Advertisement

The Dynamics of Electrons in Metals: Low-Temperature Effects

  • Colin M. Hurd
Part of the The International Cryogenics Monograph Series book series (INCMS)

Abstract

The theory of the isothermal electron transport properties of metals is concerned with the description of the motion of an electron under the combined influences of externally applied electric and magnetic fields and the internal periodic potential due to the ionic lattice. We shall find it convenient to follow Chambers1 and to classify into five categories the conditions under which the electron transport effects can be imagined to exist. These are classified according to the value of ω c τ, where ω c [defined in equation (1.15)] is the cyclotron frequency of a representative electron state in momentum space corresponding to the applied magnetic field H, and τ is the average relaxation time of an electron in a cyclotron orbit. The five categories are the following.

Keywords

Fermi Surface Brillouin Zone Hall Effect Quantum Size Effect Hall Coefficient 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. G. Chambers, “Magnetoresistance,” in: W. A. Harrison and M. B. Webb (eds.), The Fermi Surface ,John Wiley, New York, 1960, p. 100.Google Scholar
  2. 2.
    E. H. Hall, Am. J. Math. 2, 287 (1879).Google Scholar
  3. 3.
    V. A. Marsocci and T. T. Chen, J. Appl. Phys. 40, 3361 (1969).Google Scholar
  4. 4.
    C. P. Battarel and M. Galinier, IEEE Trans. Mag. MAG5, 18 (1969).Google Scholar
  5. 5.
    V. D. Ky, Zh. Eksp. Teor. Fiz. 54, 762 (1968)Google Scholar
  6. 5a.
    V. D. Ky Zh. Eksp[Soviet Phys.-JETP (Engl. trans.) 27, 407 (1968)].Google Scholar
  7. 6.
    M. L. Yu and J. T. H. Chang, J. Phys. Chem. Solids 31, 1997 (1970).Google Scholar
  8. 7.
    W. A. Harrison, Phys. Rev. 118, 1190(1960).Google Scholar
  9. 8.
    A. B. Pippard, The Dynamics of Conduction Electrons ,Blackie and Sons Ltd., London, 1965.Google Scholar
  10. 9.
    W. Mercouroff, La Surface de Fermi des Métaux ,Masson et Cie., Paris, 1967.Google Scholar
  11. 10.
    E. Fawcett, Advan. Phys. 13, 139 (1964).Google Scholar
  12. 11.
    I. M. Lifshitz and V. G. Peshanskii, Zh. Eksp. Teor. Fiz. 35, 1251 (1958)Google Scholar
  13. 11a.
    I. M. Lifshitz V. G. Peshanskii[Soviet Phys.-JETP (Engl. trans.) 35, 875 (1959)]; 38, 188 (1960)Google Scholar
  14. I. M. Lifshitz V. G. Peshanskii[Soviet Phys.-JETP (Engl. trans.) 11, 137 (1960)].Google Scholar
  15. 12.
    E. Fawcett and W. A. Reed, Phys. Rev. 131, 2463 (1963).Google Scholar
  16. 13.
    A. B. Pippard, Repts. Progr. Phys. 23, 176 (1960).Google Scholar
  17. 14.
    A. H. Kahn and H. P. R. Frederikse, Solid State Phys. 9, 257 (1959).Google Scholar
  18. 15.
    L. M. Roth and P. N. Argyres, “Magnetic Quantum Effects,” in: R. K. Willardson and A. C. Beer (eds.), Semiconductors and Semimetals, Vol. 1 ,Academic Press, New York, 1966, p. 159.Google Scholar
  19. 16.
    L. Schubnikov and W. J. de Haas, Leiden Comm. 207, 210 (1930).Google Scholar
  20. 17.
    I. M. Lifshitz, J. Phys. Chem. Solids 4, 11 (1958).Google Scholar
  21. 18.
    P. N. Argyres, Phys. Rev. 109, 1115 (1958).Google Scholar
  22. 19.
