Quantum decoherence of interacting electrons in arrays of quantum dots and diffusive conductors

Physica E: Low-Dimensional Systems and Nanostructures

Volumn 40, Issue 1, 2007, Pages 32-49

  Golubev, Dmitri S ^a,b   Zaikin, Andrei D ^a,b  

^a KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^b LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

Author keywords

Decoherence; Disorder; Electron electron interactions; Quantum dots; Weak localization

Indexed keywords

ELECTRON-ELECTRON INTERACTIONS; ELECTRONS; IMPURITIES; MAGNETIC MATERIALS;

DISORDERED CONDUCTORS; MAGNETIC IMPURITIES; WEAK LOCALIZATION;

SEMICONDUCTOR QUANTUM DOTS;

EID: 35448951777     PISSN: 13869477     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physe.2007.05.009     Document Type: Article

References (80)

1. Bergmann G. Phys. Rep. 107 (1984) 1
2. B.L. Altshuler, A.G. Aronov, in: A.L. Efros, M. Polak (Eds.), Electron-electron Interactions in Disordered Conductors, Elsevier Science Publishers B.V., New York, 1985.
3. Chakravarty S., and Schmid A. Phys. Rep. 140 (1986) 193
4. Mohanty P., Jariwala E.M.Q., and Webb R.A. Phys. Rev. Lett. 78 (1997) 3366
5. Webb R.A., Mohanty P., and Jariwala E.M.Q. Fortsch. Phys. 46 (1998) 779
6. Natelson D., Willett R.L., West K.W., and Pfeiffer L.N. Phys. Rev. Lett. 86 (2001) 1821
7. Pierre F., Gougam A.B., Anthore A., Pothier H., Esteve D., and Birge N.O. Phys. Rev. B 68 (2003) 085413
8. Mohanty P., and Webb R.A. Phys. Rev. Lett. 91 (2003) 066604
9. Schopfer F., Bäuerle C., Rabaud W., and Saminadayar L. Phys. Rev. Lett. 90 (2003) 056801
10. Lin J.F., Bird J.P., Rotkina L., and Bennett P.A. Appl. Phys. Lett. 82 (2003) 802
11. Lin J.F., Bird J.P., and Rotkina L. Physica E 19 (2003) 112
12. Trionfi A., Lee S., and Natelson D. Phys. Rev. B 72 (2005) 035407
13. Bäuerle C., Mallet F., Shopfer F., Mailly D., Eska G., and Saminadayar L. Phys. Rev. Lett. 95 (2005) 266805
14. Wakaya P., Tsukatani Y., Namasaki N., Murakami K., Abo S., and Takai M. J. Phys.: Conf. Ser. 38 (2006) 120
15. Mallet F., Ericsson J., Mailly D., Unlubayir S., Reuter D., Melnikov A., Wieck A.D., Micklitz T., Rosch A., Costi T.A., Saminadayar L., and Bäuerle C. Phys. Rev. Lett. 97 (2006) 226804
16. Alzoubi G.M., and Birge N.O. Phys. Rev. Lett. 97 (2006) 226803
17. L. Saminadayar, P. Mohanty, R.A. Webb, P. Degiovanni, C. Bäuerle, Physica E (2007), this volume.
18. Pooke D.M., Paquin N., Pepper M., and Gundlach A. J. Phys.: Condens. Matter 1 (1989) 3289
19. Noguchi M., Ikoma T., Odagiri T., Sakakibara H., and Wang S.N. J. Appl. Phys. 80 (1996) 5138
20. Khavin Yu.B., Gershenson M.E., and Bogdanov A.L. Phys. Rev. Lett. 81 (1998) 1066
21. Langer L., Bayot V., Grivei E., Issi J.-P., Heremans J.P., Olk C.H., Stockman L., Van Haesendonck C., and Bruynseraede Y. Phys. Rev. Lett. 76 (1996) 479
22. Kang N., Hu J.S., Kong W.J., Lu L., Zhang D.L., Pan Z.W., and Xie S.S. Phys. Rev. B 66 (2002) 241403
23. Tarkiainen R., Ahlskog M., Zyuzin A., Hakonen P., and Paalanen M. Phys. Rev. B 69 (2004) 033402
24. Lin J.J., and Giordano N. Phys. Rev. B 35 (1987) 585
25. Sahnoune A., Strom-Olsen J.O., and Fisher H.E. Phys. Rev. B 46 (1992) 10035
26. Echternach P.M., Gershenson M.E., and Bozler H.M. Phys Rev. B 47 (1993) 13659
27. Lin J.J., and Bird J.P. J. Phys.: Condens. Matter 14 (2002) R501 and further references therein.
28. J.J. Lin, T.C. Lee, S.W. Wang, Physica E (2007) this volume, see also further references therein.
29. Brunthaler G., Prinz A., Bauer G., and Pudalov V.M. Phys. Rev. Lett. 87 (2001) 096802
30. Proskuryakov Y.Y., Savchenko A.K., Safonov S.S., Pepper M., Simmons M.Y., and Ritchie D.A. Phys. Rev. Lett. 86 (2001) 4895
31. Y. Yaish, O. Prus, E. Buchstab, G. Ben Yosef, U. Sivan, I. Ussishkin, A. Stern, cond-mat/0109469.
32. Lin J.J., and Kao L.Y. J. Phys.: Condens. Matter 13 (2001) L119
33. Bird J.P., Ishibashi K., Ferry D.K., Ochiai Y., Aoyagi Y., and Sugano T. Phys. Rev. B 51 (1995) 18037
34. Clarke R.M., Chan I.H., Marcus C.M., Duruoz C.I., Harris J.S., Campman K., and Gossard A.C. Phys. Rev. B 52 (1995) 2656
