Advertisement

Introduction

  • Dmitry A. RyndykEmail author
Chapter
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 184)

Abstract

Some general features of quantum transport in mesoscopic and nanoscale systems are sketched. Nanoscale systems as the systems with essentially discrete energy spectrum are defined. Different types of nanojunctions are introduced depending on the ratio between the energy scales associated with electron-electron or electron-vibron interactions in the central system and coupling to the electrodes. The main models and methods considered in the book and the related history are briefly reviewed.

Keywords

Master Equation Quantum Transport Coulomb Blockade Kondo Effect Nanoscale System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    S. Datta, Electronic Transport in Mesoscopic Systems. (Cambridge University Press, Cambridge, 1995)Google Scholar
  2. 2.
    H. Haug, A.P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, vol. 123, Springer Series in Solid-State Physics (Springer, Berlin, 1996)Google Scholar
  3. 3.
    Y. Imry, Introduction to Mesoscopic Physics (Oxford University Press, New York, 1997)Google Scholar
  4. 4.
    D.K. Ferry, S.M. Goodnick, Transport in Nanostructures (Cambridge University Press, Cambridge, 1997)CrossRefGoogle Scholar
  5. 5.
    T. Dittrich, P. Hänggi, G. Ingold, G. Schön, W. Zwerger, Quantum Dissipation and Transport (Wiley-VCH, Weinheim, 1998)Google Scholar
  6. 6.
    H. Bruus, K. Flensberg, Many-Body Quantum Theory in Condensed Matter Physics (Oxford University Press, Oxford, 2004)Google Scholar
  7. 7.
    G. Cuniberti, G. Fagas, K. Richter (eds.), Introducing Molecular Electronics, vol. 680, Lecture Notes in Physics (Springer, Berlin, 2005)Google Scholar
  8. 8.
    S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, Cambridge, 2005)zbMATHCrossRefGoogle Scholar
  9. 9.
    M. Di Ventra, Electrical Transport in Nanoscale Systems (Cambridge University Press, Cambridge, 2008)Google Scholar
  10. 10.
    Y.V. Nazarov, Y.M. Blanter, Quantum Transport: Introduction to Nanoscience (Cambridge University Press, Cambridge, 2009)Google Scholar
  11. 11.
    D.K. Ferry, S.M. Goodnick, J.P. Bird, Transport in Nanostructures, 2nd edn. (Cambridge University Press, Cambridge, 2009)Google Scholar
  12. 12.
    J.C. Cuevas, E. Scheer, Molecular Electronics: An Introduction to Theory and Experiment (World Scientific, Singapore, 2010)Google Scholar
  13. 13.
    R. Landauer, IBM, J. Res. Develop. 1, 223 (1957)Google Scholar
  14. 14.
    R. Landauer, Phil. Mag. 21, 863 (1970)ADSCrossRefGoogle Scholar
  15. 15.
    E.N. Economou, C.M. Soukoulis, Phys. Rev. Lett. 46, 618 (1981)ADSCrossRefGoogle Scholar
  16. 16.
    D.S. Fisher, P.A. Lee, Phys. Rev. B 23, 6851 (1981)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    M. Büttiker, Y. Imry, R. Landauer, S. Pinhas, Phys. Rev. B 31, 6207 (1985)ADSCrossRefGoogle Scholar
  18. 18.
    M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986)ADSCrossRefGoogle Scholar
  19. 19.
    R. Landauer, IBM, J. Res. Develop. 32, 306 (1988)Google Scholar
  20. 20.
    M. Büttiker, IBM, J. Res. Develop. 32, 317 (1988)Google Scholar
  21. 21.
    A.D. Stone, A. Szafer, IBM, J. Res. Develop. 32, 384 (1988)Google Scholar
  22. 22.
    H.U. Baranger, A.D. Stone, Phys. Rev. B 40, 8169 (1989)ADSCrossRefGoogle Scholar
  23. 23.
    U. Weiss, Quantum Dissipative Systems, Series in Modern Condensed Matter Physics, vol. 10 (World Scientific, Singapore, 1999)Google Scholar
  24. 24.
    H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)zbMATHGoogle Scholar
  25. 25.
