RSS feeds
РусскийEnglish
Issue 12, 2025
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2011

 / 

October

←  →

Reviews of topical problems


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)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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 (95) ↓ Similar articles (20)

  1. Kleinherbers E, Kelly Sh P, Tserkovnyak Ya Phys. Rev. Lett. 134 (17) (2025)
  2. Saha M, Horray L et al Phys. Rev. B 112 (8) (2025)
  3. Ronetti F, Demazure N et al Phys. Rev. B 112 (12) (2025)
  4. Lavanya E, Chandrasekar L B et al Semiconductors 59 (3) 211 (2025)
  5. Brandner K, Saito K J. Phys. A: Math. Theor. 58 (43) 435002 (2025)
  6. Rifandi M-E-A, Phan Q-H et al Physica B: Condensed Matter 703 416978 (2025)
  7. ND Zhukov IgMin Res 2 (6) 406 (2024)
  8. Sergeyev D, Shunkeyev K, Solovjov A L Low Temperature Physics 50 (11) 976 (2024)
  9. Bartecki K Journal Of The Franklin Institute 361 (9) 106888 (2024)
  10. Ronetti F, Bertin-Johannet B et al Chaos: An Interdisciplinary Journal of Nonlinear Science 34 (4) (2024)
  11. Ronetti F, Bertin-Johannet B et al Phys. Rev. B 110 (24) (2024)
  12. Park G-H, Lee W et al Phys. Rev. Lett. 132 (22) (2024)
  13. Jin T, Ferreira J et al Phys. Rev. Research 5 (1) (2023)
  14. Nikolai D Zh IgMin Res 1 (2) 175 (2023)
  15. Blasi G, Giazotto F, Haack G Quantum Sci. Technol. 8 (1) 015023 (2023)
  16. Lacerda A M, Purkayastha A et al Phys. Rev. B 107 (19) (2023)
  17. Pervishko A A, Yudin D I Uspekhi Fizicheskikh Nauk 192 (03) 233 (2022) [Pervishko A A, Yudin D I Phys.-Usp. 65 (3) 215 (2022)]
  18. Setiawan F, Hofmann J Phys. Rev. Research 4 (4) (2022)
  19. Maiani A, Geier M, Flensberg K Phys. Rev. B 106 (10) (2022)
  20. Lobanov A D, Lobanova A D, Pupasov-Maksimov A M J. Phys.: Condens. Matter 34 (32) 325602 (2022)
  21. Das G D, Maiti S K Phys. Rev. B 106 (12) (2022)
  22. Tsurikov D E Appl. Phys. A 128 (1) (2022)
  23. Haack G, Giazotto F AVS Quantum Science 3 (4) (2021)
  24. Gamayun O, Slobodeniuk A et al Phys. Rev. B 103 (4) (2021)
  25. Cayao J, Burset P Phys. Rev. B 104 (13) (2021)
  26. Kobiałka A, Sedlmayr N, Ptok A Phys. Rev. B 103 (12) (2021)
  27. Frontiers Of Nanoscience Vol. Semiconductor NanodevicesNoise measurements in semiconductor nanodevices20 (2021) p. 147
  28. Potanina E, Flindt Ch et al Phys. Rev. X 11 (2) (2021)
  29. Bartecki K Energies 14 (14) 4174 (2021)
  30. Bułka B R Phys. Rev. B 104 (15) (2021)
  31. Barbier M, Gaspard P Phys. Rev. E 102 (2) (2020)
  32. Adak V, Roychowdhury K, Das S Phys. Rev. B 102 (3) (2020)
  33. Ptok A, Alspaugh D J et al Phys. Rev. B 102 (24) (2020)
  34. Terasawa D, Norimoto S et al Phys. Rev. B 101 (11) (2020)
  35. Useinov A, Lin H-H et al Journal Of Magnetism And Magnetic Materials 508 166729 (2020)
  36. Brandner K Zeitschrift für Naturforschung A 75 (5) 483 (2020)
  37. Jin T, Filippone M, Giamarchi T Phys. Rev. B 102 (20) (2020)
  38. Pashinsky B V, Goldstein M, Burmistrov I S Phys. Rev. B 102 (12) (2020)
  39. Khandelwal Sh, Palazzo N et al New J. Phys. 22 (7) 073039 (2020)
  40. Amusia M, Shaginyan V Springer Tracts In Modern Physics Vol. Strongly Correlated Fermi SystemsViolation of the Wiedemann-Franz Law in Strongly Correlated Electron Systems283 Chapter 20 (2020) p. 301
  41. Barbier M, Gaspard P J. Phys. A: Math. Theor. 52 (2) 025003 (2019)
  42. Burset P, Kotilahti Ja et al Adv Quantum Tech 2 (3-4) (2019)
  43. Tsurikov D E, Yafyasov A M J Comput Electron 18 (3) 1017 (2019)
  44. Filippone M, Bardyn Ch-E et al Phys. Rev. Lett. 123 (8) (2019)
  45. Haim A, Oreg Yu Physics Reports 825 1 (2019)
  46. Yin Y J. Phys.: Condens. Matter 31 (24) 245301 (2019)
  47. Kurilovich P D, Kurilovich V D et al Phys. Rev. Lett. 123 (5) (2019)
