Kondo effect in coupled quantum dots: A noncrossing approximation study

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 24, 2003, Pages

  Aguado, Ramón ^a,b   Langreth, David C ^b  

^a INSTITUTO DE CIENCIA DE MATERIALES DE MADRID   (Spain)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANDERSON HAMILTONIAN MODEL; ARTICLE; ELECTRIC POTENTIAL; EQUILIBRIUM CONSTANT; KONDO EFFECT; LINEAR SYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; NONCROSSING APPROXIMATION; NONLINEAR SYSTEM; PROBLEM SOLVING; QUANTUM MECHANICS; QUANTUM THEORY; TEMPERATURE MEASUREMENT;

EID: 0042665333     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.245307     Document Type: Article

References (121)

1. D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abusch-Magder, U. Meirav, and M.A. Kastner, Nature (London) 391, 156 (1998);
2. D. Goldhaber-Gordon, J. Göres, M.A. Kastner, Hadas Shtrikman, D. Mahalu, and U. Meirav, Phys. Rev. Lett. 81, 5225 (1998).
3. S.M. Cronenwett, T.H. Oosterkamp, and L.P. Kouwenhoven, Science (Washington, DC, U.S.) 281, 540 (1998).
4. J. Schmid, J. Weis, K. Eberl, and K.V. Klitzing, Physica B 256-258, 182 (1998);
5. J. Schmid J. Weis K. Eberl K.V. Klitzing Phys. Rev. Lett. 84, 5824 (2000).
6. F. Simmel, R.H. Blick, J.P. Kotthaus, W. Wegscheider, and M. Bichler, Phys. Rev. Lett. 83, 804 (1999).
7. W.G. van der Wiel, S. De Franceschi, T. Fujisawa, J.M. Elzerman, S. Tarucha, and L.P. Kouwenhoven, Science (Washington, DC, U.S.) 289, 2105 (2000).
8. Our work focus on transport properties of lateral quantum dots, small regions lithographically defined on two-dimensional electron gases. Other configurations, also termed quantum dots, include nanocrystals, self-assembled quantum dots, and vertical quantum dots. See, A.P. Alivisatos, Science (Washington, DC, U.S.) 271, 933 (1996);
9. Leo P. Kouwenhoven, Charles M. Marcus, Paul L. McEuen, Seigo Tarucha, Robert M. Westervelt, and Ned S. Wingreen, in Mesoscopic Electron Transport, edited by L. L. Sohn, L. P. Kouwenhoven, and G. Schön (Kluwer, The Netherlands, 1997).
