Interacting and Coherent Time-Dependent Transport in Semiconductor Heterostructures

  • Antti-Pekka Jauho
Part of the NATO ASI Series book series (NSSB, volume 342)


The hallmark of mesoscopic phenomena is the phase coherence of the charge carriers, which is maintained over a significant part of the transport process. The interference effects resulting from this phase coherence are reflected in a number of experimentally measurable properties. For example, phase coherence is central to the Aharonov-Bohm effect, Universal conductance fluctuations, (for a series of review articles, see Altshuler et al., 1991) and weak localization (reviewed by, e.g, Lee and Ramakrishnan, 1985), and can be affected by external controls such as temperature or magnetic field. The study of stationary mesoscopic physics is now a mature field, and in these notes we describe recent developments in a rapidly growing research area, where one uses an alternative way of affecting the phase coherence: external time-dependent perturbations. The interplay of external time-dependence and phase coherence can be phenomenologically understood as follows. If the single-particle energies acquire a time dependence, then the wave functions have an extra phase factor, \( \Psi \infty \exp \left[ { - i\smallint ^t dt'\varepsilon \left( {t'} \right)} \right] \) . For a uniform system such an overall phase factor is of no consequence. However, if the external time dependence is different in different parts of the system, and the particles can move between these regions (without being ‘dephased’ by inelastic collisions), the phase difference becomes important.


Resonant Tunneling Phase Coherence Bloch Oscillation Quantum Kinetic Equation Zener Tunneling 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abdolsalami, F., and Khan, F., 1990, Phys. Rev. B41:3494.ADSCrossRefGoogle Scholar
  2. Altshuler, B. L., Lee, P. A., and Webb, R. A, (eds.), 1991, “Mesoscopic Phenomena in Solids”, Elsevier, Amsterdam.Google Scholar
  3. Anda, E. V., and Flores, F., 1991, J. Phys.: Condens. Matter3: 9087.ADSCrossRefGoogle Scholar
  4. Ashcrof, N. W., and Mermin, N. D., 1976, “Solid State Physics”, Holt, Rinehart and Winston, New YorkGoogle Scholar
  5. Barker, J. R., 1973, J. Phys. C6:2663.ADSCrossRefGoogle Scholar
  6. Barker, J. R., and Ferry, D. K., 1979, Phys. Rev. Lett.42:1779.ADSCrossRefGoogle Scholar
  7. Bertoncini, R., Kriman, A. M., and Ferry, D. K., 1989, Phys. Rev. B40:3371.ADSCrossRefGoogle Scholar
  8. Bertoncini, R., Kriman, A. M., and Ferry, D. K., 1990, Phys. Rev. B41:1390.ADSCrossRefGoogle Scholar
  9. Bertoncini, R. and Jauho, A. P., 1991, Phys. Rev. B44:3655.ADSCrossRefGoogle Scholar
  10. Bertoncini, R. and Jauho, A. P., 1992, Phys. Rev. Lett.68:2826.ADSCrossRefGoogle Scholar
  11. Blandin, A., Nourtier, A., and Hone, D. W., 1976, J. de Physique37:369.CrossRefGoogle Scholar
  12. Bloch, F., 1928, Z. Physik52:555.ADSMATHCrossRefGoogle Scholar
  13. Brown, E. R. Soderstrom, J. R., Parker, C. D., Mahoney, L. J., Molvar, K. M., and McGill, T. C., 1991, Appl. Phys. Lett.58:2291.ADSCrossRefGoogle Scholar
  14. Bruder, C., and Schoeller, H., 1994, Phys. Rev. Lett.72:1076.ADSCrossRefGoogle Scholar
  15. Büttiker, M., Prêtre, A., and Thomas, H., 1993a, Phys. Rev. Lett.70:4114.ADSCrossRefGoogle Scholar
  16. Büttiker, M., Thomas, H., and Prêtre, A., 1993b, Physics Letters A180: 364ADSCrossRefGoogle Scholar
  17. Büttiker, M., 1993c, J. Phys. Condensed Matter5:9361.ADSCrossRefGoogle Scholar
