Nonlocal Effects in Low-Field Helicon Propagation in PbTe

J. N. Walpole; A. L. McWhorter

doi:10.1103/PhysRev.158.708

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Nonlocal Effects in Low-Field Helicon Propagation in PbTe

J. N. Walpole^*,† and A. L. McWhorter^†

Lincoln Laboratory and Electrical Engineering Department, Massachusetts Institute of Technology, Cambridge, Massachusetts

^*National Science Foundation Graduate Fellow during a portion of this work.
^†Operated with support from the U. S. Air Force.

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Phys. Rev. 158, 708 – Published 15 June, 1967

DOI: https://doi.org/10.1103/PhysRev.158.708

Abstract

Helicon propagation has been studied in the region of low magnetic fields, where band structure and nonlocal Landau damping effects produce sizable corrections to the high-field dispersion relation. Good agreement with both the phase and amplitude of 9-GHz helicons in $n - P b T e$ at 4.2°K is obtained by a semiclassical treatment of a degenerate, many-valley, ellipsoidal model. The calculation is carried out by expanding the conductivity tensor in powers of $\frac{1}{B_{0}}$ , treating $\frac{ω}{ω_{c}}$ , $\frac{1}{ω_{c} τ}$ , and $\frac{q v_{F}}{ω_{c}}$ as small quantities, where $B_{0}$ is the static magnetic field, $ω_{c}$ is the cyclotron frequency, $τ$ is the collision time, $q$ is the wave number, and $v_{F}$ is the Fermi velocity. Because of the anisotropic energy surfaces in PbTe, Landau damping occurs for propagation along the field as well as at an angle. The corrections to the phase are quite sensitive to the transverse effective mass; comparison with experiment yields a value of $0.020 m_{0}$ for the band-edge transverse mass in PbTe. It is also found that both relaxation to the local equilibrium and anisotropic scattering are important effects, although only the former is included in the theoretical calculations.

References (33)

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W. Cochran, Phys. Letters 13, 193 (1964)
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([9])
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[c1] S. J. Buchsbaum, in Plasma Effects in Solids (Dunod Cie., Paris, 1965), p. 3 R. BowersPlasma Effects in Solidsp. 19

[c2] W. Cochran, Phys. Letters 13, 193 (1964)

[c3] E. A. Stern, Phys. Rev. Letters 10, 91 (1963)

[c4] M. T. Taylor, Phys. Rev. 137, A1145 (1965)

[c5] A. W. Overhauser and S. Rodriguez, Phys. Rev. 141, 431 (1966)

[c6] J. C. McGroddy, J. L. Stanford, and E. A. Stern, Phys. Rev. 141, 437 (1966)

[c7] J. L. Stanford and E. A. Stern, Phys. Rev. 144, 534 (1966)

[c8] ([9])

[c9] A. L. McWhorter and J. N. Walpole, Phys. Rev. 158, 719 (1967)

[c10] E. A. Kaner and V. G. Skobov, Zh. Eksperim. i Teor. Fiz. 45, 610 (1963) [English transl.: Soviet Phys.—JETP 18, 419 (1964)]

[c11] C. C. Grimes, Bull. Am. Phys. Soc. 11, 570 (1966)

[c12] J. R. Houck and R. Bowers, Bull. Am. Phys. Soc. 11, 256 (1966)

[c13] A. L. McWhorter and W. G. May, IBM J. Res. Develop. 8, 285 (1964) W. G. May, Ph.D. thesis, Massachusetts Institute of Technology, 1964 (unpublished)

[c14] G. A. Williams and G. E. Smith, IBM J. Res. Develop. 8, 276 (1964)

[c15] C. C. Grimes, Bull. Am. Phys. Soc. 9, 239 (1964)

[c16] J. K. Furdyna, Phys. Rev. Letters 14, 635 (1965) Rev. Sci. Instr. 37, 462 (1966)

[c17] S. I. Novikova and N. K. Abrikosov, Fiz. Tverd. Tela 5, 1913 (1963) [English transl.: Soviet Phys.—Solid State 5, 1397 (1964)]

[c18] M. K. Norr, U. S. Naval Ordnance Laboratory Report No. T. R. 63-156, 1963 (unpublished)

[c19] R. F. Brebrick and E. Gubner, J. Chem. Phys. 36, 1283 (1962)

[c20] M. H. Cohen, M. J. Harrison, and W. A. Harrison, Phys. Rev. 117, 937 (1960)

[c21] S. Rodriguez, Phys. Rev. 112, 80 (1958)

[c22] A. L. McWhorter and J. N. Walpole (to be published)

[c23] J. J. Quinn, Phys. Rev. 135, A181 (1964)

[c24] C. R. Legendy, Phys. Rev. 135, 1713 (1964)

[c25] Omitted endnote

[c26] Omitted endnote

[c27] J. N. Walpole, Ph.D. thesis, Massachusetts Institute of Technology, 1966 (unpublished)

[c28] S. G. Eckstein, Phys. Rev. 131, 1087 (1963)

[c29] K. F. Cuff, M. R. Ellett, C. D. Kuglin, and L. R. Williams, in Proceedings of the Seventh International Conference on the Physics of Semiconductors, Paris, 1964 (Dunod Cie., Paris, 1964), p. 677

[c30] J. O. Dimmock and G. B. Wright, in Proceedings of the Seventh International Conference on the Physics of Semiconductors, Paris, 1964 (Dunod Cie., Paris, 1964), p. 77

[c31] B. Lax and J. G. Mavroides, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic Press Inc., New York, 1960), Vol. 11, p. 261

[c32] R. Nii, J. Phys. Soc. Japan 19, 58 (1964)

[c33] R. S. Allgaier, Phys. Rev. 112, 828 (1958)

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Nonlocal Effects in Low-Field Helicon Propagation in PbTe

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