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Scattering matrix approach to the description of quantum electron transport

 a,  b
a Landau Institute for Theoretical Physics, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russian Federation
b Rutgers, The State University of New Jersey, 542 George Street, New Brunswick, NJ, 08901, USA

We consider the scattering matrix approach to quantum electron transport in meso- and nanoconductors. This approach is an alternative to the more conventional kinetic equation and Green’s function approaches, and is often more efficient for coherent conductors (especially when proving general relations) and typically more transparent. We provide a description of both time-averaged quantities (for example, current—voltage characteristics) and current fluctuations in time — noise, as well as full counting statistics of charge transport in a finite time. In addition to normal conductors, we consider contacts with superconductors and Josephson junctions.

Fulltext pdf (908 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0181.201110b.1041
Keywords: mesoscopics, scattering matrix, quantum contact, transport
PACS: 72.10.−d, 73.23.−b, 73.50.Td, 74.25.F−, 74.45.+c, 74.78.Na (all)
DOI: 10.3367/UFNe.0181.201110b.1041
URL: https://ufn.ru/en/articles/2011/10/b/
000299541300002
2-s2.0-84855982483
2011PhyU...54.1007L
Citation: Lesovik G B, Sadovskyy I A "Scattering matrix approach to the description of quantum electron transport" Phys. Usp. 54 1007–1059 (2011)
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Received: 12th, December 2010, 22nd, December 2010

Оригинал: Лесовик Г Б, Садовский И А «Описание квантового электронного транспорта с помощью матриц рассеяния» УФН 181 1041–1096 (2011); DOI: 10.3367/UFNr.0181.201110b.1041

References (280) ↓ Cited by (102) Similar articles (20)

  1. Born M Z. Phys. 37 863 (1926)
  2. Wheeler J A Phys. Rev. 52 1107 (1937)
  3. Heisenberg W Z. Phys. 120 513 (1943)
  4. Heisenberg W Z. Phys. 120 673 (1943)
  5. Landauer R IBM J. Res. Dev. 1 223 (1957)
  6. Anderson P W et al. Phys. Rev. B 22 3519 (1980)
  7. Fisher D S, Lee P A Phys. Rev. B 23 6851 (1981)
  8. Economou E N, Soukoulis C M Phys. Rev. Lett. 46 618 (1981)
  9. v. Klitzing K, Dorda G, Pepper M Phys. Rev. Lett. 45 494 (1980)
  10. Imry Y Directions In Condensed Matter Physics (Eds G Grinstein, G Mazenko) (Singapore: World Scientific, 1986) p. 101
  11. Büttiker M Phys. Rev. Lett. 57 1761 (1986)
  12. Büttiker M IBM J. Res. Dev. 32 63 (1988)
  13. Büttiker M IBM J. Res. Dev. 32 317 (1988)
  14. Büttiker M Phys. Rev. B 38 9375 (1988)
  15. Takane Y, Ebisawa H J. Phys. Soc. Jpn. 61 1685 (1992)
  16. Takane Y, Ebisawa H J. Phys. Soc. Jpn. 61 2858 (1992)
  17. Lambert C J J. Phys. Condens. Matter 3 6579 (1991)
  18. Lambert C J, Hui V C, Robinson S J J. Phys. Condens. Matter 5 4187 (1993)