10. A. C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, 1993).
11. R.A. Logan and J.M. Rowell, Phys. Rev. Lett. 13, 404 (1964);
12. Phys. Rev. Lett. A.F.G. Wyatt, 13, 401 (1964);
13. Phys. Rev. Lett. J. Schewchun and R.M. Williams, 15, 160 (1965).
14. D.C. Ralph and R.A. Buhrman, Phys. Rev. Lett. 72, 3401 (1994).
15. T.K. Ng and P.A. Lee, Phys. Rev. Lett. 61, 1768 (1988);
16. L.I. Glazman and M.E. Raikh, JETP Lett. 47, 452 (1988);
17. A. Kawabata, J. Phys. Soc. Jpn. 60, 3222 (1991).
18. Selman Hershfield, John H. Davies, and John W. Wilkins, Phys. Rev. Lett. 67, 3720 (1991);
19. Selman Hershfield John H. Davies John W. Wilkins Phys. Rev. B 46, 7046 (1992).
20. Y. Meir, Ned S. Wingreen, and Patrick A. Lee, Phys. Rev. Lett. 70, 2601 (1993).
21. A.L. Yeyati, A. Martín-Rodero, and F. Flores, Phys. Rev. Lett. 71, 2991 (1993).
22. Ned S. Wingreen and Yigal Meir, Phys. Rev. B 49, 11040 (1994).
23. Noam Sivan and Ned S. Wingreen, Phys. Rev. B 54, 11622 (1996).
24. J. König, J. Schmid, H. Schoeller, and G. Schön, Phys. Rev. B 54, 16820 (1996).
25. P. Coleman, C. Hooley, and O. Parcollet, Phys. Rev. Lett. 86, 4088 (2001);
26. A. Rosch, J. Paaske, J. Kroha, and P. Wölfle, Phys. Rev. Lett. 90, 07684 (2003);
27. O. Parcollet and C. Hooley, Phys. Rev. B 66, 085315 (2002);
28. P. Coleman and W. Mao, cond-mat/0203001 (unpublished).
29. M.H. Hettler and H. Schoeller, Phys. Rev. Lett. 74, 4907 (1995).
30. T.K. Ng, Phys. Rev. Lett. 76, 487 (1996).
31. A. Schiller and S. Hershfield, Phys. Rev. Lett. 77, 1821 (1996).
32. Rosa López, Ramón Aguado, Gloria Platero, and Carlos Tejedor, Phys. Rev. Lett. 81, 4688 (1998);
33. Rosa López Ramón Aguado Gloria Platero Carlos Tejedor Phys. Rev. B 64, 075319 (2001).
34. Y. Goldin and Y. Avishai, Phys. Rev. Lett. 81, 5394 (1998).
35. A. Kaminski, Yu V. Nazarov, and L.I. Glazman, Phys. Rev. Lett. 83, 384 (1999);
36. A. Kaminski Yu V. Nazarov L.I. Glazman Phys. Rev. B 62, 8154 (2000).
37. Peter Nordlander, Ned S. Wingreen, Yigal Meir, and David C. Langreth, Phys. Rev. B 61, 2146 (2000).
38. Martin Plihal, David C. Langreth, and Peter Nordlander, Phys. Rev. B 61, R13341 (2000).
39. Avraham Schiller and Selman Hershfield, Phys. Rev. B 62, R16271 (2000).
40. P. Coleman, C. Hooley, Y. Avishai, Y. Goldin, and A.F. Ho, J. Phys.: Condens. Matter 14, 205 (2002).
41. M.A. Cazalilla and J.B. Marston, Phys. Rev. Lett. 88, 256403 (2002).
42. S. Sasaki, S. De Franceschi, J.M. Elzerman, W.G. van der Wiel, M. Eto, S. Tarucha, and L.P. Kouwenhoven, Nature (London) 405, 764 (2000);
43. M. Eto and Yu.V. Nazarov, Phys. Rev. Lett. 85, 1306 (2000);
44. Phys. Rev. Lett. M. Pustilnik, Y. Avishai, and K. Kikoin, 84, 1756 (2000);
45. Phys. Rev. Lett. D. Giuliano and A. Tagliacozzo, 84, 4677 (2000);
46. C. Tejedor and L. Martin-Moreno, Phys. Rev. B 63, 035319 (2001).
47. U. Gerland, J. von Delft, T.A. Costi, and Y. Oreg, Phys. Rev. Lett. 84, 3710 (2000);
48. Yang Ji, M. Heiblum, D. Sprinzak, D. Mahalu, and Hadas Shtrikman, Science (Washington, DC, U.S.) 290, 779 (2000).
49. Jiwoong Park, Abhay N. Pasupathy, Jonas I. Goldsmith, Connie Chang, Yuval Yaish, Jason R. Petta, Marie Rinkoski, James P. Sethna, Hector D. Abrua, Paul L. McEuen, and Daniel C. Ralph, Nature (London) 417, 722 (2002).
50. Wenjie Liang, Matthew P. Shores, Marc Bockrath, Jeffrey R. Long, and Hongkun Park, Nature (London) 417, 725 (2002).
51. J. Nygård, D.H. Cobden, and P.E. Lindelof, Nature (London) 408, 342 (2000).
52. H.C. Manoharan, C.P. Lutz, and D.M. Eigler, Nature (London) 403, 512 (2000).
53. J. Kroha, Adv. Solid State Phys. 40, 216 (2000);
54. G. Göppert and H. Grabert, Phys. Rev. B 64, 033301 (2001);
55. J. Kroha and A. Zawadowski, Phys. Rev. Lett. 88, 176803 (2002).
56. T.H. Oosterkamp, T. Fujisawa, W.G. van der Wiel, K. Ishibashi, R.V. Hijman, S. Tarucha, and L.P. Kouwenhoven, Nature (London) 395, 873 (1998).