    J. König, J. Schmid, H. Schoeller, G. Schön, Phys. Rev. B 54, 16820 (1996)ADSCrossRefGoogle Scholar
  26. 26.
    L. Kadanoff, G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962)Google Scholar
  27. 27.
    L.V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964). [Sov. Phys. JETP 20, 1018 (1965)]Google Scholar
  28. 28.
    D. Langreth, in Linear and Nonlinear Electron Transport in Solid, ed. by J. Devreese, E. van Doren (Plenum, New York, 1976)Google Scholar
  29. 29.
    J. Rammer, H. Smith, Rev. Mod. Phys. 58, 323 (1986)ADSCrossRefGoogle Scholar
  30. 30.
    G. Eliashberg, Zh. Eksp. Teor. Fiz. 61, 1254 (1971). [Sov. Phys. JETP 34, 668 (1972)]Google Scholar
  31. 31.
    A. Larkin, Y. Ovchinnikov, Zh. Eksp. Teor. Fiz. 68, 1915 (1975). [Sov. Phys. JETP 41, 960 (1975)]Google Scholar
  32. 32.
    K. Gray (ed.), Nonequilibrium Superconductivity, Phonons, and Kapitza Boundaries (Proc. NATO ASI) (Plenum, New York, 1981)Google Scholar
  33. 33.
    D. Langenberg, A. Larkin (eds.), Nonequilibrium Superconductivity, Modern Problems in Condensed Matter Sciences, vol. 12 (North-Holland, Amsterdam, 1986)Google Scholar
  34. 34.
    N.B. Kopnin, Theory of Nonequilibrium Superconductivity (Clarendon Press, Oxford, 2001)CrossRefGoogle Scholar
  35. 35.
    Y. Meir, N.S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992)ADSCrossRefGoogle Scholar
  36. 36.
    E. Runge, H. Ehrenreich, Phys. Rev. B 45, 9145 (1992)ADSCrossRefGoogle Scholar
  37. 37.
    A.P. Jauho, N.S. Wingreen, Y. Meir, Phys. Rev. B 50, 5528 (1994)ADSCrossRefGoogle Scholar
  38. 38.
    C. Caroli, R. Combescot, P. Nozieres, D. Saint-James, J. Phys. C: Solid St. Phys. 4, 916 (1971)ADSCrossRefGoogle Scholar
  39. 39.
    C. Caroli, R. Combescot, D. Lederer, P. Nozieres, D. Saint-James, J. Phys. C: Solid St. Phys. 4, 2598 (1971)ADSCrossRefGoogle Scholar
  40. 40.
    R. Combescot, J. Phys. C: Solid St. Phys. 4, 2611 (1971)ADSCrossRefGoogle Scholar
  41. 41.
    C. Caroli, R. Combescot, P. Nozieres, D. Saint-James, J. Phys. C: Solid St. Phys. 5, 21 (1972)ADSCrossRefGoogle Scholar
  42. 42.
    N.S. Wingreen, A.P. Jauho, Y. Meir, Phys. Rev. B 48, 8487 (1993)ADSCrossRefGoogle Scholar
  43. 43.
    A.P. Jauho, J. Phys.: Conf. Ser. 35, 313 (2006)Google Scholar
  44. 44.
    P.W. Anderson, Phys. Rev. 124, 41 (1961)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    J. Hubbard, Proc. R. Soc. Lond. Ser. A 276, 238 (1963)ADSCrossRefGoogle Scholar
  46. 46.
    J. Hubbard, Proc. R. Soc. Lond. Ser. A 277, 237 (1964)ADSCrossRefGoogle Scholar
  47. 47.
    J. Hubbard, Proc. R. Soc. Lond. Ser. A 281, 401 (1964)ADSCrossRefGoogle Scholar
  48. 48.
    D.V. Averin, K.K. Likharev, J. Low Temp. Phys. 62(3/4), 345 (1986)ADSCrossRefGoogle Scholar
  49. 49.
    D.V. Averin, K.K. Likharev, in Mesoscopic phenomena in solids, ed. by B.L. Altshuler, P.A. Lee, R.A. Webb (Elsevier, Amsterdam, 1991), p. 173Google Scholar
  50. 50.