  19. Anantram M P, Datta S Phys. Rev. B 53 16390 (1996)
  20. Beenakker C W J Phys. Rev. Lett. 67 3836 (1991); Beenakker C W J "Erratum" Phys. Rev. Lett. 68 1442 (1992)
  21. ’’’с’’’’ ’I ’G ’z’сь’’ Zh’e’n’s 49 513 (1989); Lesovik G B JETP Lett. 49 592 (1989)
  22. Büttiker M Phys. Rev. Lett. 65 2901 (1990)
  23. Martin Th, Landauer R Phys. Rev. B 45 1742 (1992)
  24. ’’’’’т’’ ’’ ’l, ’’’с’’’’ ’I ’G ’z’сь’’ Zh’e’n’s 58 225 (1993); Levitov L S, Lesovik G B JETP Lett. 58 230 (1993)
  25. Landauer R Philos. Mag. 21 863 (1970)
  26. Hassler F et al. Phys. Rev. B 78 165330 (2008)
  27. ’lуkh’ру’’’ ’M ’E, ’’’’’’с’’ ’R ’G Zh. Eksp. Teor. Fiz. 97 1384 (1990); Sukhorukov E V, Levinson I B Sov. Phys. JETP 70 782 (1990)
  28. Sh’р’’’ Yu ’E Zh. Eksp. Teor. Fiz. 48 984 (1965); Sharvin Yu V Sov. Phys. JETP 21 655 (1965)
  29. ’I’’’’’’ ’’ ’R, Kh’’ts’’’ ’B ’E ’z’сь’’ Zh’e’n’s 48 546 (1988); Glazman L I, Khaetskii A V JETP Lett. 48 591 (1988)
  30. Glazman L I, Khaetskii A V Europhys. Lett. 9 263 (1989)
  31. Patel N K et al. J. Phys. Condens. Matter 2 7247 (1990)
  32. Patel N K et al. Phys. Rev. B 44 13549 (1991)
  33. Matveev K A, Glazman L I Phys. Rev. Lett. 70 990 (1993)
  34. ’K’р’kh’’ ’d ’v ’z’сь’’ Zh’e’n’s 36 259 (1982); Dorokhov O N JETP Lett. 36 318 (1982)
  35. Mello P A, Pereyra P, Kumar N Ann. Physics 181 290 (1988)
  36. van Wees B J et al. Phys. Rev. Lett. 60 848 (1988)
  37. Wharam D A et al. J. Phys. C 209 (1988)
  38. Thornton T J et al. Phys. Rev. Lett. 56 1198 (1986)
  39. Fal’ko V I, Lesovik G B Coulomb and Interference Effects in Small Electronic Structures: XIVth Moriond Workshop, Switzerland, January 22 - 29, 1994 (Eds D C Glattli, M Sanquer, J Trân Thanh Vân) (Gif-sur-Yvette: Editions Frontieres, 1994) p. 389
  40. ’I’’’’’’ ’’ ’R ’ ’р. ’z’сь’’ Zh’e’n’s 48 218 (1988); Glazman L I et al. JETP Lett. 48 238 (1988)
  41. Kemble E C Phys. Rev. 48 549 (1935)
  42. ’’’’’’у ’’ ’K, ’’’фsh’ts ’M ’a ’F’’’т’’’ya ’’kh’’’’’: ’v’р’’yaт’’’стс’’ya т’’р’ya (’a.: ’s’’’’т’’т, 2004); Landau L D, Lifshitz E M Quantum Mechanics: Non-Relativistic Theory (Oxford: Pergamon Press, 1977)
  43. Kawabata A J. Phys. Soc. Jpn. 58 372 (1989)
  44. Fertig H A, Halperin B I Phys. Rev. B 36 7969 (1987)
  45. Büttiker M Phys. Rev. B 41 7906 (1990)
  46. Frank S et al. Science 280 1744 (1998)
  47. Poncharal Ph et al. Eur. Phys. J. D 9 77 (1999)
  48. Martel R et al. Appl. Phys. Lett. 73 2447 (1998)
  49. Olesen L et al. Phys. Rev. Lett. 72 2251 (1994)
  50. Krans J M et al. Nature 375 767 (1995)
  51. Scheer E et al. Phys. Rev. Lett. 78 3535 (1997)
  52. Rodrigues V, Fuhrer T, Ugarte D Phys. Rev. Lett. 85 4124 (2000)
  53. Peres N M R, Castro Neto A H, Guinea F Phys. Rev. B 73 195411 (2006); Peres N M R, Castro Neto A H, Guinea F "Erratum" Phys. Rev. B 73 239902(E) (2006)
  54. Tombros N et al. Nature Phys. 7 697 (2011)