    J. M. Reynolds, H. W. Hemstreet, T. E. Leinhardt, and D. D. Triantos, Phys. Rev. 96, 1203 (1954).Google Scholar
  23. 20.
    M. H. Cohen and L. M. Falicov, Phys. Rev. Letters 7, 231 (1961).Google Scholar
  24. 21.
    E. I. Blount, Phys. Rev. 126, 1636 (1962).Google Scholar
  25. 22.
    L. M. Falicov, A. B. Pippard, and P. R. Sievert, Phys. Rev. 151, 498 (1966).Google Scholar
  26. 23.
    L. M. Falicov and P. R. Sievert, Phys. Rev. Letters 12, 558 (1964).Google Scholar
  27. 24.
    R. C. Barklie and A. B. Pippard, Proc. Roy. Soc. (London) A317, 167 (1970).Google Scholar
  28. 25.
    R. W. Stark, Phys. Rev. Letters 9, 482 (1962).Google Scholar
  29. 26.
    R. J. Balcombe and R. A. Parker, Phil. Mag. 21, 533 (1970).Google Scholar
  30. 27.
    A. B. Pippard, “Metallic Electrons in a Magnetic Field,” in: J. M. Ziman (ed.), The Physics of Metals ,Cambridge University Press, Cambridge, 1969, p. 113.Google Scholar
  31. 28.
    A. B. Pippard, Proc. Roy. Soc. (London) A270, 1 (1962);Google Scholar
  32. 28a.
    A. B. PippardPhil. Trans. Roy. Soc. London 256, 39 (1964).Google Scholar
  33. 29.
    R. W. Stark and L. M. Falicov, Progr. Low Temp. Phys. 5, 235 (1967).Google Scholar
  34. 30.
    T. S. Jayadevaiah, Thin Solid Films 4, R37 (1969).Google Scholar
  35. 31.
    G. Brandli and J. L. Olsen, Materials Sci. Eng. (Netherlands) 4, 61 (1969).Google Scholar
  36. 32.
    R. G. Chambers, “Transport Properties: Surface and Size Effects,” in: J. M. Ziman (ed.), The Physics of Metals ,Cambridge University Press, Cambridge, 1969, p. 175.Google Scholar
  37. 33.
    K. Fuchs, Proc. Cambridge Phil. Soc. 34, 100 (1938).Google Scholar
  38. 34.
    E. H. Sondheimer, Adv. Phys. 1, 1 (1952).Google Scholar
  39. 35.
    A. N. Friedman and S. H. Koenig, IBM J. Res. Develop. 4, 158 (1960).Google Scholar
  40. 36.
    H. Schwartz, Phys. Kond. Mater. 9, 164(1969);Google Scholar
  41. 36a.
    H. SchwartzPhys. Stat. Sol. 39, 507(1970).Google Scholar
  42. 37.
    D. K. C. MacDonald and K. Sarginson, Proc. Roy. Soc. (London) A203, 223 (1950).Google Scholar
  43. 38.
    G. K. White and S. B. Woods, Phil. Mag. 1, 846 (1956).Google Scholar
  44. 39.
    E. Ditlefson and J. Lothe, Phil. Mag. 14, 759 (1966).Google Scholar
  45. 40.
    M. Ya. Azbel, Zh. Eksp. Teor. Fiz. 44, 1262 (1963)Google Scholar
  46. 40a.
    M. Ya. Azbel, [Soviet Phys.-JETP (Engl. trans.) 17, 851 (1963)].Google Scholar
  47. 41.
    W. F. Druyvesteyn, Phil. Mag. 18, 11 (1968).Google Scholar
  48. 42.
    F. Stern, Phys. Rev. Letters 21, 1687 (1968).Google Scholar
  49. 43.
    I. Holwech, Phil. Mag. 12, 117 (1965).Google Scholar
  50. 44.
    R. Lück, Phys. Stat. Sol. 18, 59 (1966).Google Scholar
  51. 45.
    E. H. Sondheimer, Phys. Rev. 80, 401 (1950).Google Scholar
  52. 46.
    H. J. Mackey and J. R. Sybert, Phys. Rev. 158, 658 (1967).Google Scholar
  53. 47.
    N. H. Zebouni, R. E. Hamburg, and H. J. Mackey, Phys. Rev. Letters 11, 260 (1963).Google Scholar
  54. 48.
    J. Feder and T. Jossang, Physica Norvegica 1, 217 (1963).Google Scholar
  55. 49.
    V. L. Gurevich, Zh. Eksp. Teor. Fiz. 35, 668 (1958)Google Scholar
  56. 49a.