    H. Grabert, M.H. Devoret (eds.), Single Charge Tunneling, NATO ASI Series B, vol. 294 (Plenum, New York, 1992)Google Scholar
  51. 51.
    H. van Houten, C.W.J. Beenakker, A.A.M. Staring, in Single Charge Tunneling. NATO ASI Series B. Vol. 294, ed. by H. Grabert, M.H. Devoret (Plenum, New York, 1992), p. 167Google Scholar
  52. 52.
    L.P. Kouwenhoven, C.M. Markus, P.L. McEuen, S. Tarucha, R.M. Westervelt, N.S. Wingreen, in Mesoscopic Electron Transport, ed. by L.L. Sohn, L.P. Kouwenhoven, G. Schön (Kluwer, 1997), NATO ASI Series E: Applied Sciences, p. 105Google Scholar
  53. 53.
    H. Schoeller, in Mesoscopic Electron Transport, ed. by L.L. Sohn, L.P. Kouwenhoven, G. Schön (Kluwer, 1997), NATO ASI Series E: Applied Sciences, p. 291Google Scholar
  54. 54.
    G. Schön, in Quantum Dissipation and Transport (Wiley-VCH, Weinheim, 1998)Google Scholar
  55. 55.
    W.G. van der Wiel, S. De Franceschi, J.M. Elzerman, T. Fujisawa, S. Tarucha, L.P. Kouwenhoven, Rev. Mod. Phys. 75, 1 (2002)ADSCrossRefGoogle Scholar
  56. 56.
    D.V. Averin, A.A. Odintsov, Phys. Lett. A 140(5), 251 (1989)ADSCrossRefGoogle Scholar
  57. 57.
    D.V. Averin, Y.V. Nazarov, Phys. Rev. Lett. 65, 2446 (1990)ADSCrossRefGoogle Scholar
  58. 58.
    D.V. Averin, Y.V. Nazarov, Macroscopic Quantum Tunneling of Charge and Co-tunneling (Plenum, 1992), NATO ASI Series B, vol. 294, Chap. 6, p. 217Google Scholar
  59. 59.
    I. Aleiner, P. Brouwer, L. Glazman, Phys. Rep. 358(56), 309 (2002)ADSCrossRefGoogle Scholar
  60. 60.
    D.V. Averin, A.N. Korotkov, K.K. Likharev, Phys. Rev. B 44, 6199 (1991)ADSCrossRefGoogle Scholar
  61. 61.
    C.W.J. Beenakker, Phys. Rev. B 44, 1646 (1991)ADSCrossRefGoogle Scholar
  62. 62.
    J. von Delft, D.C. Ralph, Phys. Rep. 345, 61 (2001)ADSCrossRefGoogle Scholar
  63. 63.
    E. Bonet, M.M. Deshmukh, D.C. Ralph, Phys. Rev. B 65, 045317 (2002)ADSCrossRefGoogle Scholar
  64. 64.
    M.H. Hettler, W. Wenzel, M.R. Wegewijs, H. Schoeller, Phys. Rev. Lett. 90, 076805 (2003)ADSCrossRefGoogle Scholar
  65. 65.
    B. Muralidharan, A.W. Ghosh, S. Datta, Phys. Rev. B 73, 155410 (2006)ADSCrossRefGoogle Scholar
  66. 66.
    G. Begemann, D. Darau, A. Donarini, M. Grifoni, Phys. Rev. B 77, 201406 (2008)ADSCrossRefGoogle Scholar
  67. 67.
    D.A. Ryndyk, A. Donarini, M. Grifoni, K. Richter, Phys. Rev. B 88, 085404 (2013)ADSCrossRefGoogle Scholar
  68. 68.
    E.G. Petrov, V. May, P. Hanggi, Chem. Phys. 296, 251 (2004)ADSCrossRefGoogle Scholar
  69. 69.
    E.G. Petrov, V. May, P. Hanggi, Chem. Phys. 319, 380 (2005)ADSCrossRefGoogle Scholar
  70. 70.