  55. Patel N K et al. Phys. Rev. B 44 10973 (1991)
  56. Thomas K J et al. Phys. Rev. Lett. 77 135 (1996)
  57. Glazman L I, Khaetskii A V J. Phys. Condens. Matter 1 5005 (1989)
  58. Laughlin R B Phys. Rev. B 23 5632 (1981)
  59. Halperin B I Phys. Rev. B 25 2185 (1982)
  60. ’K’’yaт’’ ’e ’E Usp. Fiz. Nauk 177 207 (2007); Devyatov E V Phys. Usp. 50 197 (2007)
  61. Aharonov Y, Bohm D Phys. Rev. 115 485 (1959)
  62. Yacoby A et al. Phys. Rev. Lett. 74 4047 (1995)
  63. Fano U Phys. Rev. 124 1866 (1961)
  64. Ji Y et al. Nature 422 415 (2003)
  65. Shch’’’’ch’’ ’v ’a, ’’’с’’’’ ’I ’G ’d’’’’’р’’’ р’сс’ya’’’ ’ ’’’’т’’’’ ’’kh’’’’’ ’ ’’’ ’р’’’zh’’’ya (’a.: ’a’s’n’R, 2011)
  66. Moskalets M, Büttiker M Phys. Rev. B 66 205320 (2002)
  67. Moskalets M, Büttiker M Phys. Rev. B 70 245305 (2004)
  68. Lesovik G B, Levitov L S Phys. Rev. Lett. 72 538 (1994)
  69. Levitov L S, Lee H, Lesovik G B J. Math. Phys. 37 4845 (1996)
  70. ’R’’’’’ ’K ’B, ’’’’’т’’ ’’ ’l ’z’сь’’ Zh’e’n’s 58 450 (1993); Ivanov D A, Levitov L S JETP Lett. 58 461 (1993)
  71. Ivanov D A, Lee H W, Levitov L S Phys. Rev. B 56 6839 (1997)
  72. Datta S Electronic Transport In Mesoscopic Systems (Cambridge: Cambridge Univ. Press, 1995)
  73. ’K’’’kh’’с’’’ ’E Ya, ’Eу’’’ьт’р ’I ’B ’s’’’’’ ’’’’т’’ыkh ’’’’’р’’’’р’ыkh стру’тур (’a.: ’’’’’с, 2000)
  74. Azbel M Ya Localization, Interaction, and Transport Phenomena: Proc. of the Intern. Conf., August 23 - 28, 1984, Braunschweig, Germany (Springer Series in Solid-State Sciences) Vol. 61 (Eds B Kramer, G Bergmann, Y Bruynseraede) (Berlin: Springer-Verlag, 1985) p. 162
  75. ’B’ьтshу’’р ’G ’’ ’z’сь’’ Zh’e’n’s 41 530 (1985); Al’tshuler B L JETP Lett. 41 648 (1985)
  76. Lee P A, Stone A D Phys. Rev. Lett. 55 1622 (1985)
  77. ’B’ьтshу’’р ’G ’’, Kh’’’ь’’ts’’’ ’K ’M ’z’сь’’ Zh’e’n’s 42 291 (1985); Al’tshuler B L, Khmel’nitskii D E JETP Lett. 42 359 (1985)
  78. ’’’р’’’ ’B ’R, Kh’’’ь’’ts’’’ ’K ’M Zh. Eksp. Teor. Fiz. 91 1815 (1986); Larkin A I, Khmel’nitskii D E Sov. Phys. JETP 64 1075 (1986)
  79. ’z’тр’sh’’ ’E ’n, ’i’’’’’р’ ’z, ’l’р’’’ф’р’ ’a ’z’сь’’ Zh’e’n’s 45 565 (1987); Petrashov V T, Reinders P, Springford M JETP Lett. 45 720 (1987)
  80. Washburn S IBM J. Res. Dev. 32 335 (1988)
  81. Ghosh A, Raychaudhuri A K Phys. Rev. Lett. 84 4681 (2000)
  82. Kubo R J. Phys. Soc. Jpn. 12 570 (1957)
  83. Greenwood D A Proc. Phys. Soc. London 71 585 (1958)
  84. Dorokhov O N Solid State Commun. 51 381 (1984)
  85. Beenakker C W J, Büttiker M Phys. Rev. B 46 1889 (1992)
  86. Prange R E, Girvin S M (Eds) The Quantum Hall Effect (New York: Springer-Verlag, 1987); ’zр’’’zh ’i, ’I’р’’’ ’l (’i’’.) ’F’’’т’’ы’ эфф’’т Kh’’’’ (’a.: ’a’р, 1989)
  87. Brouwer P W, Frahm K Phys. Rev. B 53 1490 (1996)
  88. ’Mф’т’’ ’F ’G, ’’’р’’’ ’B ’R Zh. Eksp. Teor. Fiz. 85 764 (1983); Efetov K B, Larkin A I Sov. Phys. JETP 58 444 (1983)
