Transport Theory in Strong Magnetic Fields

H. F. Budd

doi:10.1103/PhysRev.175.241

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Transport Theory in Strong Magnetic Fields

H. F. Budd^*

Groupe de Physique des Solides de l'Ecole Normale Supérieure 9, quai Saint-Bernard, Paris, France

^*Associated with Centre National de la Recherche Scientifique.

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Phys. Rev. 175, 241 – Published 5 November, 1968

DOI: https://doi.org/10.1103/PhysRev.175.241

Abstract

A unified treatment of transport phenomena in crossed electric and magnetic fields is presented. This theory is limited to strong magnetic fields, $ω_{c} \bar{τ} ≫ 1$ , where $ω_{c}$ and $\frac{1}{\bar{τ}}$ are the cyclotron and mean collision frequencies, respectively. It is not, however, limited to linear response in the electric field nor is a relaxation time approximation introduced. The semiclassical and quantum theories are developed along parallel lines.

An irreversible transport equation is derived for the asymptotic state of the system, $ω_{c} τ \to \infty$ , and it is shown that the asymptotic electron distribution is independent of the absolute values of the coupling constants to the scattering system, but dependent on the form of the scattering interaction. A perturbation theory in $\frac{1}{ω_{c} \bar{τ}}$ is performed and a generalized orbit-jump formula for the dissipative current is derived. Explicit expressions are derived for the ohmic case and are applied as an example to polar optical-phonon scattering.

References (25)

H. F. Budd, Phys. Rev. Letters 20, 1099 (1968) ibid.21, 425 (1968)
W. Shockley, Phys. Rev. 79, 191 (1950) R. G. Chambers, Proc. Phys. Soc. (London) A65, 458 (1952) H. F. Budd, J. Phys. Soc. (Japan) 18, 142 (1963)
A. C. Beer, Solid State Physics, Suppl. 4 (Academic Press Inc., New York, 1963)
E. M. Conwell, Solid State Physics, Suppl. 9 (Academic Press, Inc., New York, 1967)
Ryogo Kubo, Satoru J. Mayake, and Natsuki Hashitsume, Solid State Physics (Academic Press, Inc., New York, 1965), Vol. 17, p. 269
S. Titeica, Ann. Physik 22, 129 (1935)
H. Budd, Phys. Rev. 158, 795 (1967)
Lifschitz, M. Ia. Azbel, and M. I. Kaganov, Zh. Eksperim. i Teor. Fiz. 31, 63 (1956) [English transl.: Soviet Phys.-JETP 4, 41 (1957)]
R. F. Kazarinov and V. G. Skobov, Zh. Eksperim, i Teor. Fiz. 42, 1047 (1962) [English transl.: Soviet Phys.-JETP 15, 726 (1962)]
H. F. Budd, Phys. Rev. 131, 1520 (1963) ibid.140, A2170 (1965)
H. Ehrenreich, J. Phys. Chem. Solids 2, 131 (1957)
[4], p. 156
A. Erdelyi, W. Magnus, F. Oberhattinger, and F. G. Triconi, The Bateman Manuscript Project - Table of Integral Transforms (McGraw-Hill Book Co., Inc., New York, 1954), Vol. 1
V. Gurevich and Yu Firsov, Zh. Eksperim. i Teor. Fiz. 40, 198 (1961) [English transl.: Soviet Phys. -JETP 13, 137 (1961)]
Petros Argyres, Phys. Rev. 117, 315 (1960)
E. N. Adams and T. D. Holstein, J. Phys. Chem. Solids 10, 254 (1959)
A. H. Kahn and H. P. R. Frederikse, Solid State Physics (Academic Press, Inc., New York, 1959), Vol. 9, p. 257
D. Calecki, J. Phys. Chem. Solids 28, 1409 (1967)
J. Yamashita, Progr. Theoret. Phys. (Kyoto) 33, 343 (1965)
L. Van Hove, Physica 21, 517 (1955) ibid.23, 441 (1957)
W. Kohn and J. M. Luttinger, Phys. Rev. 108, 590 (1957)
Robert Zwanzig, in Lectures in Theoretical Physics (Interscience Publishers, Inc., New York, 1961), Vol. 3, p. 106
Elliot Montroll, in [22], p. 221
P. Argyres, in Lectures in Theoretical Physics (Interscience Publishers, Inc., New York 1961), Vol. 8a, p. 183
P. Argyres, J. Phys. Chem. Solids 19, 66 (1961)