    E.G. Petrov, V. May, P. Hanggi, Phys. Rev. B 73, 045408 (2006)ADSCrossRefGoogle Scholar
  71. 71.
    F. Elste, C. Timm, Phys. Rev. B 71, 155403 (2005)ADSCrossRefGoogle Scholar
  72. 72.
    U. Harbola, M. Esposito, S. Mukamel, Phys. Rev. B 74, 235309 (2006)Google Scholar
  73. 73.
    J.N. Pedersen, B. Lassen, A. Wacker, M.H. Hettler, Phys. Rev. B 75, 235314 (2007)ADSCrossRefGoogle Scholar
  74. 74.
    L. Mayrhofer, M. Grifoni, Eur. Phys. J. B 56, 107 (2007)ADSCrossRefGoogle Scholar
  75. 75.
    H. Schoeller, G. Schön, Phys. Rev. B 50, 18436 (1994)ADSCrossRefGoogle Scholar
  76. 76.
    J. König, H. Schoeller, G. Schön, Phys. Rev. Lett. 76, 1715 (1996)ADSCrossRefGoogle Scholar
  77. 77.
    J. König, H. Schoeller, G. Schön, Phys. Rev. Lett. 78, 4482 (1997)ADSCrossRefGoogle Scholar
  78. 78.
    J. König, H. Schoeller, G. Schön, Phys. Rev. B 58, 7882 (1998)ADSCrossRefGoogle Scholar
  79. 79.
    A. Thielmann, M.H. Hettler, J. König, G. Schön, Phys. Rev. B 68, 115105 (2003)ADSCrossRefGoogle Scholar
  80. 80.
    A. Thielmann, M.H. Hettler, J. Konig, G. Schon, Phys. Rev. Lett. 95, 146806 (2005)ADSCrossRefGoogle Scholar
  81. 81.
    J. Aghassi, A. Thielmann, M.H. Hettler, G. Schon, Phys. Rev. B 73, 195323 (2006)ADSCrossRefGoogle Scholar
  82. 82.
    C. Timm, Phys. Rev. B 77, 195416 (2008)ADSCrossRefGoogle Scholar
  83. 83.
    C. Lacroix, J. Phys. F: Met. Phys. 11, 2389 (1981)ADSCrossRefGoogle Scholar
  84. 84.
    Y. Meir, N.S. Wingreen, P.A. Lee, Phys. Rev. Lett. 66, 3048 (1991)ADSCrossRefGoogle Scholar
  85. 85.
    Y. Meir, N.S. Wingreen, P.A. Lee, Phys. Rev. Lett. 70, 2601 (1993)ADSCrossRefGoogle Scholar
  86. 86.
    C. Niu, L.J. Liu, T.H. Lin, Phys. Rev. B 51, 5130 (1995)ADSCrossRefGoogle Scholar
  87. 87.
    P. Pals, A. MacKinnon, J. Phys.: Condens. Matter 8, 5401 (1996)ADSGoogle Scholar
  88. 88.
    S. Lamba, S.K. Joshi, Phys. Rev. B 62, 1580 (2000)ADSCrossRefGoogle Scholar
  89. 89.
    B. Song, D.A. Ryndyk, G. Cuniberti, Phys. Rev. B 76, 045408 (2007)ADSCrossRefGoogle Scholar
  90. 90.
    J.J. Palacios, L. Liu, D. Yoshioka, Phys. Rev. B 55, 15735 (1997)ADSCrossRefGoogle Scholar
  91. 91.
    L. Yi, J.S. Wang, Phys. Rev. B 66, 085105 (2002)ADSCrossRefGoogle Scholar
  92. 92.
    C. Niu, D.L. Lin, T.H. Lin, J. Phys.: Condens. Matter 11, 1511 (1999)ADSGoogle Scholar
  93. 93.
    R. Swirkowicz, J. Barnas, M. Wilczynski, Phys. Rev. B 68, 195318 (2003)ADSCrossRefGoogle Scholar
  94. 94.
    B.R. Bulka, T. Kostyrko, Phys. Rev. B 70, 205333 (2004)ADSCrossRefGoogle Scholar
  95. 95.
    T. Fujii, K. Ueda, Phys. Rev. B 68, 155310 (2003)ADSCrossRefGoogle Scholar
  96. 96.