35. Pivin D.P., Andresen A., Bird J.P., and Ferry D.K. Phys. Rev. Lett. 82 (1999) 4687
36. Huibers A.G., Folk J.A., Patel S.R., Marcus C.M., Duruoz C.I., and Harris J.S. Phys. Rev. Lett. 83 (1999) 5090
37. Hackens B., Faniel S., Gustin C., Wallart X., Bollaert S., Cappy A., and Bayot V. Phys. Rev. Lett. 94 (2005) 146802
38. Golubev D.S., and Zaikin A.D. Phys. Rev. Lett. 81 (1998) 1074
39. Golubev D.S., and Zaikin A.D. Phys. Rev. B 59 (1999) 9195
40. Golubev D.S., and Zaikin A.D. Phys. Rev. B 62 (2000) 14061
41. Golubev D.S., and Zaikin A.D. J. Low Temp. Phys. 132 (2003) 11
42. Feynman R.P., and Hibbs A.R. Quantum Mechanics and Path Integrals (1965), McGraw Hill, NY (Chapter 12)
43. Caldeira A.O., and Leggett A.J. Ann. Phys. (NY) 149 (1983) 347
44. Schön G., and Zaikin A.D. Phys. Rep. 198 (1990) 237
45. Weiss U. Quantum Dissipative Systems. second ed. (1999), World Scientific, Singapore
46. Golubev D.S., and Zaikin A.D. Physica B 255 (1998) 164
47. Golubev D.S., Zaikin A.D., and Schön G. J. Low Temp. Phys. 126 (2002) 1355
48. S.M. Huang, H. Akimoto, K. Kono, J.J. Lin, unpublished.
49. Golubev D.S., and Zaikin A.D. Phys. Rev. B 74 (2006) 245329
50. Beenakker C.W.J. Rev. Mod. Phys. 69 (1997) 731
51. Golubev D.S., and Zaikin A.D. Phys. Rev. B 69 (2004) 075318
52. Brouwer P.W., Lamacraft A., and Flensberg K. Phys. Rev. B 72 (2005) 075316
53. Golubev D.S., and Zaikin A.D. Phys. Rev. Lett. 86 (2001) 4887
54. Bagrets D.A., and Nazarov Yu.V. Phys. Rev. Lett. 94 (2005) 056801
55. Taniguchi N., Simons B.D., and Altshuler B.L. Phys. Rev. B 53 (1996) 7618
56. Panyukov S.V., and Zaikin A.D. Phys. Rev. Lett. 67 (1991) 3168
57. Nazarov Yu.V. Phys. Rev. Lett. 82 (1999) 1245
58. Golubev D.S., Galaktionov A.V., and Zaikin A.D. Phys. Rev. B 72 (2005) 205417
59. G.L. Ingold, Yu.V. Nazarov, in: H. Grabert, M.H. Devoret (Eds.), Single Charge Tunneling, NATO ASI Series B, vol. 294, Plenum Press, New York 1992, p. 21.
60. Strictly speaking, Eq. (32) applies at times not exceeding the inverse Thouless energy, while at longer times a somewhat different dependence holds.
61. Panyukov S.V., and Zaikin A.D. J. Low Temp. Phys. 73 (1998) 1
62. Fukuyama H., and Abrahams E. Phys. Rev. B 27 (1983) 5976
63. Aleiner I.L., Altshuler B.L., and Gershenson M.E. Waves Random Media 9 (1999) 201
64. 2 (0), can be interpreted as an effective renormalization of the non-interacting result (13). This assumption turns out to be inconsistent with our exact result (25) either.
65. Golubev D.S., and Zaikin A.D. Phys. Rev. B 70 (2004) 165423
66. Altshuler B.L., Aronov A.G., and Khmelnitskii D.E. J. Phys. C 15 (1982) 7367
67. Golubev D.S., and Zaikin A.D. Phys. Rev. Lett. 82 (1999) 3191 cond-mat/9811185
68. Zarand G., Borda L., von Delft J., and Andrei N. Phys. Rev. Lett. 93 (2004) 107204
69. see also G. Zarand, L. Borda, Physica E (this volume) and further references therein.
70. Echternach P.M., Gershenson M.E., Bozler H.M., Bogdanov A.L., and Nilsson B. Phys. Rev. B 48 (1993) 11516
71. P. Mohanty, private communication, 2003.
72. N. Birge, private communication, 2003.
73. Altomare F., Chang A.M., Melloch M.R., Hong Y., and Tu C.W. Appl. Phys. Lett. 86 (2005) 172501 Erratum, cond-mat/0412210
74. φ{symbol} obtained from fits with the Airy function [6,10] should be adjusted (moved upwards) by a numerical factor ∼ 4. For further discussion of this point we refer the reader to Appendix B in Ref. [7]. We also note that the adjustment of the data points [6,10] was carried out only in Fig. 7 but not in Fig. 6.
75. φ{symbol} to our theory. This procedure was described in details in Ref. [46].
76. Ramaswamy G., Raychaudhuri K.A., Goswami J., and Shivashankar S.A. J. Appl. Phys. 82 (1997) 3797
77. Lee W.J., Min J.S., Rha S.K., Chun S.S., and Park C.O. J. Mater. Sci.: Mater. Electr. 7 (1996) 111
78. Kang S.W., Han S.H., and Rhee S.W. Thin Solid Films 350 (1999) 10
79. φ{symbol} for the samples G and H are, respectively, 1.9 μ m and 2.6 μ m [78]. Their ratio ≈ 0.73 matches perfectly with our theoretical prediction ≈ 0.75, cf. Table II in Ref. [11].
80. D. Natelson, private communication, 2007.