  48. Alase A Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter Springer Theses Chapter 3 (2019) p. 65
  49. Pershoguba S S, Glazman L I Phys. Rev. B 99 (13) (2019)
  50. Bułka B R, Łuczak Ja Entropy 21 (5) 527 (2019)
  51. Elo T, Tan Zh et al Phys. Rev. B 100 (23) (2019)
  52. Kirsanov N  S, Tan Z  B et al Phys. Rev. B 99 (11) (2019)
  53. Patra M, Maiti S K Phys. Rev. B 100 (16) (2019)
  54. Barbier M, Gaspard P J. Phys. A: Math. Theor. 51 (35) 355001 (2018)
  55. Poklonski N A, Vyrko S A, Dzeraviaha A N Semiconductors 52 (6) 692 (2018)
  56. Tan Z B, Elo T et al Sci Rep 8 (1) (2018)
  57. Cobanera E, Alase A et al Phys. Rev. B 98 (24) (2018)
  58. Demin G D, Popkov A F Jetp Lett. 106 (12) 821 (2017)
  59. Lv P, Guo A-M et al Phys. Rev. B 95 (10) (2017)
  60. van Heck B, Väyrynen J I, Glazman L I Phys. Rev. B 96 (7) (2017)
  61. Nakata K, Simon P, Loss D J. Phys. D: Appl. Phys. 50 (11) 114004 (2017)
  62. Kerimi M B Semiconductors 51 (8) 1052 (2017)
  63. Shuba M V, Melnikov A V et al Phys. Rev. B 96 (20) (2017)
  64. Shaternik V E, Shapovalov A P et al IEEE Trans. Appl. Supercond. 27 (4) 1 (2017)
  65. Sánchez R, Sothmann B, Jordan A N Physica E: Low-dimensional Systems And Nanostructures 82 359 (2016)
  66. Altimiras C, Portier F, Joyez P Phys. Rev. X 6 (3) (2016)
  67. Lebedev A V, Lesovik G B, Blatter G Phys. Rev. B 93 (11) (2016)
  68. Albert M, Chevallier D, Devillard P Physica E: Low-dimensional Systems And Nanostructures 76 209 (2016)
  69. Oehri D, Lebedev A V et al Phys. Rev. B 93 (4) (2016)
  70. Sánchez R, Sothmann B, Jordan A N Physica E: Low-dimensional Systems And Nanostructures 75 86 (2016)
  71. Mintchev M, Santoni L, Sorba P J. Phys. A: Math. Theor. 49 (26) 265002 (2016)
  72. Sergeyev D M Russ Phys J 59 (3) 456 (2016)
  73. Albert M, Chevallier D, Devillard P Physica E: Low-dimensional Systems And Nanostructures 82 85 (2016)
  74. Sadovskyy I A Uspekhi Fizicheskikh Nauk 185 (9) 941 (2015) [Sadovskyy I A Phys.-Usp. 58 (9) 872 (2015)]
  75. Klavsyuk A L, Saletsky A M Uspekhi Fizicheskikh Nauk 185 (10) 1009 (2015) [Klavsyuk A L, Saletsky A M Phys.-Usp. 58 (10) 933 (2015)]
  76. Mintchev M, Santoni L, Sorba P J. Phys. A: Math. Theor. 48 (28) 285002 (2015)
  77. Amusia M Ya, Popov K G et al Springer Series In Solid-State Sciences Vol. Theory of Heavy-Fermion CompoundsViolation of the Wiedemann-Franz Law in HF Metals182 Chapter 14 (2015) p. 251
  78. Kanzieper E Constr Approx 41 (3) 615 (2015)
  79. Tan Z  B, Cox D et al Phys. Rev. Lett. 114 (9) (2015)
  80. Sadovskyy I A, Lesovik G B, Vinokur V M New J. Phys. 17 (10) 103016 (2015)
  81. Wolf G V, Chuburin Yu P Physics Letters A 378 (30-31) 2211 (2014)
  82. Komnik A, Langhanke G W Phys. Rev. B 90 (16) (2014)
  83. Klapwijk T M, Ryabchun S A J. Exp. Theor. Phys. 119 (6) 997 (2014)
  84. Danilovskii E Yu, Bagraev N T Semiconductors 48 (12) 1636 (2014)
  85. Haack G, Albert M, Flindt Ch Phys. Rev. B 90 (20) (2014)
  86. Albert M, Devillard P Phys. Rev. B 90 (3) (2014)
  87. Oehri D, Lebedev A V et al Phys. Rev. B 90 (7) (2014)
  88. Bulnes C G, Esposito M et al Phys. Rev. B 88 (11) (2013)
  89. Beaud V, Graf G M et al J Stat Phys 153 (2) 177 (2013)
  90. Ivanov D A, Abanov A G Phys. Rev. E 87 (2) (2013)
  91. Gaspard P New J. Phys. 15 (11) 115014 (2013)
  92. Chuburin Yu P, Wolf G V Physica E: Low-dimensional Systems And Nanostructures 54 331 (2013)
  93. POKLONSKI N A, VLASSOV A T et al Physics, Chemistry and Applications of Nanostructures, (2013) p. 36
  94. Oehri D, Lebedev A V et al Phys. Rev. B 86 (12) (2012)
  95. Albert M, Haack G et al Phys. Rev. Lett. 108 (18) (2012)
© 1918–2025 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions