Ground state and excitations of quantum dots with magnetic impurities

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 3, 2009, Pages

  Kaul, Ribhu K ^a,b   Ullmo, Denis ^c   Zaránd, Gergely ^b,d   Chandrasekharan, Shailesh ^a   Baranger, Harold U ^a  

^a DUKE UNIVERSITY   (United States)

^b UNIVERSITY OF KARLSRUHE   (Germany)

^c UNIVERSITÉ PARIS SUD   (France)

^d BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 69549108469     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.035318     Document Type: Article

References (66)

1. A. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, England, 1993).
2. L. Glazman and M. Raikh, Pis'ma Zh. Eksp. Teor. Fiz. 47, 378 (1988)
3. L. Glazman and M. Raikh, [JETP Lett. 47, 452 (1988)].
4. T. K. Ng and P. A. Lee, Phys. Rev. Lett. 61, 1768 (1988). 10.1103/PhysRevLett.61.1768
5. L. Glazman and M. Pustilnik, in Nanophysics: Coherence and Transport, edited by, H. Bouchiat, Y. Gefen, S. Gueron, G. Montambaux, and, J. Dalibard, (Elsevier, New York, 2005), pp. 427-478.
6. G. Zaránd, Philos. Mag. 86, 2043 (2006). 10.1080/14786430500469069
7. M. Grobis, I. G. Rau, R. M. Potok, and D. Goldhaber-Gordon, in Handbook of Magnetism and Advanced Magnetic Materials, edited by, H. Kronmüller, and, S. Parkin, (Wiley, New York, 2007), Vol. 5.
8. D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abusch-Magder, U. Meirav, and M. A. Kastner, Nature (London) 391, 156 (1998). 10.1038/34373
9. S. M. Cronenwett, T. H. Oosterkamp, and L. P. Kouwenhoven, Science 281, 540 (1998). 10.1126/science.281.5376.540
10. M. Pustilnik, L. Glazman, D. Cobden, and L. Kouwenhoven, Lect. Notes Phys. 579, 3 (2001). 10.1007/3-540-45532-9-1
11. Y. Oreg and D. Goldhaber-Gordon, Phys. Rev. Lett. 90, 136602 (2003). 10.1103/PhysRevLett.90.136602
12. R. M. Potok, I. G. Rau, H. Shtrikman, Y. Oreg, and D. Goldhaber-Gordon, Nature (London) 446, 167 (2007). 10.1038/nature05556
13. L. Borda, G. Zaránd, W. Hofstetter, B. I. Halperin, and J. von Delft, Phys. Rev. Lett. 90, 026602 (2003). 10.1103/PhysRevLett.90.026602
14. K. Le Hur and P. Simon, Phys. Rev. B 67, 201308 (R) (2003). 10.1103/PhysRevB.67.201308
15. K. Le Hur, P. Simon, and L. Borda, Phys. Rev. B 69, 045326 (2004). 10.1103/PhysRevB.69.045326
16. M. R. Galpin, D. E. Logan, and H. R. Krishnamurthy, Phys. Rev. Lett. 94, 186406 (2005). 10.1103/PhysRevLett.94.186406
17. K. Le Hur, P. Simon, and D. Loss, Phys. Rev. B 75, 035332 (2007). 10.1103/PhysRevB.75.035332
18. M.-S. Choi, R. Lopez, and R. Aguado, Phys. Rev. Lett. 95, 067204 (2005). 10.1103/PhysRevLett.95.067204
19. A. Makarovski, A. Zhukov, J. Liu, and G. Finkelstein, Phys. Rev. B 75, 241407 (R) (2007). 10.1103/PhysRevB.75.241407
20. A. Makarovski, J. Liu, and G. Finkelstein, Phys. Rev. Lett. 99, 066801 (2007). 10.1103/PhysRevLett.99.066801
21. L. P. Kouwenhoven, C. M. Marcus, P. L. McEuen, S. Tarucha, R. M. Wetervelt, and N. S. Wingreen, in Mesoscopic Electron Transport, edited by, L. L. Sohn, G. Schön, and, L. P. Kouwenhoven, (Kluwer, Dordrecht, 1997), pp. 105-214.
