Supercurrent and multiple singlet-doublet phase transitions of a quantum dot Josephson junction inside an Aharonov-Bohm ring

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 4, 2009, Pages

  Karrasch, C ^a   Meden, V ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 59249099414     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.045110     Document Type: Article

References (46)

1. A. A. Abrikosov and L. P. Gorkov, Sov. Phys. JETP 12, 1243 (1961).
2. H. Shiba and T. Soda, Prog. Theor. Phys. 41, 25 (1969). 10.1143/PTP.41.25
3. J. Zittartz and E. Müller-Hartmann, Z. Phys. 232, 11 (1970). 10.1007/BF01394943
4. M. R. Buitelaar, T. Nussbaumer, and C. Schönenberger, Phys. Rev. Lett. 89, 256801 (2002). 10.1103/PhysRevLett.89.256801
5. M. R. Buitelaar, W. Belzig, T. Nussbaumer, B. Babić, C. Bruder, and C. Schönenberger, Phys. Rev. Lett. 91, 057005 (2003). 10.1103/PhysRevLett.91.057005
6. J. A. van Dam, Y. V. Nazarov, E. P. A. M. Bakkers, S. De Francheschi, and L. P. Kouwenhoven, Nature (London) 442, 667 (2006). 10.1038/nature05018
7. J.-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, T. Ondarcuhu, and M. Monthioux, Nat. Nanotechnol. 1, 53 (2006). 10.1038/nnano.2006.54
8. P. Jarillo-Herrero, J. A. van Dam, and L. P. Kouwenhoven, Nature (London) 439, 953 (2006). 10.1038/nature04550
9. H. I. Jørgensen, K. Grove-Rasmussen, T. Novotný, K. Flensbert, and P. E. Lindelof, Phys. Rev. Lett. 96, 207003 (2006). 10.1103/PhysRevLett.96.207003
10. A. Eichler, M. Weiss, S. Oberholzer, C. Schönenberger, A. Levy Yeyati, J. C. Cuevas, and A. Martín-Rodero, Phys. Rev. Lett. 99, 126602 (2007). 10.1103/PhysRevLett.99.126602
11. 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. Nygard, Phys. Rev. Lett. 99, 126603 (2007). 10.1103/PhysRevLett.99.126603
12. H. I. Jørgensen, T. Novotný, K. Grove-Rasmussen, K. Flensberg, and P. E. Lindelof, Nano Lett. 7, 2441 (2007). 10.1021/nl071152w
13. K. Grove-Rasmussen, H. I. Jørgensen, and P. E. Lindelof, New J. Phys. 9, 124 (2007). 10.1088/1367-2630/9/5/124
14. A. Eichler, R. Deblock, M. Weiss, C. Karrasch, V. Meden, C. Schönenberger, and H. Bouchiat, arXiv:0810:1671 (unpublished).
15. L. I. Glazman and K. A. Matveev, JETP Lett. 49, 659 (1989).
16. A. V. Rozhkov and D. P. Arovas, Phys. Rev. Lett. 82, 2788 (1999). 10.1103/PhysRevLett.82.2788
17. E. Vecino, A. Martín-Rodero, and A. L. Yeyati, Phys. Rev. B 68, 035105 (2003). 10.1103/PhysRevB.68.035105
18. A. Oguri, Y. Tanaka, and A. C. Hewson, J. Phys. Soc. Jpn. 73, 2494 (2004). 10.1143/JPSJ.73.2494
19. M.-S. Choi, M. Lee, K. Kang, and W. Belzig, Phys. Rev. B 70, 020502 (R) (2004). 10.1103/PhysRevB.70.020502
20. T. Novotný, A. Rossini, and K. Flensberg, Phys. Rev. B 72, 224502 (2005). 10.1103/PhysRevB.72.224502
21. F. Siano and R. Egger, Phys. Rev. Lett. 93, 047002 (2004) 10.1103/PhysRevLett.93.047002
22. F. Siano and R. Egger, Phys. Rev. Lett. 94, 039902 (E) (2005). 10.1103/PhysRevLett.94.039902
23. Y. Tanaka, A. Oguri, and A. C. Hewson, New J. Phys. 9, 115 (2007). 10.1088/1367-2630/9/5/115
24. C. Karrasch, A. Oguri, and V. Meden, Phys. Rev. B 77, 024517 (2008). 10.1103/PhysRevB.77.024517
25. K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, Phys. Rev. Lett. 88, 256806 (2002). 10.1103/PhysRevLett.88.256806
26. A. C. Johnson, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Phys. Rev. Lett. 93, 106803 (2004). 10.1103/PhysRevLett.93.106803
27. H. Aikawa, K. Kobayashi, A. Sano, S. Katsumoto, and Y. Iye, J. Phys. Soc. Jpn. 73, 3235 (2004). 10.1143/JPSJ.73.3235
28. A. Yacoby, M. Heiblum, D. Mahalu, and H. Shtrikman, Phys. Rev. Lett. 74, 4047 (1995). 10.1103/PhysRevLett.74.4047