  18. Caroli, C., Combescot, R., Nozieres, P., and Saint-James, D., 1971a, J. Phys. C.4:916.ADSCrossRefGoogle Scholar
  19. Caroli, C., Combescot, R., Lederer, D., Nozieres, P., and Saint-James, D., 1971b, J. Phys. C4:2589.ADSGoogle Scholar
  20. Caroli, C., Combescot, R., Nozieres, P., and Saint-James, D., 1972, J. Phys. C5:21.ADSCrossRefGoogle Scholar
  21. Chen, L. Y. and Su, Z. B., 1989, Phys. Rev. B40:9309.ADSCrossRefGoogle Scholar
  22. Chen, L. Y. and Ting, C. S., 1991, Phys. Rev. B43:2097.ADSCrossRefGoogle Scholar
  23. Davies, J. H., Hershfield, S., Hyldgaard, P., and Wilkins, J. W., 1993, Phys. Rev. B47:4603.ADSCrossRefGoogle Scholar
  24. Esaki, L. and Tsu, R., 1970, IBM J. Res. Dev.14:61.CrossRefGoogle Scholar
  25. Fu, Y. and Dudley, S. C., 1993, Phys. Rev. Lett.70:65.ADSCrossRefGoogle Scholar
  26. Fukuyama, H., Bari, R.A., and Fogedby, H. C., 1973, Phys. Rev. B8:5579.ADSCrossRefGoogle Scholar
  27. Glazman, L. I. and Shekter, R. I., 1987, Zh. Eksp. Teor. Fiz.94: 292(1988, Sov. Phys. JETP 67:163).Google Scholar
  28. Guimarães, P. S. S., Keay, B. J., Kaminski, J. P., Allen, S. J. Jr., Hopkins, P. F., Gossard, A. C., Florez, L. T., and Harbison, J. P., 1993, Phys. Rev. Lett.70:3792.ADSCrossRefGoogle Scholar
  29. Haug, H., and Jauho, A. P., 1994, “Quantum Kinetics in Transport and Optics of Semiconductors”, to be published by Springer, Frankfurt.Google Scholar
  30. Hershfield, S., and Ambegaokar, V., 1986, Phys. Rev.34:2147.ADSCrossRefGoogle Scholar
  31. Hershfield, S., Davies, J. H., and Wilkins, J. W., 1991, Phys. Rev. Lett.67:3720.ADSCrossRefGoogle Scholar
  32. Holthaus, M., 1992a, Phys. Rev. Lett.69:351.ADSCrossRefGoogle Scholar
  33. Holthaus, M., 1992b, Z. Phys. B.-Condensed Matter89:251.ADSCrossRefGoogle Scholar
  34. Holthaus, ML, and Hone, D., 1993, Phys. Rev. B47:6499.ADSCrossRefGoogle Scholar
  35. Ignatov, A. A., Renk, K. F., and Dodin, E. P, 1993, Phys. Rev. Lett.70:1996.ADSCrossRefGoogle Scholar
  36. Imam, H. T., Ponomarenko, V. V., and Averin, D.V., 1994 (unpublished).Google Scholar
  37. Jauho, A. P., and Wilkins, J. W., 1982, Phys. Rev. Lett.49:762.ADSCrossRefGoogle Scholar
  38. Jauho, A. P., and Wilkins, J. W., 1984, Phys. Rev. B29:1919.ADSCrossRefGoogle Scholar
  39. Jauho, A. P., 1989, Solid State Electronics32:1265.ADSCrossRefGoogle Scholar
  40. Jauho, A. P., 1991, in “Granular Nanoelectronics”, Vol. 251 of Nato Advanced Study Institute, Series B: Physics, Eds.Ferry, D. K., Barker, J.R., and Jacoboni, C., Plenum Press, New York.Google Scholar
  41. Jauho, A. P., Wingreen, N. S., and Meir, Y., 1994, Nordita Preprint 94/19 (to appear in Phys. Rev. B)Google Scholar
  42. Jonson, M., and Grinczajg, A., 1987, Appl. Phys. Lett.51:1729.ADSCrossRefGoogle Scholar
  43. Kazarinov, R. F., and Suris, R. A., 1972, Fiz. Tekh. Poluprov.6:148(1972, Sov. Phys. Semicond. 6:120). Khan, F.S., Davies, J.H., and Wilkins, J.W., 1987, Phys. Rev. B 36:2578.Google Scholar
  44. Kirk, W. P., and Reed, M. A., (eds.), 1992, “Nanostructures and Mesoscopic Systems”, Academic Press, San Diego.Google Scholar
  45. Kadanoff, L. P., and Baym, G., 1962, “Quantum Statistical Mechanics”, Benjamin, New York.MATHGoogle Scholar
  46. Keldysh, L.V., 1964, Zh. Eksp. Teor. Fiz47:1515(1965, Sov. Phys. JETP 20:1018).Google Scholar
  47. Krieger, J. B., and Iatrate, G. J., 1986, Phys. Rev. B33:5494.ADSCrossRefGoogle Scholar
  48. Krieger, J. B., and Iatrate, G. J., 1987, Phys. Rev. B35:9644.ADSCrossRefGoogle Scholar
  49. Krieger, J. B., and Iatrate, G. J., 1988, Phys. Rev. B38:6324.ADSCrossRefGoogle Scholar
