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The Dynamics of Electrons in Metals: Low-Temperature Effects

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The Hall Effect in Metals and Alloys

Part of the book series: The International Cryogenics Monograph 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.

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References

  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. E. H. Hall, Am. J. Math. 2, 287 (1879).

    Google Scholar 

  3. V. A. Marsocci and T. T. Chen, J. Appl. Phys. 40, 3361 (1969).

    Google Scholar 

  4. C. P. Battarel and M. Galinier, IEEE Trans. Mag. MAG5, 18 (1969).

    Google Scholar 

  5. V. D. Ky, Zh. Eksp. Teor. Fiz. 54, 762 (1968)

    Google Scholar 

  6. V. D. Ky Zh. Eksp[Soviet Phys.-JETP (Engl. trans.) 27, 407 (1968)].

    Google Scholar 

  7. M. L. Yu and J. T. H. Chang, J. Phys. Chem. Solids 31, 1997 (1970).

    Google Scholar 

  8. W. A. Harrison, Phys. Rev. 118, 1190(1960).

    Google Scholar 

  9. A. B. Pippard, The Dynamics of Conduction Electrons ,Blackie and Sons Ltd., London, 1965.

    Google Scholar 

  10. W. Mercouroff, La Surface de Fermi des Métaux ,Masson et Cie., Paris, 1967.

    Google Scholar 

  11. E. Fawcett, Advan. Phys. 13, 139 (1964).

    Google Scholar 

  12. I. M. Lifshitz and V. G. Peshanskii, Zh. Eksp. Teor. Fiz. 35, 1251 (1958)

    Google Scholar 

  13. 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. E. Fawcett and W. A. Reed, Phys. Rev. 131, 2463 (1963).

    Google Scholar 

  16. A. B. Pippard, Repts. Progr. Phys. 23, 176 (1960).

    Google Scholar 

  17. A. H. Kahn and H. P. R. Frederikse, Solid State Phys. 9, 257 (1959).

    Google Scholar 

  18. 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. L. Schubnikov and W. J. de Haas, Leiden Comm. 207, 210 (1930).

    Google Scholar 

  20. I. M. Lifshitz, J. Phys. Chem. Solids 4, 11 (1958).

    Google Scholar 

  21. P. N. Argyres, Phys. Rev. 109, 1115 (1958).

    Google Scholar 

  22. J. M. Reynolds, H. W. Hemstreet, T. E. Leinhardt, and D. D. Triantos, Phys. Rev. 96, 1203 (1954).

    Google Scholar 

  23. M. H. Cohen and L. M. Falicov, Phys. Rev. Letters 7, 231 (1961).

    Google Scholar 

  24. E. I. Blount, Phys. Rev. 126, 1636 (1962).

    Google Scholar 

  25. L. M. Falicov, A. B. Pippard, and P. R. Sievert, Phys. Rev. 151, 498 (1966).

    Google Scholar 

  26. L. M. Falicov and P. R. Sievert, Phys. Rev. Letters 12, 558 (1964).

    Google Scholar 

  27. R. C. Barklie and A. B. Pippard, Proc. Roy. Soc. (London) A317, 167 (1970).

    Google Scholar 

  28. R. W. Stark, Phys. Rev. Letters 9, 482 (1962).

    Google Scholar 

  29. R. J. Balcombe and R. A. Parker, Phil. Mag. 21, 533 (1970).

    Google Scholar 

  30. 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. A. B. Pippard, Proc. Roy. Soc. (London) A270, 1 (1962);

    Google Scholar 

  32. A. B. PippardPhil. Trans. Roy. Soc. London 256, 39 (1964).

    Google Scholar 

  33. R. W. Stark and L. M. Falicov, Progr. Low Temp. Phys. 5, 235 (1967).

    Google Scholar 

  34. T. S. Jayadevaiah, Thin Solid Films 4, R37 (1969).

    Google Scholar 

  35. G. Brandli and J. L. Olsen, Materials Sci. Eng. (Netherlands) 4, 61 (1969).

    Google Scholar 

  36. 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. K. Fuchs, Proc. Cambridge Phil. Soc. 34, 100 (1938).