[c1] H. F. Budd, Phys. Rev. Letters 20, 1099 (1968) ibid.21, 425 (1968)

[c2] W. Shockley, Phys. Rev. 79, 191 (1950) R. G. Chambers, Proc. Phys. Soc. (London) A65, 458 (1952) H. F. Budd, J. Phys. Soc. (Japan) 18, 142 (1963)

[c3] A. C. Beer, Solid State Physics, Suppl. 4 (Academic Press Inc., New York, 1963)

[c4] E. M. Conwell, Solid State Physics, Suppl. 9 (Academic Press, Inc., New York, 1967)

[c5] Ryogo Kubo, Satoru J. Mayake, and Natsuki Hashitsume, Solid State Physics (Academic Press, Inc., New York, 1965), Vol. 17, p. 269

[c6] S. Titeica, Ann. Physik 22, 129 (1935)

[c7] H. Budd, Phys. Rev. 158, 795 (1967)

[c8] Lifschitz, M. Ia. Azbel, and M. I. Kaganov, Zh. Eksperim. i Teor. Fiz. 31, 63 (1956) [English transl.: Soviet Phys.-JETP 4, 41 (1957)]

[c9] R. F. Kazarinov and V. G. Skobov, Zh. Eksperim, i Teor. Fiz. 42, 1047 (1962) [English transl.: Soviet Phys.-JETP 15, 726 (1962)]

[c10] H. F. Budd, Phys. Rev. 131, 1520 (1963) ibid.140, A2170 (1965)

[c11] H. Ehrenreich, J. Phys. Chem. Solids 2, 131 (1957)

[c12] [4], p. 156

[c13] A. Erdelyi, W. Magnus, F. Oberhattinger, and F. G. Triconi, The Bateman Manuscript Project - Table of Integral Transforms (McGraw-Hill Book Co., Inc., New York, 1954), Vol. 1

[c14] V. Gurevich and Yu Firsov, Zh. Eksperim. i Teor. Fiz. 40, 198 (1961) [English transl.: Soviet Phys. -JETP 13, 137 (1961)]

[c15] Petros Argyres, Phys. Rev. 117, 315 (1960)

[c16] E. N. Adams and T. D. Holstein, J. Phys. Chem. Solids 10, 254 (1959)

[c17] A. H. Kahn and H. P. R. Frederikse, Solid State Physics (Academic Press, Inc., New York, 1959), Vol. 9, p. 257

[c18] D. Calecki, J. Phys. Chem. Solids 28, 1409 (1967)

[c19] J. Yamashita, Progr. Theoret. Phys. (Kyoto) 33, 343 (1965)

[c20] L. Van Hove, Physica 21, 517 (1955) ibid.23, 441 (1957)

[c21] W. Kohn and J. M. Luttinger, Phys. Rev. 108, 590 (1957)

[c22] Robert Zwanzig, in Lectures in Theoretical Physics (Interscience Publishers, Inc., New York, 1961), Vol. 3, p. 106

[c23] Elliot Montroll, in [22], p. 221

[c24] P. Argyres, in Lectures in Theoretical Physics (Interscience Publishers, Inc., New York 1961), Vol. 8a, p. 183

[c25] P. Argyres, J. Phys. Chem. Solids 19, 66 (1961)

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Transport Theory in Strong Magnetic Fields

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