22. E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Phonons (Cambridge University Press, Cambridge, UK, 2007).
23. N. Argaman, Y. Imry, and U. Smilansky, Phys. Rev. B 47, 4440 (1993). 10.1103/PhysRevB.47.4440
24. G. Zaránd and L. Udvardi, Phys. Rev. B 54, 7606 (1996). 10.1103/PhysRevB.54.7606
25. S. Kettemann, in Quantum Information and Decoherence in Nanosystems, edited by, D. C. Glattli, M. Sanquer, and, J. T. T. Van, (The Gioi Publishers, Hanoi, Vietnam 2004), p. 259
26. arXiv:cond-mat/0409317 (unpublished).
27. R. K. Kaul, D. Ullmo, S. Chandrasekharan, and H. U. Baranger, EPL 71, 973 (2005). 10.1209/epl/i2005-10184-1
28. J. Yoo, S. Chandrasekharan, R. K. Kaul, D. Ullmo, and H. U. Baranger, Phys. Rev. B 71, 201309 (R) (2005). 10.1103/PhysRevB.71.201309
29. D. Ullmo, Rep. Prog. Phys. 71, 026001 (2008). 10.1088/0034-4885/71/2/ 026001
30. S. Kettemann and E. R. Mucciolo, Pis'ma Zh. Eksp. Teor. Fiz. 83, 284 (2006)
31. S. Kettemann and E. R. Mucciolo, [JETP Lett. 83, 240 (2006)]. 10.1134/S0021364006060051
32. S. Kettemann and E. R. Mucciolo, Phys. Rev. B 75, 184407 (2007). 10.1103/PhysRevB.75.184407
33. A. Zhuravlev, I. Zharekeshev, E. Gorelov, A. Lichtenstein, E. Mucciolo, and S. Kettemann, Phys. Rev. Lett. 99, 247202 (2007). 10.1103/PhysRevLett.99. 247202
34. W. B. Thimm, J. Kroha, and J. von Delft, Phys. Rev. Lett. 82, 2143 (1999). 10.1103/PhysRevLett.82.2143
35. P. Simon and I. Affleck, Phys. Rev. Lett. 89, 206602 (2002). 10.1103/PhysRevLett.89.206602
36. P. S. Cornaglia and C. A. Balseiro, Phys. Rev. Lett. 90, 216801 (2003). 10.1103/PhysRevLett.90.216801
37. I. Affleck and P. Simon, Phys. Rev. Lett. 86, 2854 (2001). 10.1103/PhysRevLett.86.2854
38. P. Simon and I. Affleck, Phys. Rev. B 64, 085308 (2001). 10.1103/PhysRevB.64.085308
39. C. H. Lewenkopf and H. A. Weidenmuller, Phys. Rev. B 71, 121309 (R) (2005). 10.1103/PhysRevB.71.121309
40. P. Simon, J. Salomez, and D. Feinberg, Phys. Rev. B 73, 205325 (2006). 10.1103/PhysRevB.73.205325
41. P. S. Cornaglia and C. A. Balseiro, Phys. Rev. B 66, 115303 (2002). 10.1103/PhysRevB.66.115303
42. R. K. Kaul, G. Zaránd, S. Chandrasekharan, D. Ullmo, and H. U. Baranger, Phys. Rev. Lett. 96, 176802 (2006). 10.1103/PhysRevLett.96.176802
43. R. G. Pereira, N. Laflorencie, I. Affleck, and B. I. Halperin, Phys. Rev. B 77, 125327 (2008). 10.1103/PhysRevB.77.125327
44. G. Murthy, Phys. Rev. Lett. 94, 126803 (2005). 10.1103/PhysRevLett.94. 126803
45. S. Rotter, H. E. Türeci, Y. Alhassid, and A. D. Stone, Phys. Rev. Lett. 100, 166601 (2008). 10.1103/PhysRevLett.100.166601
46. D. C. Mattis, Phys. Rev. Lett. 19, 1478 (1967). 10.1103/PhysRevLett.19. 1478
47. W. Marshall, Proc. R. Soc. London, Ser. A 232, 48 (1955). 10.1098/rspa.1955.0200
48. A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer-Verlag, New York, 1994).
49. K. G. Wilson, Rev. Mod. Phys. 47, 773 (1975). 10.1103/RevModPhys.47.773