  89. Efetov K B Adv. Phys. 32 53 (1983)
  90. Pruisken A M M, Škorić B, Baranov M A Phys. Rev. B 60 16838 (1999)
  91. Lesovick G B Mod. Phys. Lett. B 3 611 (1989)
  92. ’B’’с’’’ch ’B ’E ’ ’р. ’z’сь’’ Zh’e’n’s 45 237 (1987); Anisovich A V et al. JETP Lett. 45 295 (1987)
  93. ’’’с’’’’ ’I ’G, Kh’’’ь’’ts’’’ ’K ’M Zh. Eksp. Teor. Fiz. 94 (5) 164 (1988); Lesovik G B, Khmel’nitskii D E Sov. Phys. JETP 67 957 (1988)
  94. Franz R, Wiedemann G Ann. Physik 165 497 (1853)
  95. ’’’фsh’ts ’M ’a, ’z’т’’’с’’’ ’’ ’z ’s’’’ch’с’’ya ’’’’т’’’ (’a.: ’s’’’’т’’т, 2007); Lifshitz E M, Pitaevskii L P Physical Kinetics (New York: Pergamon Press, 1981)
  96. Engquist H-L, Anderson P W Phys. Rev. B 24 1151 (1981)
  97. Landauer R Physica D 38 226 (1989)
  98. Landauer R, Martin Th Physica B 175 167 (1991)
  99. Landauer R, Martin Th Physica B 182 288 (1992)
  100. Schönhammer K Phys. Rev. B 75 205329 (2007)
  101. Stone A D, Szafer A IBM J. Res. Dev. 32 384 (1988)
  102. ’F’’’ыsh ’’ ’E Zh. Eksp. Teor. Fiz. 47 1515 (1964); Keldysh L V Sov. Phys. JETP 20 1018 (1965)
  103. ’’’’’’у ’’ ’K, ’’’фsh’ts ’M ’a ’lт’т’ст’ch’с’’ya ф’’’’’ Т. 1 (’a.: ’s’’’’т’’т, 2010); Landau L D, Lifshitz E M Statistical Physics Vol. 1 (Oxford: Pergamon Press, 1980)
  104. Lesovik G B, Loosen R ’z’сь’’ Zh’e’n’s 65 280 (1997); Lesovik G B, Loosen R JETP Lett. 65 295 (1997)
  105. Gavish U, Levinson Y, Imry Y Phys. Rev. B 10637 (2000)
  106. Aguado R, Kouwenhoven L P Phys. Rev. Lett. 84 1986 (2000)
  107. Basset J, Bouchiat H, Deblock R Phys. Rev. Lett. 105 166801 (2010)
  108. Onac E et al. Phys. Rev. Lett. 96 176601 (2006)
  109. Gustavsson S et al. Phys. Rev. Lett. 99 206804 (2007)
  110. Deblock R et al. Science 301 203 (2003)
  111. Gavish U et al. cond-mat/0211646
  112. Kh’ус ’E ’B Zh. Eksp. Teor. Fiz. 93 2179 (1987); Khlus V A Sov. Phys. JETP 66 1243 (1987)
  113. Reznikov M et al. Phys. Rev. Lett. 75 3340 (1995)
  114. Kumar A et al. Phys. Rev. Lett. 76 2778 (1996)
  115. Steinbach A, Martinis J, Devoret M H Bull. Am. Phys. Soc. 40 400 (1995)
  116. Liefrink F et al. Phys. Rev. B 49 14066 (1994)
  117. Lesovik G B, Loosen R Z. Phys. B 91 531 (1993)
  118. Saminadayar L et al. Phys. Rev. Lett. 79 2526 (1997)
  119. de-Picciotto R et al. Nature 389 162 (1997)
  120. Lefloch F et al. Phys. Rev. Lett. 90 067002 (2003)
  121. Reznikov M et al. Nature 399 238 (1999)
  122. Blanter Ya M, Büttiker M Phys. Rep. 336 1 (2000)
  123. Martin T Nanophysics: Coherence and Transport: Lecture Notes of the Les Houches Summer School 2004, Session LXXXI (Eds H Bouchiat et al.) (Amsterdam: Elsevier, 2005) p. 283
  124. ’’’’’т’’ ’’ ’l, ’’’с’’’’ ’I ’G ’z’сь’’ Zh’e’n’s 55 534 (1992); Levitov L S, Lesovik G B JETP Lett. 55 555 (1992)
  125. ’’’с’’’’ ’I ’G ’z’сь’’ Zh’e’n’s 60 806 (1994); Lesovik G B JETP Lett. 60 820 (1994)
