A. van Dam, Y. V. Nazarov, E. P. A. M. Bakkers, S. De Franceschi, and L. P. Kouwenhoven, Nature (London) NATUAS 0028-0836 10.1038/nature05018 442, 667 (2006)
6. T. Sand-Jespersen, J. Paaske, B. M. Andersen, K. Grove-Rasmussen, H. I. Jørgensen, M. Aagesen, C. B. Sørensen, P. E. Lindelof, K. Flensberg, and J. Nygård, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.126603 99, 126603 (2007).
7. C. Buizert, A. Oiwa, K. Shibata, K. Hirakawa, and S. Tarucha, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.136806 99, 136806 (2007).
8. R. Fazio and R. Raimondi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.2913 80, 2913 (1998)
9. R. Fazio and R. Raimondi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.4950 82, 4950 (1999).
10. K. Kang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.9641 58, 9641 (1998).
11. P. Schwab and R. Raimondi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.1637 59, 1637 (1999).
12. A. A. Clerk, V. Ambegaokar, and S. Hershfield, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.3555 61, 3555 (2000).
13. S. Shapira, E. H. Linfield, C. J. Lambert, R. Seviour, A. F. Volkov, and A. V. Zaitsev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.159 84, 159 (2000).
14. J. C. Cuevas, A. L. Yeyati, and A. Martín-Rodero, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.63.094515 63, 094515 (2001).
15. C. W. J. Beenakker and H. van Houten, in Single-Electron Tunneling and Mesoscopic Devices, edited by, H. Koch, and, H. Lübbig, (Springer, Berlin, 1992), pp. 175-179.
16. L. I. Glazman and K. A. Matveev, JETP Lett. 49, 659 (1989). 0021-3640
17. B. I. Spivak and S. A. Kivelson, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.43.3740 43, 3740 (1991).
18. A. V. Rozhkov, D. P. Arovas, and F. Guinea, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.233301 64, 233301 (2001).
19. A. A. Clerk and V. Ambegaokar, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.9109 61, 9109 (2000).
20. Y. Avishai, A. Golub, and A. D. Zaikin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.041301 67, 041301 (R) (2003).
21. G. Sellier, T. Kopp, J. Kroha, and Y. S. Barash, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.174502 72, 174502 (2005).
22. R. López, Mahn-Soo Choi, and R. Aguado, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.045132 75, 045132 (2007).
23. F. S. Bergeret, A. L. Yeyati, and A. Martin-Rodero, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.132505 74, 132505 (2006).
24. C. Karrasch, A. Oguri, and V. Meden, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.77.024517 77, 024517 (2008).
25. Z. Nussinov, A. Shnirman, D. P. Arovas, A. V. Balatsky, and J. X. Zhu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.214520 71, 214520 (2005).
26. A. L. Yeyati, J. C. Cuevas, A. López-Dávalos, and A. Martín-Rodero, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.55.R6137 55, R6137 (1997).
27. G. Johansson, E. N. Bratus, V. S. Shumeiko, and G. Wendin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.60.1382 60, 1382 (1999).
28. I. A. Sadovskyy, G. B. Lesovik, and G. Blatter, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.195334 75, 195334 (2007).
29. S. Ishizaka, J. Sone, and T. Ando, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.8358 52, 8358 (1995).
30. Mahn-Soo Choi, Minchul Lee, K. Kang, and W. Belzig, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.020502 70, 020502 (R) (2004).
31. F. Siano and R. Egger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.047002 93, 047002 (2004).
32. E. Vecino, A. Martín-Rodero, and A. L. Yeyati, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.035105 68, 035105 (2003).
33. Mahn-Soo Choi, C. Bruder, and D. Loss, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.13569 62, 13569 (2000).
34. M. G. Pala, M. Governale, and J. König, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/8/278 9, 278 (2007).
35. A. F. Volkov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74. 4730 74, 4730 (1995)
36. F. K. Wilhelm, G. Schön, and A. D. Zaikin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.1682 81, 1682 (1998)
37. S.-K. Yip, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.5803 58, 5803 (1998)
38. P. Samuelsson, J. Lantz, V. S. Shumeiko, and G. Wendin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.1319 62, 1319 (2000)
39. E. V. Bezuglyi, V. S. Shumeiko, and G. Wendin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.134506 68, 134506 (2003)
40. F. Giazotto, T. T. Heikkilä, F. Taddei, R. Fazio, J. P. Pekola, and F. Beltram, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.137001 92, 137001 (2004).
41. J. J. A. Baselmans, A. F. Morpurgo, B. J. van Wees, and T. M. Klapwijk, Nature (London) NATUAS 0028-0836 10.1038/16204 397, 43 (1999).
42. J. Bardeen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.9.147 9, 147 (1962)
43. B. D. Josephson, Phys. Lett. PHLTAM 0031-9163 10.1016/0031-9163(62)91369- 0 1, 251 (1962).
44. J. König, H. Schoeller, and G. Schön, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1715 76, 1715 (1996)
45. J. König, J. Schmid, H. Schoeller, and G. Schön, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.16820 54, 16820 (1996).
46. Y. Meir and N. S. Wingreen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.2512 68, 2512 (1992).
47. In Ref., the Josephson current was defined with the opposite sign. The present choice is the most natural one to identify the π -junction behavior.
48. In the case of a normal line, the factor | Δ/ω | is not present, but the argument remains the same.