Two-channel Kondo phases and frustration-induced transitions in triple quantum dots

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 7, 2010, Pages

  Mitchell, Andrew K ^a   Logan, David E ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954838864     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.075126     Document Type: Article

References (91)

1. A. C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, 1993). 10.1017/CBO9780511470752
2. L. P. Kouwenhoven, C. M. Marcus, P. L. McEuen, S. Tarucha, R. M. Westervelt, and N. S. Wingreen, Mesoscopic Electron Transport, edited by, L. L. Sohn,,, L. P. Kouwenhoven,, and, G. Schön, (Kluwer, Dordrecht, 1997).
3. M. Pustilnik and L. I. Glazman, J. Phys.: Condens. Matter R513, 16 (2004).
4. D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abusch-Magder, U. Meirav, and M. A. Kastner, Nature (London) 391, 156 (1998). 10.1038/34373
5. S. M. Cronenwett, T. H. Oosterkamp, and L. P. Kouwenhoven, Science 281, 540 (1998). 10.1126/science.281.5376.540
6. H. Jeong, A. M. Chang, and M. R. Melloch, Science 293, 2221 (2001). 10.1126/science.1063182
7. W. G. van der Wiel, S. D. Franceschi, T. Fukisawa, J. M. Elzerman, S. Tarucha, and L. P. Kowenhoven, Science 289, 2105 (2000). 10.1126/science.289. 5487.2105
8. J. Nygard, D. H. Cobden, and P. E. Lindelof, Nature (London) 408, 342 (2000). 10.1038/35042545
9. M. Ferrero, L. D. Leo, P. Lecheminant, and M. Fabrizio, J. Phys.: Condens. Matter 19, 433201 (2007). 10.1088/0953-8984/19/43/433201
10. L. Borda, G. Zaránd, W. Hofstetter, B. I. Halperin, and J. von Delft, Phys. Rev. Lett. 90, 026602 (2003). 10.1103/PhysRevLett.90.026602
11. T. Kuzmenko, K. Kikoin, and Y. Avishai, Phys. Rev. B 73, 235310 (2006). 10.1103/PhysRevB.73.235310
12. M. R. Galpin, D. E. Logan, and H. R. Krishna-murthy, Phys. Rev. Lett. 94, 186406 (2005). 10.1103/PhysRevLett.94.186406
13. A. K. Mitchell, T. F. Jarrold, and D. E. Logan, Phys. Rev. B 79, 085124 (2009). 10.1103/PhysRevB.79.085124
14. E. Vernek, C. A. Büsser, G. B. Martins, E. V. Anda, N. Sandler, and S. E. Ulloa, Phys. Rev. B 80, 035119 (2009). 10.1103/PhysRevB.80.035119
15. T. Numata, Y. Nisikawa, A. Oguri, and A. C. Hewson, Phys. Rev. B 80, 155330 (2009). 10.1103/PhysRevB.80.155330
16. L. G. G. V. Dias da Silva, K. Ingersent, N. Sandler, and S. E. Ulloa, Phys. Rev. B 78, 153304 (2008). 10.1103/PhysRevB.78.153304
17. M. Pustilnik, L. Borda, L. I. Glazman, and J. von Delft, Phys. Rev. B 69, 115316 (2004). 10.1103/PhysRevB.69.115316
18. R. Žitko and J. Bonča, Phys. Rev. Lett. 98, 047203 (2007). 10.1103/PhysRevLett.98.047203
19. A. Georges and A. M. Sengupta, Phys. Rev. Lett. 74, 2808 (1995). 10.1103/PhysRevLett.74.2808
20. Y. Oreg and D. Goldhaber-Gordon, Phys. Rev. Lett. 90, 136602 (2003). 10.1103/PhysRevLett.90.136602
21. G. Zarand, C.-H. Chung, P. Simon, and M. Vojta, Phys. Rev. Lett. 97, 166802 (2006). 10.1103/PhysRevLett.97.166802
22. F. B. Anders, E. Lebanon, and A. Schiller, Phys. Rev. B 70, 201306 (R) (2004). 10.1103/PhysRevB.70.201306
23. K. Kikoin and Y. Avishai, Phys. Rev. Lett. 86, 2090 (2001). 10.1103/PhysRevLett.86.2090
24. M. Vojta, R. Bulla, and W. Hofstetter, Phys. Rev. B 65, 140405 (R) (2002). 10.1103/PhysRevB.65.140405
25. A. K. Mitchell, M. R. Galpin, and D. E. Logan, Europhys. Lett. 76, 95 (2006). 10.1209/epl/i2006-10219-1
26. F. B. Anders, D. E. Logan, M. R. Galpin, and G. Finkelstein, Phys. Rev. Lett. 100, 086809 (2008). 10.1103/PhysRevLett.100.086809