    J. Schwinger, PNAS 37, 452Google Scholar
  97. 97.
    P.C. Martin, J. Schwinger, Phys. Rev. 115, 1342 (1959)ADSMathSciNetCrossRefGoogle Scholar
  98. 98.
    G. Baym, L.P. Kadanoff, Phys. Rev. 124, 287 (1961)ADSMathSciNetCrossRefGoogle Scholar
  99. 99.
    G. Baym, Phys. Rev. 127, 1391 (1962)ADSMathSciNetCrossRefGoogle Scholar
  100. 100.
    L. Hedin, Phys. Rev. 139, A796 (1965)ADSCrossRefGoogle Scholar
  101. 101.
    F. Aryasetiawany, O. Gunnarsson, Rep. Prog. Phys. 61, 237 (1988)ADSCrossRefGoogle Scholar
  102. 102.
    J.A. White, Phys. Rev. B 45, 1100Google Scholar
  103. 103.
    G. Onida, L. Reining, A. Rubio, Rev. Mod. Phys. 74, 601 (2002)ADSCrossRefGoogle Scholar
  104. 104.
    K.S. Thygesen, A. Rubio, J. Chem. Phys. 126, 091101 (2007)ADSCrossRefGoogle Scholar
  105. 105.
    K.S. Thygesen, Phys. Rev. Lett. 100, 166804 (2008)ADSCrossRefGoogle Scholar
  106. 106.
    K.S. Thygesen, A. Rubio, Phys. Rev. B 77, 115333 (2008)ADSCrossRefGoogle Scholar
  107. 107.
    X. Wang, C.D. Spataru, M.S. Hybertsen, A.J. Millis, Phys. Rev. B 77, 045119 (2008)ADSCrossRefGoogle Scholar
  108. 108.
    I.G. Lang, Y.A. Firsov, Sov. Phys. JETP 16, 1301 (1963)ADSGoogle Scholar
  109. 109.
    A.C. Hewson, D.M. Newns, Jpn. J. Appl. Phys. Suppl. 2(Pt. 2), 121 (1974)ADSCrossRefGoogle Scholar
  110. 110.
    G. Mahan, Many-Particle Physics, 2nd edn. (Plenum, New York, 1990)CrossRefGoogle Scholar
  111. 111.
    L.I. Glazman, R.I. Shekhter, Zh. Eksp. Teor. Fiz. 94, 292 (1988). [Sov. Phys. JETP 67, 163 (1988)]Google Scholar
  112. 112.
    N.S. Wingreen, K.W. Jacobsen, J.W. Wilkins, Phys. Rev. Lett. 61, 1396 (1988)ADSCrossRefGoogle Scholar
  113. 113.
    N.S. Wingreen, K.W. Jacobsen, J.W. Wilkins, Phys. Rev. B 40, 11834 (1989)ADSCrossRefGoogle Scholar
  114. 114.
    M. Jonson, Phys. Rev. B 39, 5924 (1989)ADSCrossRefGoogle Scholar
  115. 115.
    M. Cízek, M. Thoss, W. Domcke, Phys. Rev. B 70, 125406 (2004)ADSCrossRefGoogle Scholar
  116. 116.
    M. Cízek, Czech. J. of Phys. 55, 189 (2005)ADSCrossRefGoogle Scholar
  117. 117.
    S. Braig, K. Flensberg, Phys. Rev. B 68, 205324 (2003)ADSCrossRefGoogle Scholar
  118. 118.
    V. Aji, J.E. Moore, C.M. Varma, cond-mat/0302222 (2003)
  119. 119.
    A. Mitra, I. Aleiner, A.J. Millis, Phys. Rev. B 69, 245302 (2004)ADSCrossRefGoogle Scholar
  120. 120.
    J. Koch, F. von Oppen, Phys. Rev. Lett. 94, 206804 (2005)ADSCrossRefGoogle Scholar
  121. 121.
    J. Koch, M. Semmelhack, F. von Oppen, A. Nitzan, Phys. Rev. B 73, 155306 (2006)ADSCrossRefGoogle Scholar
  122. 122.