  126. Falci G, Paladino E, Fazio R Quantum Phenomena in Mesoscopic Systems: Proc. of the Intern. School of Physics "Enrico Fermi", 2002, Varenna, Italy, Course 151 (Eds B Altshuler, A Tagliacozzo, V Tognetti) (Amsterdam: IOS Press, 2003)
  127. Galperin Y M et al. Phys. Rev. Lett. 96 097009 (2006)
  128. Neder I et al. Nature Phys. 3 534 (2007)
  129. Averin D V, Sukhorukov E V Phys. Rev. Lett. 95 126803 (2005)
  130. Levitov L S, Lesovik G B cond-mat/9401004
  131. Bachmann S, Graf G M, Lesovik G B J. Stat. Phys. 138 333 (2010)
  132. Shelankov A, Rammer J Europhys. Lett. 63 485 (2003)
  133. Lesovik G B, Hassler F, Blatter G Phys. Rev. Lett. 96 106801 (2006)
  134. Muzykantskii B A, Adamov Y Phys. Rev. B 68 155304 (2003)
  135. Avron J E et al. Commun. Math. Phys. 280 807 (2008)
  136. Hassler F, Lesovik G B, Blatter G Phys. Rev. Lett. 99 076804 (2007)
  137. Büttiker M Phys. Rev. B 46 12485 (1992)
  138. ’’’с’’’’ ’I ’G ’K’сс. ... ’-р’ ф’’.-’’т. ’’у’ (Ch’р’’’’’’’’’: ’R’-т ф’’’’’ т’’р’’’’ т’’’ ’i’B’v, 1997)
  139. Burkard G, Loss D, Sukhorukov E V Phys. Rev. B 16303 (2000)
  140. Fève G et al. Science 316 1169 (2007)
  141. Mahé A et al. Phys. Rev. B 82 201309(R) (2010)
  142. Keeling J, Klich I, Levitov L S Phys. Rev. Lett. 97 116403 (2006)
  143. ’’’’’’’’ ’a ’E, Shch’’’’ ’B ’B, ’a’с’ch’’ ’d ’E ’F’’’т’’’ya э’’’тр’’. 38 710 (2008); Lebedev M V, Shchekin A A, Misochko O V Quantum Electron. 38 710 (2008)
  144. Abanov A G, Ivanov D A Phys. Rev. Lett. 100 086602 (2008)
  145. Abanov A G, Ivanov D A Phys. Rev. B 79 205315 (2009)
  146. Roothaan C C J Rev. Mod. Phys. 23 69 (1951)
  147. Kambly D, Ivanov D A Phys. Rev. B 80 193306 (2009)
  148. Courant R, Hilbert D Methoden Der Mathematischen Physik 4th ed. (Berlin: Springer-Verlag, 1993); Courant R, Hilbert D Methods Of Mathematical Physics (New York: Interscience Publ., 1989)
  149. ’G’ya’’’’ ’F ’E, ’’’’’’’’ ’B ’E, ’’’с’’’’ ’I ’G ’z’сь’’ Zh’e’n’s, ’’’р’’’’’’
  150. ’G’ya’’’’ ’F ’E, ’’’’’’’’ ’B ’E, ’’’с’’’’ ’I ’G Zh. Eksp. Teor. Fiz. 133 140 (2008); Bayandin K V, Lebedev A V, Lesovik G B JETP 106 117 (2008)
  151. Bomze Yu et al. Phys. Rev. Lett. 95 176601 (2005)
  152. Gershon G et al. Phys. Rev. Lett. 101 016803 (2008)
  153. Timofeev A V et al. Phys. Rev. Lett. 98 207001 (2007)
  154. Reulet B et al. Perspectives Of Mesoscopic Physics: Dedicated To Yoseph Imry’s 70th Birthday (Eds A Aharony, O Entin-Wohlman) (Singapore: World Scientific, 2010) p. 211
  155. Gustavsson S et al. Phys. Rev. Lett. 96 076605 (2006)
  156. Petersson K D et al. Phys. Rev. Lett. 105 246804 (2010)
  157. Lesovik G B, Suslov M V, Blatter G Phys. Rev. A 82 012316 (2010)
  158. Ivanov D A, Abanov A G Europhys. Lett. 92 37008 (2010)
  159. Jalabert R A, Pichard J-L, Beenakker C W J Europhys. Lett. 27 255 (1994)
  160. Lee H, Levitov L S, Yakovetz A Yu Phys. Rev. B 51 4079 (1995)
  161. Danneau R et al. Phys. Rev. Lett. 100 196802 (2008)