    V. L. Gurevich,[Soviet Phys.-JETP (Engl. trans.) 35, 464 (1959)].Google Scholar
  57. 50.
    H. J. Mackey and J. R. Sybert, Phys. Rev. 164, 982 (1967).Google Scholar
  58. 51.
    T. Alstadheim and R. Risnes, Phil. Mag. 18, 885 (1968).Google Scholar
  59. 52.
    D. Shoenberg, “Electronic Structure: The Experimental Results,” in: J. M. Ziman (ed.), The Physics of Metals ,Cambridge University Press, Cambridge, 1969, p. 62.Google Scholar
  60. 53.
    C. G. Grenier, K. R. Efferson, and J. M. Reynolds, Phys. Rev. 143, 406 (1966).Google Scholar
  61. 54.
    D. E. Soule and J. C. Abele, Phys. Rev. Letters 23, 1287 (1969).Google Scholar
  62. 55.
    S. B. Soffer, Phys. Rev. 176, 861 (1968).Google Scholar
  63. 56.
    V. P. Duggal, R. Rup, and P. Tripathi, Appl. Phys. Letters 9, 293 (1966).Google Scholar
  64. 57.
    H. E. Bennett and J. M. Bennett, “Validity of the Drude Theory for Ag, Au and Al in the Infra-Red,” in: F. Abeles (ed.), Optical Properties and Electronic Structure of Metals and Alloys ,North-Holland, Amsterdam, 1966, p. 175.Google Scholar
  65. 58.
    V. P. Duggal and R. Rup, J. Appl. Phys. 40, 492 (1969).Google Scholar
  66. 59.
    Yu. F. Ogrin, V. N. Lutskii, and M. I. Elinson, Zh. Eksp. Teor. Fiz. Pis. Red. 3, 114 (1966)Google Scholar
  67. 59a.
    Yu. F. Ogrin, V. N. Lutskii, and M. I. Elinson, [Soviet Phys.-JETP Letters (Engl. trans.) 3, 71 (1966)].Google Scholar
  68. 60.
    V. B. Sandomirskii, Zh. Eksp. Teor. Fiz. 52, 158 (1967)Google Scholar
  69. V. B. Sandomirskii,[Soviet Phys.-JETP (Engl. trans.) 25, 101 (1967)].Google Scholar
  70. 61.
    B. A. Tavger and V. Demikovskii, Fiz. Tverd. Tela 5, 644 (1963) [Soviet Phys.-Solid State (Engl. trans.) 5, 469 (1963)].Google Scholar
  71. 62.
    L. V. Iogansen, Zh. Eksp. Teor. Fiz. 50, 709 (1966)Google Scholar
  72. 62a.
    L. V. Iogansen,[Soviet Phys.-JETP (Engl. trans.) 23, 470 (1966)].Google Scholar
  73. 63.
    R. G. Chambers and B. K. Jones, Proc. Roy. Soc. (London) A270, 417 (1962).Google Scholar
  74. 64.
    J. E. A. Alderson and T. Farrell, Phys. Rev. 185, 876 (1969).Google Scholar
  75. 65.
    F. E. Rose, M. T. Taylor, and R. Bowers, Phys. Rev. 127 ,1122 (1962).Google Scholar
  76. 66.
    R. D. Barnard, J. E. A. Alderson, T. Farrell, and C. M. Hurd, Phys. Rev. 176, 761 (1968).Google Scholar
  77. 67.
    N. E. Alekseevskii and Yu. P. Gaidukov, Zh. Eksp. Teor. Fiz. 42, 69 (1962) [Soviet Phys.-JETP (Engl. trans.) 15, 49 (1962)].Google Scholar
  78. 68.
    J. R. Merrill, Phys. Rev. 166, 716 (1968).Google Scholar
  79. 69.
    V. G. Volotskaya, Zh. Eksp. Teor. Fiz. 44, 80 (1963) [Soviet Phys.-JETP (Engl. trans.) 17, 56 (1963)].Google Scholar
  80. 70.
    E. S. Borovik and V. G. Volotskaya, Zh. Eksp. Teor. Fiz. 48, 1554 (1965) [Soviet Phys.-JETP (Engl. trans.) 21, 1041 (1965)].Google Scholar
  81. 71.
    R. Lück, Phys. Stat. Sol. 18, 49 (1966).Google Scholar
  82. 72.
    D. Shoenberg, Phil. Trans. Roy. Soc. London A245, 1 (1952).Google Scholar
  83. 73.
    R. A. Cornell and J. A. Marcus, Phys. Rev. 107, 940 (1957).Google Scholar
  84. 74.
    W. C. Overton and T. G. Berlincourt, Phys. Rev. 99, 1165 (1955).Google Scholar
  85. 75.
    J. Babiskin, Phys. Rev. 107, 981 (1957).Google Scholar