    J. Koch, F. von Oppen, A.V. Andreev, Phys. Rev. B 74, 205438 (2006)ADSCrossRefGoogle Scholar
  123. 123.
    K.C. Nowack, M.R. Wegewijs, cond-mat/0506552 (2005)
  124. 124.
    A. Zazunov, D. Feinberg, T. Martin, Phys. Rev. B 73, 115405 (2006)ADSCrossRefGoogle Scholar
  125. 125.
    D.A. Ryndyk, P. D’Amico, G. Cuniberti, K. Richter, Phys. Rev. B 78, 085409 (2008)ADSCrossRefGoogle Scholar
  126. 126.
    D.A. Ryndyk, P. D’Amico, K. Richter, Phys. Rev. B 81, 115333 (2010)ADSCrossRefGoogle Scholar
  127. 127.
    S. Tikhodeev, M. Natario, K. Makoshi, T. Mii, H. Ueba, Surf. Sci. 493, 63 (2001)ADSCrossRefGoogle Scholar
  128. 128.
    T. Mii, S. Tikhodeev, H. Ueba, Surf. Sci. 502, 26 (2002)ADSCrossRefGoogle Scholar
  129. 129.
    T. Mii, S. Tikhodeev, H. Ueba, Phys. Rev. B 68, 205406 (2003)ADSCrossRefGoogle Scholar
  130. 130.
    S. Tikhodeev, H. Ueba, Phys. Rev. B 70, 125414 (2004)ADSCrossRefGoogle Scholar
  131. 131.
    M. Galperin, M.A. Ratner, A. Nitzan, Nano Lett. 4, 1605 (2004)ADSCrossRefGoogle Scholar
  132. 132.
    M. Galperin, M.A. Ratner, A. Nitzan, J. Chem. Phys. 121(23), 11965 (2004)ADSCrossRefGoogle Scholar
  133. 133.
    M. Galperin, A. Nitzan, M.A. Ratner, D.R. Stewart, J. Phys. Chem. B 109, 8519 (2005)CrossRefGoogle Scholar
  134. 134.
    T. Frederiksen, Inelastic electron transport in nanosystems. Master’s thesis, Technical University of Denmark (2004)Google Scholar
  135. 135.
    T. Frederiksen, M. Brandbyge, N. Lorente, A.P. Jauho, Phys. Rev. Lett. 93, 256601 (2004)ADSCrossRefGoogle Scholar
  136. 136.
    M. Hartung, Vibrational effects in transport through molecular junctions. Master’s thesis, University of Regensburg (2004)Google Scholar
  137. 137.
    D.A. Ryndyk, J. Keller, Phys. Rev. B 71, 073305 (2005)ADSCrossRefGoogle Scholar
  138. 138.
    D.A. Ryndyk, M. Hartung, G. Cuniberti, Phys. Rev. B 73, 045420 (2006)ADSCrossRefGoogle Scholar
  139. 139.
    D.A. Ryndyk, G. Cuniberti, Phys. Rev. B 76, 155430 (2007)ADSCrossRefGoogle Scholar
  140. 140.
    M. Paulsson, T. Frederiksen, M. Brandbyge, Phys. Rev. B 72, 201101 (2005). [Erratum: 75, 129901(E) (2007)]Google Scholar
  141. 141.
    M. Paulsson, T. Frederiksen, M. Brandbyge, J. Phys.: Conf. Series 35, 247 (2006)Google Scholar
  142. 142.
    P.I. Arseyev, N.S. Maslova, JETP Lett. 82, 297 (2005)ADSCrossRefGoogle Scholar
  143. 143.
    P.I. Arseyev, N.S. Maslova, JETP Lett. 84, 93 (2006)CrossRefGoogle Scholar
  144. 144.
    A. Zazunov, R. Egger, C. Mora, T. Martin, Phys. Rev. B 73, 214501 (2006)ADSCrossRefGoogle Scholar
  145. 145.
    A.C. Hewson, D.M. Newns, J. Phys. C: Solid State Phys. 12, 1665 (1979)ADSCrossRefGoogle Scholar
  146. 146.