27. R. López, D. Sánchez, M. Lee, M.-S. Choi, P. Simon, and K. Le Hur, Phys. Rev. B 71, 115312 (2005). 10.1103/PhysRevB.71.115312
28. B. Lazarovits, P. Simon, G. Zaránd, and L. Szunyogh, Phys. Rev. Lett. 95, 077202 (2005). 10.1103/PhysRevLett.95.077202
29. A. Oguri, Y. Nisikawa, and A. C. Hewson, J. Phys. Soc. Jpn. 74, 2554 (2005). 10.1143/JPSJ.74.2554
30. R. Žitko, J. Bonča, A. Ramšak, and T. Rejec, Phys. Rev. B 73, 153307 (2006). 10.1103/PhysRevB.73.153307
31. A. M. Lobos and A. A. Aligia, Phys. Rev. B 74, 165417 (2006). 10.1103/PhysRevB.74.165417
32. W. Z. Wang, Phys. Rev. B 76, 115114 (2007). 10.1103/PhysRevB.76.115114
33. F. Delgado and P. Hawrylak, J. Phys.: Condens. Matter 20, 315207 (2008). 10.1088/0953-8984/20/31/315207
34. R. Žitko and J. Bonča, Phys. Rev. B 77, 245112 (2008). 10.1103/PhysRevB.77.245112
35. K. Ingersent, A. W. W. Ludwig, and I. Affleck, Phys. Rev. Lett. 95, 257204 (2005). 10.1103/PhysRevLett.95.257204
36. R. H. Blick, R. J. Haug, J. Weis, D. Pfannkuche, K. v. Klitzing, and K. Eberl, Phys. Rev. B 53, 7899 (1996). 10.1103/PhysRevB.53.7899
37. N. Roch, S. Florens, V. Bouchiat, W. Wernsdorfer, and F. Balestro, Nature (London) 453, 633 (2008). 10.1038/nature06930
38. L. Gaudreau, S. A. Studenikin, A. S. Sachrajda, P. Zawadzki, A. Kam, J. Lapointe, M. Korkusinski, and P. Hawrylak, Phys. Rev. Lett. 97, 036807 (2006). 10.1103/PhysRevLett.97.036807
39. D. Schröer, A. D. Greentree, L. Gaudreau, K. Eberl, L. C. L. Hollenberg, J. P. Kotthaus, and S. Ludwig, Phys. Rev. B 76, 075306 (2007). 10.1103/PhysRevB.76.075306
40. A. Vidan, R. M. Westervelt, M. Stopa, M. Hanson, and A. Gossard, J. Supercond. Novel Magn 18, 223 (2005). 10.1007/s10948-005-3373-8
41. M. C. Rogge and R. J. Haug, Phys. Rev. B 77, 193306 (2008). 10.1103/PhysRevB.77.193306
42. K. Grove-Rasmussen, H. I. Jørgensen, T. Hayashi, P. E. Lindelof, and T. Fujisawa, Nano Lett. 8, 1055 (2008). 10.1021/nl072948y
43. R. M. Potok, I. G. H. Shtrikman, Y. Oreg, and D. Goldhaber-Gordon, Nature (London) 446, 167 (2007). 10.1038/nature05556
44. T. Jamneala, V. Madhavan, and M. F. Crommie, Phys. Rev. Lett. 87, 256804 (2001). 10.1103/PhysRevLett.87.256804
45. T. Uchihashi, J. Zhang, J. Kröger, and R. Berndt, Phys. Rev. B 78, 033402 (2008). 10.1103/PhysRevB.78.033402
46. P. Nozières and A. Blandin, J. Phys. (Paris) 41, 193 (1980).
47. D. L. Cox and A. Zawadowski, Adv. Phys. 47, 599 (1998). 10.1080/000187398243500
48. N. Andrei and C. Destri, Phys. Rev. Lett. 52, 364 (1984). 10.1103/PhysRevLett.52.364
49. A. M. Tsvelick, J. Phys. C 18, 159 (1985). 10.1088/0022-3719/18/1/020
50. P. D. Sacramento and P. Schlottmann, Phys. Lett. A 142, 245 (1989). 10.1016/0375-9601(89)90323-X
51. I. Affleck and A. W. W. Ludwig, Phys. Rev. B 48, 7297 (1993). 10.1103/PhysRevB.48.7297
52. D. L. Cox, Phys. Rev. Lett. 59, 1240 (1987). 10.1103/PhysRevLett.59.1240
53. C. L. Seaman, M. B. Maple, B. W. Lee, S. Ghamaty, M. S. Torikachvili, J.-S. Kang, L. Z. Liu, J. W. Allen, and D. L. Cox, Phys. Rev. Lett. 67, 2882 (1991). 10.1103/PhysRevLett.67.2882
54. C. J. Bolech and N. Andrei, Phys. Rev. Lett. 88, 237206 (2002). 10.1103/PhysRevLett.88.237206
55. D. C. Ralph and R. A. Buhrman, Phys. Rev. Lett. 69, 2118 (1992). 10.1103/PhysRevLett.69.2118
56. D. C. Ralph, A. W. W. Ludwig, J. von Delft, and R. A. Buhrman, Phys. Rev. Lett. 72, 1064 (1994). 10.1103/PhysRevLett.72.1064
57. K. Vladár and A. Zawadowski, Phys. Rev. B 28, 1564 (1983). 10.1103/PhysRevB.28.1564
58. K. Sengupta and G. Baskaran, Phys. Rev. B 77, 045417 (2008). 10.1103/PhysRevB.77.045417
59. I. Affleck and A. W. W. Ludwig, Nucl. Phys. B 360, 641 (1991). 10.1016/0550-3213(91)90419-X
60. N. Andrei and A. Jerez, Phys. Rev. Lett. 74, 4507 (1995). 10.1103/PhysRevLett.74.4507
61. K. Ingersent, B. A. Jones, and J. W. Wilkins, Phys. Rev. Lett. 69, 2594 (1992). 10.1103/PhysRevLett.69.2594
62. K. Kikoin and Y. Oreg, Phys. Rev. B 76, 085324 (2007). 10.1103/PhysRevB.76.085324
63. T. Kuzmenko, K. Kikoin, and Y. Avishai, Europhys. Lett. 64, 218 (2003). 10.1209/epl/i2003-00296-0
64. C. Jayaprakash, H. R. Krishnamurthy, and J. W. Wilkins, Phys. Rev. Lett. 47, 737 (1981). 10.1103/PhysRevLett.47.737
65. B. A. Jones and C. M. Varma, Phys. Rev. Lett. 58, 843 (1987). 10.1103/PhysRevLett.58.843
66. I. Affleck, A. W. W. Ludwig, and B. A. Jones, Phys. Rev. B 52, 9528 (1995). 10.1103/PhysRevB.52.9528
67. J. Gan, Phys. Rev. Lett. 74, 2583 (1995). 10.1103/PhysRevLett.74.2583
68. A. L. Moustakas and D. S. Fisher, Phys. Rev. B 55, 6832 (1997). 10.1103/PhysRevB.55.6832
69. R. Peters, T. Pruschke, and F. B. Anders, Phys. Rev. B 74, 245114 (2006). 10.1103/PhysRevB.74.245114
70. A. Weichselbaum and J. von Delft, Phys. Rev. Lett. 99, 076402 (2007). 10.1103/PhysRevLett.99.076402
71. K. G. Wilson, Rev. Mod. Phys. 47, 773 (1975). 10.1103/RevModPhys.47.773
72. H. R. Krishnamurthy, J. W. Wilkins, and K. G. Wilson, Phys. Rev. B 21, 1044 (1980). 10.1103/PhysRevB.21.1044
73. R. Bulla, T. Costi, and T. Pruschke, Rev. Mod. Phys. 80, 395 (2008). 10.1103/RevModPhys.80.395
74. P. A. M. Dirac, The Principles of Quantum Mechanics (OUP, Oxford, 1930).
75. J. Schrieffer and P. Wolff, Phys. Rev. 149, 491 (1966). 10.1103/PhysRev.149.491
76. The essential physics is of course the same whether J ∼ U or U, since the dots remain singly occupied; and we consider here a relatively large J / U ∼ O (1) largely for numerical convenience, albeit noting that quantum dots in graphene typically have J / U ∼ 1 3.
77. J. Ye, Phys. Rev. B 56, 1316 (1997). 10.1103/PhysRevB.56.1316
78. In practice the systems in Fig. flow directly to the LM FP from the FO FP, with no ln (8) entropy plateau since there is not a wide scale separation between U and J.
79. D. N. Zubarev, Sov. Phys. Usp. 3, 320 (1960). 10.1070/ PU1960v003n03ABEH003275
80. R. Bulla, A. C. Hewson, and T. Pruschke, J. Phys.: Condens. Matter 10, 8365 (1998). 10.1088/0953-8984/10/37/021
81. Y. Meir and N. S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992). 10.1103/PhysRevLett.68.2512
82. A. I. Tóth, L. Borda, J. von Delft, and G. Zaránd, Phys. Rev. B 76, 155318 (2007). 10.1103/PhysRevB.76.155318
83. H. Johannesson, C. J. Bolech, and N. Andrei, Phys. Rev. B 71, 195107 (2005). 10.1103/PhysRevB.71.195107
84. F. B. Anders, Phys. Rev. B 71, 121101 (R) (2005). 10.1103/PhysRevB.71. 121101
85. A. I. Tóth and G. Zaránd, Phys. Rev. B 78, 165130 (2008). 10.1103/PhysRevB.78.165130
86. We have developed a scheme for an accurate determination of G s (ω) itself, in the spirit of and analogous to the determination of G 1 (ω) via Eqs..
87. N. L. Dickens and D. E. Logan, J. Phys.: Condens. Matter 13, 4505 (2001). 10.1088/0953-8984/13/20/311
88. M. R. Galpin, A. B. Gilbert, and D. E. Logan, J. Phys.: Condens. Matter 21, 375602 (2009). 10.1088/0953-8984/21/37/375602
89. H. Shiba, J. Low Temp. Phys. 25, 587 (1976). 10.1007/BF00657285
90. S. C. Bradley, R. Bulla, A. C. Hewson, and G.-M. Zhang, Eur. Phys. J. B 11, 535 (1999). 10.1007/s100510051181
91. For E Δ TKc, the leading low- ω behavior of TKc χ1 (ω) is in fact well described by TKc χ1 (ω) ∼ TKc χ1 (0) +αω (with α a constant).