  162. Tworzydlo J et al. Phys. Rev. Lett. 96 246802 (2006)
  163. Katsnelson M I Eur. Phys. J. B 51 157 (2006)
  164. Lebedev A V, Lesovik G B, Blatter G Phys. Rev. Lett. 100 226805 (2008)
  165. Goorden M C, Büttiker M Phys. Rev. Lett. 99 146801 (2007)
  166. Gogolin A O et al. Ann. Physik 16 678 (2007)
  167. Beenakker C W J, Schomerus H Phys. Rev. Lett. 86 700 (2001)
  168. Lebedev A V, Lesovik G B, Blatter G Phys. Rev. B 81 155421 (2010)
  169. de Gennes P G Rev. Mod. Phys. 36 225 (1964)
  170. de Gennes P G Superconductivity Of Metals And Alloys (New York: W. A. Benjamin, 1966); ’K’ Zh’’ ’z ’l’’рkh’р’’’’’’’сть ’’т’’’’’ ’ с’’’’’’ (’a.: ’a’р, 1968)
  171. ’l’’’’’’с’’’ ’B ’E ’zр’стр’’ст’’’’’-’’’’’’р’’’ы’ ’’’’ch’ т’’р’’ с’’рkh’р’’’’’’’ст’ (’a.: ’v’у’’, 1982)
  172. ’B’’р’’’ ’B ’s Zh. Eksp. Teor. Fiz. 46 1823 (1964); Andreev A F Sov. Phys. JETP 19 1228 (1964)
  173. ’B’’р’’’ ’B ’s Zh. Eksp. Teor. Fiz. 47 2222 (1964); Andreev A F Sov. Phys. JETP 20 1490 (1965)
  174. ’B’’р’’’ ’B ’s Zh. Eksp. Teor. Fiz. 49 655 (1965); Andreev A F Sov. Phys. JETP 22 455 (1966)
  175. Blonder G E, Tinkham M, Klapwijk T M Phys. Rev. B 25 4515 (1982)
  176. Lesovik G B, Martin T, Blatter G Eur. Phys. J. B 24 287 (2001)
  177. Recher P, Sukhorukov E V, Loss D Phys. Rev. B 63 165314 (2001)
  178. Chtchelkatchev N M et al. Phys. Rev. B 66 161320(R) (2002)
  179. Bayandin K V, Lesovik G B, Martin T Phys. Rev. B 74 085326 (2006)
  180. Beenakker C W J Phys. Rev. B 46 12841 (1992)
  181. Büttiker M et al. Phys. Rev. B 31 6207 (1985)
  182. Anderson P W J. Phys. Chem. Solids 11 26 (1959)
  183. Nazarov Yu V, Stoof T H Phys. Rev. Lett. 76 823 (1996)
  184. Stoof T H, Nazarov Yu V Phys. Rev. B 53 14496 (1996)
  185. Hekking F W J, Nazarov Yu V Phys. Rev. B 49 6847 (1994)
  186. Volkov A F, Zaitsev A V, Klapwijk T M Physica C 210 21 (1993)
  187. Petrashov V T et al. Phys. Rev. Lett. 74 5268 (1995)
  188. Courtois H et al. Phys. Rev. Lett. 76 130 (1996)
  189. Lesovik G B, Fauchère A L, Blatter G Phys. Rev. B 55 3146 (1997)
  190. Leadbeater M, Lambert C J J. Phys. Condens. Matter 8 L345 (1996)
  191. Magnée P H C et al. Phys. Rev. B 50 4594 (1994)
  192. Poirier W, Mailly D, Sanquer M, unpublished
  193. Christen T, Büttiker M Europhys. Lett. 35 523 (1996)
  194. Giaever I Phys. Rev. Lett. 5 147 (1960)
  195. Giaever I, Hart H R (Jr.), Megerle K Phys. Rev. 126 941 (1962)
  196. Giaever I Rev. Mod. Phys. 46 245 (1974)
  197. Beenakker C W J Rev. Mod. Phys. 69 731 (1997)
  198. Artemenko S N, Volkov A F, Zaitsev A V Solid State Commun. 30 771 (1979)
  199. Pothier H et al. Phys. Rev. Lett. 73 2488 (1994)
  200. Marmorkos I K, Beenakker C W J, Jalabert R A Phys. Rev. B 48 2811 (1993)
  201. Yip S Phys. Rev. B 52 15504 (1995)
  202. Kastalsky A et al. Phys. Rev. Lett. 67 3026 (1991)