    M. Galperin, M.A. Ratner, A. Nitzan, Nano Lett. 5, 125 (2005)ADSCrossRefGoogle Scholar
  147. 147.
    P. D’Amico, D.A. Ryndyk, G. Cuniberti, K. Richter, New J. Phys. 10, 085002 (2008)CrossRefGoogle Scholar
  148. 148.
    P. Král, Phys. Rev. B 56, 7293 (1997)ADSCrossRefGoogle Scholar
  149. 149.
    U. Lundin, R.H. McKenzie, Phys. Rev. B 66, 075303 (2002)ADSCrossRefGoogle Scholar
  150. 150.
    J.X. Zhu, A.V. Balatsky, Phys. Rev. B 67, 165326 (2003)ADSCrossRefGoogle Scholar
  151. 151.
    A.S. Alexandrov, A.M. Bratkovsky, Phys. Rev. B 67(23), 235312 (2003)ADSCrossRefGoogle Scholar
  152. 152.
    K. Flensberg, Phys. Rev. B 68, 205323 (2003)ADSCrossRefGoogle Scholar
  153. 153.
    M. Galperin, M.A. Ratner, A. Nitzan, Phys. Rev. B 73, 045314 (2006)ADSCrossRefGoogle Scholar
  154. 154.
    A. Zazunov, T. Martin, Phys. Rev. B 76, 033417 (2007)ADSCrossRefGoogle Scholar
  155. 155.
    A. Mitra, I. Aleiner, A.J. Millis, Phys. Rev. Lett. 94, 076404 (2005)ADSCrossRefGoogle Scholar
  156. 156.
    D. Mozyrsky, M.B. Hastings, I. Martin, Phys. Rev. B 73, 035104 (2006)ADSCrossRefGoogle Scholar
  157. 157.
    L.Y. Gorelik, A. Isacsson, M.V. Voinova, B. Kasemo, R.I. Shekhter, M. Jonson, Phys. Rev. Lett. 80, 4526 (1998)ADSCrossRefGoogle Scholar
  158. 158.
    D. Boese, H. Schoeller, Europhys. Lett. 54, 668 (2001)ADSCrossRefGoogle Scholar
  159. 159.
    D. Fedorets, L.Y. Gorelik, R.I. Shekhter, M. Jonson, Europhys. Lett. 58, 99 (2002)ADSCrossRefGoogle Scholar
  160. 160.
    D. Fedorets, Phys. Rev. B 68, 033106 (2003)ADSCrossRefGoogle Scholar
  161. 161.
    D. Fedorets, L.Y. Gorelik, R.I. Shekhter, M. Jonson, Phys. Rev. Lett. 92, 166801 (2004)ADSCrossRefGoogle Scholar
  162. 162.
    K.D. McCarthy, N. Prokof’ev, M.T. Tuominen, Phys. Rev. B 67, 245415 (2003)ADSCrossRefGoogle Scholar
  163. 163.
    T. Novotný, A. Donarini, A.P. Jauho, Phys. Rev. Lett. 90, 256801 (2003)ADSCrossRefGoogle Scholar
  164. 164.
    T. Novotný, A. Donarini, C. Flindt, A.P. Jauho, Phys. Rev. Lett. 92, 248302 (2004)ADSCrossRefGoogle Scholar
  165. 165.
    Ya.M. Blanter, O. Usmani, Yu.V. Nazarov, Phys. Rev. Lett. 93, 136802 (2004)Google Scholar
  166. 166.
    A.Y. Smirnov, L.G. Mourokh, N.J.M. Horing, Phys. Rev. B 69, 155310 (2004)ADSCrossRefGoogle Scholar
  167. 167.
    N.M. Chtchelkatchev, W. Belzig, C. Bruder, Phys. Rev. B 70, 193305 (2004)ADSCrossRefGoogle Scholar
  168. 168.
    J. Bardeen, Phys. Rev. Lett. 6, 57 (1961)ADSCrossRefGoogle Scholar
  169. 169.
    W.A. Harrison, Phys. Rev. 123, 85 (1961)ADSCrossRefGoogle Scholar
  170. 170.
    M.H. Cohen, L.M. Falicov, J.C. Phillips, Phys. Rev. Lett. 8, 316 (1962)ADSCrossRefGoogle Scholar
  171. 171.
    R.E. Prange, Phys. Rev. 131, 1083 (1963)ADSMathSciNetCrossRefGoogle Scholar
  172. 172.
    C.B. Duke, Tunneling in Solids (Academic Press, New York, 1969). Chapter VIIGoogle Scholar
  173. 173.
    J. Tersoff, D.R. Hamann, Phys. Rev. Lett. 50, 1998 (1983)ADSCrossRefGoogle Scholar
  174. 174.
    J. Tersoff, D.R. Hamann, Phys. Rev. B 31, 805 (1985)ADSCrossRefGoogle Scholar
  175. 175.
    B.N.J. Persson, A. Baratoff, Phys. Rev. Lett. 59, 339 (1987)ADSCrossRefGoogle Scholar
  176. 176.
    M.A. Gata, P.R. Antoniewicz, Phys. Rev. B 47, 13797 (1993)ADSCrossRefGoogle Scholar
  177. 177.
    H. Raza, K.H. Bevan, D. Kienle, Phys. Rev. B 77, 035432 (2008)ADSCrossRefGoogle Scholar
  178. 178.
    M. Galperin, M.A. Ratner, A. Nitzan, J. Phys.: Condens. Matter 19, 103201 (2007)ADSGoogle Scholar
  179. 179.
    L.I. Glazman, M.E. Raikh, Pis’ma Zh. Eksp. Teor. Fiz. 47, 378 (1988). [JETP Lett. 47, 452 (1988)]Google Scholar
  180. 180.
    T.K. Ng, P.A. Lee, Phys. Rev. Lett. 61, 1768 (1988)ADSCrossRefGoogle Scholar
  181. 181.
    S. Hershfield, J.H. Davies, J.W. Wilkins, Phys. Rev. B 46, 7046 (1992)ADSCrossRefGoogle Scholar
  182. 182.
    N.S. Wingreen, Y. Meir, Phys. Rev. B 49, 11040 (1994)ADSCrossRefGoogle Scholar
  183. 183.
    R. Aguado, D.C. Langreth, Phys. Rev. Lett. 85, 1946 (2000)ADSCrossRefGoogle Scholar
  184. 184.
    T.S. Kim, S. Hershfield, Phys. Rev. B 63, 245326 (2001)ADSCrossRefGoogle Scholar
  185. 185.
    M. Plihal, J.W. Gadzuk, Phys. Rev. B 63, 085404 (2001)ADSCrossRefGoogle Scholar
  186. 186.
    S. Sanvito, A.R. Rocha, J. Comp. Theor. Nanosci. 3, 624 (2006)CrossRefGoogle Scholar
  187. 187.
    A.R. Rocha, V.M. García-Suárez, S. Bailey, C. Lambert, J. Ferrer, S. Sanvito, Phys. Rev. B 73, 085414 (2006)ADSCrossRefGoogle Scholar
  188. 188.
    W.J.M. Naber, S. Faez, W.G. van der Wiel, J. Phys. D: Appl. Phys. 40, R205 (2007)ADSCrossRefGoogle Scholar
  189. 189.
    Y. Ke, K. Xia, H. Guo, Phys. Rev. Lett. 100, 166805 (2008)ADSCrossRefGoogle Scholar
  190. 190.
    Z. Ning, Y. Zhu, J. Wang, H. Guo, Phys. Rev. Lett. 100, 056803 (2008)ADSCrossRefGoogle Scholar
  191. 191.
    M. Grifoni, P. Hänggi, Phys. Rep. 304, 229 (1998)ADSMathSciNetCrossRefGoogle Scholar
  192. 192.
    S. Kohler, J. Lehmann, P. Hänggi, Phys. Rep. 406, 379 (2005)ADSCrossRefGoogle Scholar
  193. 193.
    R. Sanchez, E. Cota, R. Aguado, G. Platero, Phys. Rev. B 74, 035326 (2006)ADSCrossRefGoogle Scholar
  194. 194.
    J. Maciejko, J. Wang, H. Guo, Phys. Rev. B 74 (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.TU DresdenDresdenGermany

Personalised recommendations