29. R. Schuster, E. Buks, M. Heiblum, D. Mahalu, V. Umansky, and H. Shtrikman, Nature (London) 385, 417 (1997). 10.1038/385417a0
30. M. Avinun-Kalish, M. Heiblum, O. Zarchin, D. Mahalu, and V. Umansky, Nature (London) 436, 529 (2005). 10.1038/nature03899
31. W. Hofstetter, J. König, and H. Schoeller, Phys. Rev. Lett. 87, 156803 (2001). 10.1103/PhysRevLett.87.156803
32. C. Karrasch, T. Hecht, A. Weichselbaum, Y. Oreg, J. von Delft, and V. Meden, Phys. Rev. Lett. 98, 186802 (2007) 10.1103/PhysRevLett.98.186802
33. C. Karrasch, T. Hecht, A. Weichselbaum, Y. Oreg, J. von Delft, and V. Meden, New J. Phys. 9, 123 (2007). 10.1088/1367-2630/9/5/123
34. Z.-Y. Zhang, J. Phys.: Condens. Matter 17, 4637 (2005). 10.1088/0953-8984/17/29/006
35. This was already pointed out in Ref..
36. K. Osawa, S. Kurihara, and N. Yokoshi, Phys. Rev. B 78, 224508 (2008). 10.1103/PhysRevB.78.224508
37. The FRG approximation introduced in Sec. 3 does not allow for computing the impurity spectral function. Thus, we cannot address the question whether there is actually a Kondo resonance or a BCS gap governing the low-energy behavior for the problem at hand. However, numerical renormalization-group calculations for the simple quantum dot Josephson junction (td =0) (Ref.) as well as for the nonsuperconducting setup (Δ=0) (Ref.) showed that at sufficiently large U the physics is crucially influenced by the Kondo effect. It is reasonable to assume that Kondo correlations are still present for the problem at hand.
38. J. Bauer, A. Oguri, and A. C. Hewson, J. Phys.: Condens. Matter 19, 486211 (2007). 10.1088/0953-8984/19/48/486211
39. Focusing on the limit of small Δ/ TK, this issue was previously raised in Ref.. However, the author fails to treat the noninteracting limit U=0 correctly (Ref.), rendering his results a priori questionable.
40. H. Bruus and K. Flensberg, Many-Body Quantum Theory in Condensed Matter Physics (Oxford University Press, Oxford, 2004).
41. M. Salmhofer, Renormalization (Springer, Berlin, 1998).
42. C. Karrasch, T. Enss, and V. Meden, Phys. Rev. B 73, 235337 (2006). 10.1103/PhysRevB.73.235337
43. In the discussion of the phase boundary we implicitly assume that the hybridization strength Γ is chosen as the unit of energy.
44. Since our FRG scheme turns out to be quantitatively reliable only up to some intermediate Coulomb interaction U/Γ≈8 (where Kondo correlations start to become important), we cannot describe the singlet-doublet phase transition in the extreme limit of Δ/Γ≪1 (as this would require TK /Γ≪1), no matter which quantity is used to describe the phase boundary. However, for the simple quantum dot Josephson junction (td =0), it was demonstrated that generic physics shows up for small values of TK /Δ (but not necessarily extremely small TK itself). Since we do not observe any qualitative changes apart from an overall increase in the size of the singlet phase in going from Δ=∞ to Δ/Γ≈0.2, it is reasonable to assume that the same holds for the problem at hand.
45. For the simple quantum dot Josephson junction (td =0), it was previously observed that in the doublet phase the supercurrent obtained from the FRG is completely independent of both the two-particle interaction strength U and the impurity energy (Ref.). Even though this is an artifact of the approximative approach, numerical RG calculations showed that physical properties only vary slightly in this regime (Ref.).
46. Some generalized perturbative approach (Ref.) could be employed in order to get some intuitive understanding why J can become negative in the singlet phase. This is, however, out of the scope of this paper.