    Google Scholar 

  38. E. H. Sondheimer, Adv. Phys. 1, 1 (1952).

    Google Scholar 

  39. A. N. Friedman and S. H. Koenig, IBM J. Res. Develop. 4, 158 (1960).

    Google Scholar 

  40. H. Schwartz, Phys. Kond. Mater. 9, 164(1969);

    Google Scholar 

  41. H. SchwartzPhys. Stat. Sol. 39, 507(1970).

    Google Scholar 

  42. D. K. C. MacDonald and K. Sarginson, Proc. Roy. Soc. (London) A203, 223 (1950).

    Google Scholar 

  43. G. K. White and S. B. Woods, Phil. Mag. 1, 846 (1956).

    Google Scholar 

  44. E. Ditlefson and J. Lothe, Phil. Mag. 14, 759 (1966).

    Google Scholar 

  45. M. Ya. Azbel, Zh. Eksp. Teor. Fiz. 44, 1262 (1963)

    Google Scholar 

  46. M. Ya. Azbel, [Soviet Phys.-JETP (Engl. trans.) 17, 851 (1963)].

    Google Scholar 

  47. W. F. Druyvesteyn, Phil. Mag. 18, 11 (1968).

    Google Scholar 

  48. F. Stern, Phys. Rev. Letters 21, 1687 (1968).

    Google Scholar 

  49. I. Holwech, Phil. Mag. 12, 117 (1965).

    Google Scholar 

  50. R. Lück, Phys. Stat. Sol. 18, 59 (1966).

    Google Scholar 

  51. E. H. Sondheimer, Phys. Rev. 80, 401 (1950).

    Google Scholar 

  52. H. J. Mackey and J. R. Sybert, Phys. Rev. 158, 658 (1967).

    Google Scholar 

  53. N. H. Zebouni, R. E. Hamburg, and H. J. Mackey, Phys. Rev. Letters 11, 260 (1963).

    Google Scholar 

  54. J. Feder and T. Jossang, Physica Norvegica 1, 217 (1963).

    Google Scholar 

  55. V. L. Gurevich, Zh. Eksp. Teor. Fiz. 35, 668 (1958)

    Google Scholar 

  56. V. L. Gurevich,[Soviet Phys.-JETP (Engl. trans.) 35, 464 (1959)].

    Google Scholar 

  57. H. J. Mackey and J. R. Sybert, Phys. Rev. 164, 982 (1967).

    Google Scholar 

  58. T. Alstadheim and R. Risnes, Phil. Mag. 18, 885 (1968).

    Google Scholar 

  59. 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. C. G. Grenier, K. R. Efferson, and J. M. Reynolds, Phys. Rev. 143, 406 (1966).

    Google Scholar 

  61. D. E. Soule and J. C. Abele, Phys. Rev. Letters 23, 1287 (1969).

    Google Scholar 

  62. S. B. Soffer, Phys. Rev. 176, 861 (1968).

    Google Scholar 

  63. V. P. Duggal, R. Rup, and P. Tripathi, Appl. Phys. Letters 9, 293 (1966).

    Google Scholar 

  64. 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. V. P. Duggal and R. Rup, J. Appl. Phys. 40, 492 (1969).

    Google Scholar 

  66. Yu. F. Ogrin, V. N. Lutskii, and M. I. Elinson, Zh. Eksp. Teor. Fiz. Pis. Red. 3, 114 (1966)

    Google Scholar 

  67. Yu. F. Ogrin, V. N. Lutskii, and M. I. Elinson, [Soviet Phys.-JETP Letters (Engl. trans.) 3, 71 (1966)].

    Google Scholar 

  68. 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. B. A. Tavger and V. Demikovskii, Fiz. Tverd. Tela 5, 644 (1963) [Soviet Phys.-Solid State (Engl. trans.) 5, 469 (1963)].

    Google Scholar 

  71. L. V. Iogansen, Zh. Eksp. Teor. Fiz. 50, 709 (1966)

    Google Scholar 

  72. L. V. Iogansen,[Soviet Phys.-JETP (Engl. trans.) 23, 470 (1966)].

    Google Scholar 

  73. R. G. Chambers and B. K. Jones, Proc. Roy. Soc. (London) A270, 417 (1962).

    Google Scholar 

  74. J. E. A. Alderson and T. Farrell, Phys. Rev. 185, 876 (1969).

    Google Scholar 

  75. F. E. Rose, M. T. Taylor, and R. Bowers, Phys. Rev. 127 ,1122 (1962).

    Google Scholar 

  76. R. D. Barnard, J. E. A. Alderson, T. Farrell, and C. M. Hurd, Phys. Rev. 176, 761 (1968).

    Google Scholar 

  77. 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. J. R. Merrill, Phys. Rev. 166, 716 (1968).

    Google Scholar 

  79. V. G. Volotskaya, Zh. Eksp. Teor. Fiz. 44, 80 (1963) [Soviet Phys.-JETP (Engl. trans.) 17, 56 (1963)].

    Google Scholar 

  80. 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. R. Lück, Phys. Stat. Sol. 18, 49 (1966).