57. T. Fujisawa, T.H. Oosterkamp, W.G. van der Wiel, B.W. Broer, R. Aguado, S. Tarucha, and L.P. Kouwenhoven, Science (Washington, DC, U.S.) 282, 932 (1998).
58. R.H. Blick, D. Pfannkuche, R.J. Haug, K.V. Klitzing, and K. Eberl, Phys. Rev. Lett. 80, 4032 (1998);
59. H. Qin, A.W. Holleitner, K. Eberl, and R.H. Blick, Phys. Rev. B 64, 241302(R) (2001);
60. A.W. Holleitner, C.R. Decker, H. Qin, K. Eberl, and R.H. Blick, Phys. Rev. Lett. 87, 256802 (2001);
61. Alexander W. Holleitner, Robert H. Blick, Andreas K. Hüttel, Karl Eberl, and Jörg P. Kotthaus, Science (Washington, DC, U.S.) 297, 70 (2002).
62. H. Jeong, A.M. Chang, and M.R. Melloch, Science (Washington, DC, U.S.) 293, 2221 (2001).
63. Tomosuke Aono, Mikio Eto, and Kiyoshi Kawamura, J. Phys. Soc. Jpn. 67, 1860 (1998).
64. Tomosuke Aono and Mikio Eto, Phys. Rev. B 63, 125327 (2001).
65. A. Georges and Y. Meir, Phys. Rev. Lett. 82, 3508 (1999).
66. C.A. Büsser, E.V. Anda, A.L. Lima, M.A. Davidovich, and G. Chiappe, Phys. Rev. B 62, 9907 (2000);
67. Phys. Rev. B W. Izumida and O. Sakai, 62, 10260 (2000).
68. N. Andrei, Gergely T. Zimanyi, and Gerd Schön, Phys. Rev. B 60, R5125 (1999).
69. T. Ivanov, Europhys. Lett. 40, 183 (1997).
70. T. Pohjola, J. König, M.M. Salomaa, J. Schmid, H. Schoeller, and Gerd Schön, Europhys. Lett. 40, 189 (1997);
71. Teemu Pohjola, Daniel Boese, Jürgen König, Herbert Schoeller, and Gerd Schön, J. Low Temp. Phys. 118, 391 (2000).
72. Ramón Aguado and David C. Langreth, Phys. Rev. Lett. 85, 1946 (2000).
73. Rosa López, Ramón Aguado, and Gloria Platero, Phys. Rev. Lett. 89, 136802 (2002).
74. H. Keiter and J.C. Kimball, J. Appl. Phys. 42, 1460 (1971);
75. N. Grewe and H. Keiter, Phys. Rev. B 24, 4420 (1981);
76. Y. Kuramoto, Z. Phys. B: Condens. Matter 53, 37 (1983);
77. Z. Phys. B: Condens. Matter E. Müller-Hartmann, 57, 281 (1984).
78. See also, N.E. Bickers, Rev. Mod. Phys. 59, 845 (1987), for a review.
79. A.A. Abrikosov, Physics (Long Island City, N.Y.) 2, 21 (1965).
80. S.E. Barnes, J. Phys. F: Met. Phys. 6, 1375 (1976);
81. J. Phys. F: Met. Phys. S.E. Barnes 7, 2637 (1977).
82. P. Coleman, Phys. Rev. B 29, 3035 (1984).
83. N. Read and D.M. Newns, J. Phys. C 16, 3273 (1983);
84. J. Phys. C N. Read D.M. Newns 16, L1055 (1983);
85. N. Read D.M. Newns Adv. Phys. 36, 799 (1988).
86. N. Read, J. Phys. C 18, 2651 (1985);
87. P. Coleman, J. Magn. Magn. Mater. 47, 323 (1985).
88. G. Baym and L.P. Kadanoff, Phys. Rev. 124, 287 (1961);
89. Phys. Rev. G. Baym, 127, 1391 (1962).
90. T.A. Costi, J. Kroha, and P. Wölfle, Phys. Rev. B 53, 1850 (1996).
91. D.L. Cox and A. Zawadowski, Adv. Phys. 47, 599 (1998).
92. A theory which corrects this deficiency is developed in J. Kroha, P. Wölfle, and T.A. Costi, Phys. Rev. Lett. 79, 261 (1997);