  203. Nguyen C, Kroemer H, Hu E L Phys. Rev. Lett. 69 2847 (1992)
  204. Nitta J, Akazaki T, Takayanagi H Phys. Rev. B 49 3659 (1994)
  205. Bakker S J M et al. Phys. Rev. B 49 13275 (1994)
  206. Melson J A, Beenakker C W J Physica B 203 219 (1994)
  207. Chaudhuri S, Bagwell P F Phys. Rev. B 51 16936 (1995)
  208. Edwards J T, Thouless D J J. Phys. C 5 807 (1972)
  209. Altland A, Gefen Y, Montambaux G Phys. Rev. Lett. 76 1130 (1996)
  210. van Wees B J et al. Phys. Rev. Lett. 69 510 (1992)
  211. Josephson B D Phys. Lett. 1 251 (1962)
  212. van Wees B J, Lenssen K-M H, Harmans C J P M Phys. Rev. B 44 470 (1991)
  213. Takayanagi H, Akazaki T, Nitta J Phys. Rev. Lett. 75 3533 (1995)
  214. Akazaki T et al. Appl. Phys. Lett. 68 418 (1996)
  215. Schäpers Th et al. Appl. Phys. Lett. 73 2348 (1998)
  216. Sutton A P Curr. Opin. Solid State Mater. Sci. 1 827 (1996)
  217. Morpurgo A F, Klapwijk T M, van Wees B J Appl. Phys. Lett. 72 966 (1998)
  218. Baselmans J J A et al. Nature 397 43 (1999)
  219. Krans J M et al. Phys. Rev. B 48 14721 (1993)
  220. Muller C J, van Ruitenbeek J M, de Jongh L J Phys. Rev. Lett. 69 140 (1992)
  221. Scheer E et al. Nature 394 154 (1998)
  222. Kasumov A Yu et al. Science 284 1508 (1999)
  223. Jarillo-Herrero P, van Dam J A, Kouwenhoven L P Nature 439 953 (2006)
  224. Cleuziou J-P et al. Nature Nanotech. 1 53 (2006)
  225. Eichler A et al. Phys. Rev. B 79 161407(R) (2009)
  226. Roch N et al. Nature 453 633 (2008)
  227. Winkelmann C B et al. Nature Phys. 5 876 (2009)
  228. Heersche H B et al. Nature 446 56 (2007)
  229. Du X, Skachko I, Andrei E Y Phys. Rev. B 77 184507 (2008)
  230. Ojeda-Aristizabal C et al. Phys. Rev. B 79 165436 (2009)
  231. Ohta H, Ishii C (Eds) Physics And Applications Of Mesoscopic Josephson Junctions (Tokyo: The Physical Society of Japan, 1999)
  232. Furusaki A, Takayanagi H, Tsukada M Phys. Rev. Lett. 67 132 (1991)
  233. Furusaki A, Takayanagi H, Tsukada M Phys. Rev. B 45 10563 (1992)
  234. Chtchelkatchev N M, Lesovik G B, Blatter G Phys. Rev. B 62 3559 (2000)
  235. Kuhn D D et al. Phys. Rev. B 63 054520 (2001)
  236. Sadovskyy I A, Lesovik G B, Blatter G Phys. Rev. B 75 195334 (2007)
  237. Sadovskyy I A, Lesovik G B, Blatter G ’z’сь’’ Zh’e’n’s 86 239 (2007); Sadovskyy I A, Lesovik G B, Blatter G JETP Lett. 86 210 (2007)
  238. Sadovskyy I A et al. Phys. Rev. B 82 235310 (2010)
  239. Beenakker C W J, van Houten H Phys. Rev. Lett. 66 3056 (1991)
  240. Sh’’’т ’E ’E ’E’’’’’’’ ’ ф’’’’у с’’рkh’р’’’’’’’’’ (’a.: ’aTs’v’a’d, 2000); Schmidt V V The Physics Of Superconductors: Introduction To Fundamentals And Applications (Berlin: Springer, 1997)
  241. Clarke J Superconductor Applications: SQUIDs And Machines (Eds B B Schwartz, S Foner) (New York: Plenum Press, 1977) p. 67
  242. Clarke J, Braginski A I (Eds) The SQUID Handbook Vol. 1 Fundamentals And Technology Of SQUIDs And SQUID Systems (Berlin: Wiley-VCH, 2004)