  50. Landauer, R., 1957, IBM J. Res. Dev.1:233.MathSciNetCrossRefGoogle Scholar
  51. Landauer, R., 1970, Philos. Mag.21:863.ADSCrossRefGoogle Scholar
  52. Langreth, D. C., 1976, in “Linear and Nonlinear Electron Transport in Solids”, Vol. 17 of Nato Advanced Study Institute, Series B: Physics, eds.Devreese, J.T. and Van Doren, V.E., Plenum, New York.Google Scholar
  53. Langreth, D. C. and Nordlander, P., 1991, Phys. Rev. B43:2541.ADSCrossRefGoogle Scholar
  54. Lake, R., and Datta, S., 1992, Phys. Rev. B45:6670.ADSCrossRefGoogle Scholar
  55. Lake, R., Klimeck, G., Anantram, M., and Datta, S., 1993, Phys. Rev. B48:15132.ADSCrossRefGoogle Scholar
  56. Lee, P. A., and Ramakrishnan, T. V., 1985, Rev. Mod. Phys.57:287.ADSCrossRefGoogle Scholar
  57. Leo, K., Haring Bolivar, P., Brüggemann, F., Schwelder, R., and Köhler, K., 1992, Solid State Commun.84:943.ADSCrossRefGoogle Scholar
  58. Lipavsky, P., Spicka, V., and Velicky, B., 1986, Phys. Rev. B34:6933.ADSCrossRefGoogle Scholar
  59. Lipavsky, P., Khan, F. S., Abdolsalami, F., and Wilkins, J. S., 1991, Phys. Rev. B43:4885.ADSCrossRefGoogle Scholar
  60. Mahan, G. D., 1984, Physics Reports110:231.CrossRefGoogle Scholar
  61. Mahan, G. D., 1987, Physics Reports145:253.ADSCrossRefGoogle Scholar
  62. Martin, P. C., and Schwinger, J., 1959, J. Math. Phys.2:407.Google Scholar
  63. Meir, Y. and Wingreen, N. S., 1992, Phys. Rev. Lett.68:2512.ADSCrossRefGoogle Scholar
  64. Meir, Y., Wingreen, N. S., and Lee, P. A., 1993, Phys. Rev. Lett.70:2601.ADSCrossRefGoogle Scholar
  65. Ng, T. K., 1993, Phys. Rev. Lett.70:3635.ADSCrossRefGoogle Scholar
  66. Pastawski, H. M., 1992, Phys. Rev. B46:4053.ADSCrossRefGoogle Scholar
  67. Ralph, D. C., and Buhrman, R. A., 1994, Phys. Rev. Lett.21:3401.ADSCrossRefGoogle Scholar
  68. Rammer, J., and Smith, H., 1986, Rev. Mod. Phys.58:323.ADSCrossRefGoogle Scholar
  69. Reggiani, L., Lugli, P., and Jauho, A. P., 1987, Phys. Rev. B36:6602.ADSCrossRefGoogle Scholar
  70. Rubo, Yu. G., 1993, Zh. Eksp. Teor. Fiz.104:3536(1993, JETP 77:685).Google Scholar
  71. Runge, E., and Ehrenreich, H., 1992a, Annals of Physics219:55.ADSCrossRefGoogle Scholar
  72. Runge, E., and Ehrenreich, H., 1992b, Phys. Rev. B45:9145.ADSCrossRefGoogle Scholar
  73. Schwinger, J., 1961, Phys. Rev.115:1342.MathSciNetGoogle Scholar
  74. Suhrke, M., and Wilke, S., 1992, Phys. Rev. B46:2400.ADSCrossRefGoogle Scholar
  75. Strinati, G., Castellani, C., and Di Castro, D., 1989, Phys. Rev. B40:12237.ADSCrossRefGoogle Scholar
  76. Vasko, F. T., 1983, Fiz. Tverd. Tela25:20(1983, Sov. Phys. Solid. State 25:10).Google Scholar
  77. Waschke, Ch., Roskos, H. G., Schwedler, K., Leo, K., Kurz, H., and Köhler, K., 1993, Phys. Rev. Lett.70:3319.ADSCrossRefGoogle Scholar
  78. Weil, T., and Vinter, B., 1987, Appl. Phys. Lett.50:1281.ADSCrossRefGoogle Scholar
  79. Wingreen, N. S., Jacobsen, K. W., and Wilkins, J. W., 1989, Phys. Rev. B40:11834.ADSCrossRefGoogle Scholar
  80. Wingreen, N. S., Jauho, A. P., and Meir, Y., 1993, Phys. Rev. B47:8487.ADSCrossRefGoogle Scholar
  81. Yeyati, A. L., Martin-Rodero, A., and Flores, F., 1993, Phys. Rev. Lett.71:2991.ADSCrossRefGoogle Scholar
  82. Zener, C., 1934, Proc. Roy. Soc. London Ser. A145:523.ADSCrossRefGoogle Scholar
  83. Zhang, C., Lerch, M. L. F., Martin, A. D., Simmonds, P. E., and Eaves, L., 1994, Phys. Rev. Lett.72:3397.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Antti-Pekka Jauho
    • 1
  1. 1.Mikroelektronik CentretDenmark’s Technical UniversityLyngbyDenmark

Personalised recommendations