  86. 76.
    A. S. Joseph and W. L. Gordon, Phys. Rev. 126, 489 (1962).Google Scholar
  87. 77.
    W. A. Reed and G. F. Brennert, Phys. Rev. 130, 565 (1963).Google Scholar
  88. 78.
    V. Frank, Appl. Sci. Research B7, 41 (1958).Google Scholar
  89. 79.
    G. T. Croft, W. F. Love, and F. C. Nix, Phys. Rev. 95, 1403 (1954).Google Scholar
  90. 80.
    P. B. Alers, Phys. Rev. 107, 959 (1957).Google Scholar
  91. 81.
    J. R. Sybert, H. J. Mackey, and R. E. Miller, Phys. Letters 24A, 655 (1967).Google Scholar
  92. 82.
    C. Miziumski and A. W. Lawson, Phys. Rev. 180, 749 (1969).Google Scholar
  93. 83.
    J. Yahia and J. A. Marcus, Phys. Rev. 113, 137 (1959).Google Scholar
  94. 84.
    M. C. Steel, Phys. Rev. 99, 1751 (1955).Google Scholar
  95. 85.
    J. Ketterson and Y. Eckstein, Phys. Rev. 132, 1,885 (1963).Google Scholar
  96. 86.
    D. K. C. MacDonald, Nature 163, 637 (1949).Google Scholar
  97. 87.
    J. Babiskin and P. G. Siebenmann, Phys. Rev. 107, 1249 (1957).Google Scholar
  98. 88.
    W. Cirkler, Z. Physik 147, 481 (1957).Google Scholar
  99. 89.
    H. J. Mackey, J. R. Sybert, and J. T. Fielder, Phys. Rev. 157, 578 (1967).Google Scholar
  100. 90.
    E. R. Andrew, Proc. Phys. Soc. (London) 62, 77 (1949).Google Scholar
  101. 91.
    A. F. Mayadas, J. Appl. Phys. 39, 4241 (1968).Google Scholar
  102. 92.
    T. Amundsen, Phil. Mag. 17, 107 (1968).Google Scholar
  103. 93.
    T. Amundsen and T. Olsen, Phil. Mag. 11, 561 (1965).Google Scholar
  104. 94.
    H. J. Mackey, J. R. Sybert, and R. D. Hight, Phys. Rev. Bl, 2385 (1970).Google Scholar
  105. 95.
    K. Forsvoll and I. Holwech, Phil. Mag. 10, 921 (1964); 9, 435 (1964).Google Scholar
  106. 96.
    R. Risnes and V. Sollien, Phil. Mag. 20, 895 (1969).Google Scholar
  107. 97.
    A. von Bassewitz and E. N. Mitchell, Phys. Rev. 182, 712 (1969).Google Scholar
  108. 98.
    I. Holwech and J. Jeppesen, Phil. Mag. 15, 217 (1967).Google Scholar
  109. 99.
    H. J. Mackey, J. R. Sybert, and H. C. Mollenkopf, Phys. Rev. 161, 611 (1967).Google Scholar
  110. 100.
    M. Yaqub and J. F. Cochran, Phys. Rev. 137, A1182 (1965).Google Scholar
  111. 101.
    J. A. Munarin, J. A. Marcus, and P. E. Bloomfield, Phys. Rev. 172, 718 (1968).Google Scholar
  112. 102.
    J. L. Olsen, Helv. Phys. Acta 31, 713 (1958).Google Scholar
  113. 103.
    P. Wyder, Phys. Kond. Mater. 3, 263 (1965).Google Scholar
  114. 104.
    B. N. Aleksandrov, Zh. Eksp. Teor. Fiz. 43, 399 (1962) [Soviet Phys.-JETP (Engl. trans.) 16, 286 (1963)].Google Scholar
  115. 105.
    J.-Y. Le Traon and H.-A. Combet, Compt. Rend. 268B, 502 (1969).Google Scholar
  116. 106.
    Yu. F. Komnik and E. I. Bukhshtab, Zh. Eksp. Teor. Fiz. 54, 63 (1968) [Soviet Phys.-JETP (Engl. trans.) 27, 34 (1968)].Google Scholar
  117. 107.
    D. D. Thornburg and C. M. Wayman, Phil. Mag. 20, 1153 (1969).Google Scholar
  118. 108.
    N. C. McGill, Physica 40, 91 (1968).Google Scholar

Copyright information

© Plenum Press, New York 1972

Authors and Affiliations

  • Colin M. Hurd
    • 1
  1. 1.Division of ChemistryNational Research Council of CanadaOttawaCanada

Personalised recommendations