  243. Clarke J, Braginski A I (Eds) The SQUID Handbook Vol. 2 Applications Of SQUIDs And SQUID Systems (Berlin: Wiley-VCH, 2004)
  244. Kleiner R et al. Proc. IEEE 92 1534 (2004)
  245. ’Fу’’’ ’R ’d Zh. Eksp. Teor. Fiz. 57 1745 (1969); Kulik I O Sov. Phys. JETP 30 944 (1970)
  246. Ishii C Prog. Theor. Phys. 44 1525 (1970)
  247. van Houten H Appl. Phys. Lett. 58 1326 (1991)
  248. Chrestin A, Matsuyama T, Merkt U Phys. Rev. B 49 498 (1994)
  249. Wendin G, Shumeiko V S Superlat. Microstruct. 20 569 (1996)
  250. Wendin G et al. Jpn. J. Appl. Phys. 38 354 (1999)
  251. Wendin G, Shumeiko V S, Samuelsson P Superlat. Microstruct. 25 983 (1999)
  252. Wendin G, Shumeiko V S Phys. Rev. B 6006 (1996)
  253. Shch’’’’ch’’ ’v ’a ’K’сс. ... ’-т’ ф’’.-’’т. ’’у’ (’a.: ’R’n’s ’’. ’’.’K. ’’’’’’у, 2002)
  254. Krichevsky A et al. Phys. Rev. B 61 3723 (2000)
  255. Akkermans E et al. Phys. Rev. Lett. 66 76 (1991)
  256. Beenakker C W J, van Houten H Single-Electron Tunneling and Mesoscopic Devices: Proc. of the 4th Intern. Conf., SQUID’91, Berlin, Germany, June 18 - 21, 1991 (Eds H Koch, H Lübbig) (Berlin: Springer, 1992) p. 175
  257. Novoselov K S et al. Science 306 666 (2004)
  258. Katsnelson M I, Novoselov K S, Geim A K Nature Phys. 2 620 (2006)
  259. Cheianov V V, Fal’ko V I Phys. Rev. B 74 041403(R) (2006)
  260. Beenakker C W J Rev. Mod. Phys. 80 1337 (2008)
  261. Beenakker C W J Phys. Rev. Lett. 97 067007 (2006)
  262. Titov M, Beenakker C W J Phys. Rev. B 74 041401(R) (2006)
  263. Cuevas J C, Yeyati A L Phys. Rev. B 74 180501(R) (2006)
  264. González J, Perfetto E J. Phys. Condens. Matter 20 145218 (2008)
  265. Hagymási I, Kormányos A, Cserti J Phys. Rev. B 82 134516 (2010)
  266. Muzykantskii B A, Khmelnitskii D E Phys. Rev. B 50 3982 (1994)
  267. de Jong M J M, Beenakker C W J Phys. Rev. B 49 16070 (1994)
  268. Hessling J P et al. Europhys. Lett. 34 49 (1996)
  269. Averin D, Imam H T Phys. Rev. Lett. 76 3814 (1996)
  270. Dieleman P et al. Phys. Rev. Lett. 79 3486 (1997)
  271. Martin T Phys. Lett. A 220 137 (1996)
  272. Johnson M B Phys. Rev. 29 367 (1927)
  273. Nyquist H Phys. Rev. 32 110 (1928)
  274. de Jong M J M, Beenakker C W J Mesoscopic Electron Transport (Eds L L Sohn, L P Kouwenhoven, G Schön) (Dordrecht: Kluwer Acad. Publ., 1997) p. 225
  275. Jehl X et al. Phys. Rev. Lett. 83 1660 (1999)
  276. Jehl X et al. Nature 405 50 (2000)
  277. Rowell J M, McMillan W L Phys. Rev. Lett. 16 453 (1966)
  278. Fauchère A L, Lesovik G B, Blatter G Phys. Rev. B 58 11177 (1998)
  279. Chen L Y, Ting C S Phys. Rev. B 43 4534 (1991)
  280. ’’’’’’у ’’ ’K, ’’’фsh’ts ’M ’a ’n’’р’ya ’’’ya (’a.: ’s’’’’т’’т, 2006); Landau L D, Lifshitz E M The Classical Theory Of Fields (Oxford: Pergamon Press, 1980)
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