    Google Scholar 

  82. D. Shoenberg, Phil. Trans. Roy. Soc. London A245, 1 (1952).

    Google Scholar 

  83. R. A. Cornell and J. A. Marcus, Phys. Rev. 107, 940 (1957).

    Google Scholar 

  84. W. C. Overton and T. G. Berlincourt, Phys. Rev. 99, 1165 (1955).

    Google Scholar 

  85. J. Babiskin, Phys. Rev. 107, 981 (1957).

    Google Scholar 

  86. A. S. Joseph and W. L. Gordon, Phys. Rev. 126, 489 (1962).

    Google Scholar 

  87. W. A. Reed and G. F. Brennert, Phys. Rev. 130, 565 (1963).

    Google Scholar 

  88. V. Frank, Appl. Sci. Research B7, 41 (1958).

    Google Scholar 

  89. G. T. Croft, W. F. Love, and F. C. Nix, Phys. Rev. 95, 1403 (1954).

    Google Scholar 

  90. P. B. Alers, Phys. Rev. 107, 959 (1957).

    Google Scholar 

  91. J. R. Sybert, H. J. Mackey, and R. E. Miller, Phys. Letters 24A, 655 (1967).

    Google Scholar 

  92. C. Miziumski and A. W. Lawson, Phys. Rev. 180, 749 (1969).

    Google Scholar 

  93. J. Yahia and J. A. Marcus, Phys. Rev. 113, 137 (1959).

    Google Scholar 

  94. M. C. Steel, Phys. Rev. 99, 1751 (1955).

    Google Scholar 

  95. J. Ketterson and Y. Eckstein, Phys. Rev. 132, 1,885 (1963).

    Google Scholar 

  96. D. K. C. MacDonald, Nature 163, 637 (1949).

    Google Scholar 

  97. J. Babiskin and P. G. Siebenmann, Phys. Rev. 107, 1249 (1957).

    Google Scholar 

  98. W. Cirkler, Z. Physik 147, 481 (1957).

    Google Scholar 

  99. H. J. Mackey, J. R. Sybert, and J. T. Fielder, Phys. Rev. 157, 578 (1967).

    Google Scholar 

  100. E. R. Andrew, Proc. Phys. Soc. (London) 62, 77 (1949).

    Google Scholar 

  101. A. F. Mayadas, J. Appl. Phys. 39, 4241 (1968).

    Google Scholar 

  102. T. Amundsen, Phil. Mag. 17, 107 (1968).

    Google Scholar 

  103. T. Amundsen and T. Olsen, Phil. Mag. 11, 561 (1965).

    Google Scholar 

  104. H. J. Mackey, J. R. Sybert, and R. D. Hight, Phys. Rev. Bl, 2385 (1970).

    Google Scholar 

  105. K. Forsvoll and I. Holwech, Phil. Mag. 10, 921 (1964); 9, 435 (1964).

    Google Scholar 

  106. R. Risnes and V. Sollien, Phil. Mag. 20, 895 (1969).

    Google Scholar 

  107. A. von Bassewitz and E. N. Mitchell, Phys. Rev. 182, 712 (1969).

    Google Scholar 

  108. I. Holwech and J. Jeppesen, Phil. Mag. 15, 217 (1967).

    Google Scholar 

  109. H. J. Mackey, J. R. Sybert, and H. C. Mollenkopf, Phys. Rev. 161, 611 (1967).

    Google Scholar 

  110. M. Yaqub and J. F. Cochran, Phys. Rev. 137, A1182 (1965).

    Google Scholar 

  111. J. A. Munarin, J. A. Marcus, and P. E. Bloomfield, Phys. Rev. 172, 718 (1968).

    Google Scholar 

  112. J. L. Olsen, Helv. Phys. Acta 31, 713 (1958).

    Google Scholar 

  113. P. Wyder, Phys. Kond. Mater. 3, 263 (1965).

    Google Scholar 

  114. B. N. Aleksandrov, Zh. Eksp. Teor. Fiz. 43, 399 (1962) [Soviet Phys.-JETP (Engl. trans.) 16, 286 (1963)].

    Google Scholar 

  115. J.-Y. Le Traon and H.-A. Combet, Compt. Rend. 268B, 502 (1969).

    Google Scholar 

  116. 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. D. D. Thornburg and C. M. Wayman, Phil. Mag. 20, 1153 (1969).

    Google Scholar 

  118. N. C. McGill, Physica 40, 91 (1968).

    Google Scholar 

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Hurd, C.M. (1972). The Dynamics of Electrons in Metals: Low-Temperature Effects. In: The Hall Effect in Metals and Alloys. The International Cryogenics Monograph Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0465-5_2

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