93. J. Kroha and P. Wölfle, Adv. Solid State Phys. 39, 271 (1999).
94. Th. Pruschke and N. Grewe, Z. Phys. B: Condens. Matter 74, 439 (1989);
95. D. Gerace, E. Pavarini, and L.C. Andreani, Phys. Rev. B 65, 155331 (2002).
96. K. Haule, S. Kirchner, J. Kroha, and P. Wölfle, Phys. Rev. B 64, 155111 (2001).
97. David C. Langreth and Peter Nordlander, Phys. Rev. B 43, 2541 (1991).
98. Hongxiao Shao, David C. Langreth, and Peter Nordlander, Phys. Rev. B 49, 13929 (1994).
99. T. Brunner and D.C. Langreth, Phys. Rev. B 55, 2578 (1997).
100. Takeshi Inoshita, Yoshio Kuramoto, and Hiroyuki Sakaki, Superlattices Microstruct. 22, 75 (1997).
101. Tae-Suk Kim and S. Hershfield, Phys. Rev. B 63, 245326 (2001).
102. Eran Lebanon and Avraham Schiller, Phys. Rev. B 65, 035308 (2002).
103. Matthias H. Hettler, Johann Kroha, and Selman Hershfield, Phys. Rev. Lett. 73, 1967 (1994);
104. Matthias H. Hettler Johann Kroha Selman Hershfield Phys. Rev. B 58, 5649 (1998).
105. M. Plihal and David C. Langreth, Phys. Rev. B 60, 5969 (1999).
106. Martin Plihal, David C. Langreth, and Peter Nordlander, Phys. Rev. B 59, 13322 (1999).
107. M. Plihal and J.W. Gadzuk, Phys. Rev. B 63, 085404 (2001).
108. Peter Nordlander, Michael Pustilnik, Yigal Meir, Ned S. Wingreen, and David C. Langreth, Phys. Rev. Lett. 83, 808 (1999).
109. A. Rosch, J. Kroha, and P. Wölfle, Phys. Rev. Lett. 87, 156802 (2001).
110. This is not the only physical realization of a double quantum dot. For instance, it is possible to reach the opposite limit, large interdot interaction, by using a floating interdot capacitor. See, I.H. Chan, R.M. Westervelt, K.D. Maranowski, and A.C. Gossard, Appl. Phys. Lett. 80, 1818 (2002).
111. L.P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962).
112. D.C. Langreth, in Linear and Nonlinear Electron Transport in Solids, Vol. 17 of NATO Advanced Studies Institute, Series B: Physics, edited by J.T. Devreese and V. E. Van Doren (Plenum, New York, 1976).
113. It is not always true that a static voltage preserves time-translational invariance. In nonlinear systems driven away from equilibrium by a static voltage, one can have situations where at the stability limit of the stationary state a bifurcation to a time-dependent solution, which spontaneously breaks the time-translational symmetry, does develop. See, for instance, M. Büttiker and H. Thomas, Z. Phys. B 34, 301 (1979).
114. For a general discussion see, M.P. Shaw, V.V. Mitin, E. Schöll, and H.L. Grubin, The Physics of Instabilities in Solid State Electron Devices (Plenum Press, New York, 1992).
115. 2), see Ref. 53, which makes the NCA approximation correct to order O(1/N).
116. Wolfgang B. Thimm, Johann Kroha, and Jan von Delft, Phys. Rev. Lett. 82, 2143 (1999).
117. Aashish A. Clerk, Vinay Ambegaokar, and Selman Hershfield, Phys. Rev. B 61, 3555 (2000).
118. Y. Meir and Ned S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992).
119. Qing-feng Sun and Hong Guo, Phys. Rev. B 64, 153306 (2001).
120. S. De Franceschi, R. Hanson, W.G. van der Wiel, J.M. Elzerman, J.J. Wijpkema, T. Fujisawa, S. Tarucha, and L.P. Kouwenhoven, Phys. Rev. Lett. 89, 156801 (2002).
121. Here, we focus on a projection procedure which is valid for diagonal (in the left/right index sense) operators. As we mentioned in Sec. IV A, we can construct a fully self-consistent NCA theory to order O(1/N) by just including diagonal propagators/self-energies.