50. P. Nozières, J. Low Temp. Phys. 17, 31 (1974). 10.1007/BF00654541
51. P. Nozières, J. Phys. (Paris) 39, 1117 (1978). 10.1051/jphys:0197800390100111700
52. W. G. van der Wiel, S. De Franceschi, J. M. Elzerman, S. Tarucha, L. P. Kouwenhoven, J. Motohisa, F. Nakajima, and T. Fukui, Phys. Rev. Lett. 88, 126803 (2002). 10.1103/PhysRevLett.88.126803
53. Ph. Nozières and A. Blandin, J. Phys. (Paris) 41, 193 (1980). 10.1051/jphys:01980004103019300
54. J. von Delft and D. Ralph, Phys. Rep. 345, 61 (2001). 10.1016/S0370-1573(00)00099-5
55. C. W. J. Beenakker, Phys. Rev. B 44, 1646 (1991). 10.1103/PhysRevB.44. 1646
56. Assumptions (1) and (2) do not affect the spacing between the peaks in G, but they do affect the relative peak heights at BZ =0. The peak spacings contain enough information to extract all the energy splittings illustrated in Fig. 5.
57. The energies Ei [N] are assumed to contain a term originating from the equilibrium chemical potential EF N.
58. The case Γ2 / Γ1 =1 is clearly outside the region of validity of our Γ2 / Γ1 1 treatment but is included in the plot nonetheless in order to make the trends clear.
59. I. L. Aleiner, P. W. Brouwer, and L. I. Glazman, Phys. Rep. 358, 309 (2002), and references therein. 10.1016/S0370-1573(01)00063-1
60. S. De Franceschi, S. Sasaki, J. M. Elzerman, W. G. van der Wiel, S. Tarucha, and L. P. Kouwenhoven, Phys. Rev. Lett. 86, 878 (2001). 10.1103/PhysRevLett.86.878
61. D. M. Zumbühl, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Phys. Rev. Lett. 93, 256801 (2004). 10.1103/PhysRevLett.93.256801
62. A. Makarovski, L. An, J. Liu, and G. Finkelstein, Phys. Rev. B 74, 155431 (2006). 10.1103/PhysRevB.74.155431
63. A. M. Clogston and P. W. Anderson, Bull. Am. Phys. Soc. 6, 124 (1961).
64. V. Barzykin and I. Affleck, Phys. Rev. B 57, 432 (1998). 10.1103/PhysRevB.57.432
65. In a finite system, a naive estimate gives a ΔR / TK finite-size correction to the local susceptibility from the second term in Eq. 23.
66. The spin-chain mapping (Refs.) of Ref. is easily modified to simulate the canonical ensemble for the Kondo problem. Fixing the number of fermions in the Kondo box corresponds to simulating the spin chain at fixed magnetization, while the grand-canonical case corresponds to a fixed magnetic field. During the loop update, the magnetization of the spin chain is updated when loops wrap around the imaginary time direction (they have temporal winding). If we prevent our loops from winding temporally, the magnetization of the spin chain stays fixed, and we are simulating the canonical ensemble in the Kondo problem. A simple approach to restricting loops to the zero temporal winding sector is to finish the growth of a loop and then reject loops that wind in time. A more efficient approach and the one that we have used here is to force the loops to bounce back if they cross a certain time slice. It is possible to show that this algorithm satisfies detailed balance and at the same time forbids temporal winding.