‘‘Inductive’’ response from nonlinear mixing in sliding charge-density waves

S. N. Coppersmith; P. B. Littlewood

doi:10.1103/PhysRevB.31.4049

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‘‘Inductive’’ response from nonlinear mixing in sliding charge-density waves

S. N. Coppersmith

P. B. Littlewood

Brookhaven National Laboratories, Upton, New York 11973

AT&T Bell Laboratories, Murray Hill, New Jersey 07974

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Phys. Rev. B 31, 4049(R) – Published 15 March, 1985

DOI: https://doi.org/10.1103/PhysRevB.31.4049

Abstract

It is a paradox that the measured frequency-dependent linear conductivity of sliding charge-density-wave (CDW) materials is well described by a purely dissipative model of CDW motion, but several experiments involving the nonlinear response have demonstrated inductive effects characteristic of inertial systems. We show here that these results can be reconciled within a strongly dissipative model of CDW dynamics, provided the internal elastic degrees of freedom are taken into account. As a consequence, we predict a ‘‘ringing’’ oscillation of the CDW when the dc driving field is suddenly changed above the threshold.

References (26)

For reviews, see G. Grüner, Physica D 8, 1 (1983); and N. P. Ong, Can. J. Phys. 60, 757 (1982).
H. Fukuyama and P. A. Lee, Phys. Rev. B 17, 535 (1978).
P. A. Lee and T. M. Rice, Phys. Rev. B 19, 3970 (1979).
L. Sneddon, M. C. Cross and D. S. Fisher, Phys. Rev. Lett. 49, 292 (1982).
D. S. Fisher, Phys. Rev. Lett. 50, 1486 (1983); and (unpublished).
L. Sneddon, Phys. Rev. B 29, 719, 725 (1984).
R. A. Klemm and J. R. Schrieffer, Phys. Rev. Lett. 51, 47 (1983).
G. Grüner, A. Zawadowski and P. M. Chaikin, Phys. Rev. Lett. 46, 511 (1981).
G. Grüner, A. Zettl and W. G. Clark, Phys. Rev. B 26, 5773 (1982).
G. X. Tessema and N. P. Ong, Phys. Rev. B 27, 1417 (1983); ibid. 31, 1055 (1985).
S. E. Brown, G. Mozurkewich and G. Grüner, Phys. Rev. Lett. 52, 2277 (1984).
M. Sherwin and A. Zettl (unpublished); P. Bak, T. Bohr, M. H. Jensen, and P. V. Christiansen (unpublished).
M. Azbel and P. Bak, Phys. Rev. B 30, 3722 (1984).
R. Fleming, L. F. Schneemeyer and R. J. Cava, Phys. Rev. B 31, 1181 (1985).
An anisotropic medium can be accounted for by using scaled variables (see Refs. 2 and 7).
A. Schmid and W. Hauger, J. Low Temp. Phys. 11, 667 (1973).
These results lead to scaling between the high-field dc nonlinear conductivty and the high-frequency linear conductivity in the form σ ( ω / $ω_{c}$ ) α j (E)/E, as established experimentally.
S. N. Coppersmith (unpublished); L. Sneddon, Phys. Rev. Lett. 52, 65 (1984).
See, for example, S. N. Coppersmith and D. S. Fisher, Phys. Rev. B 28, 2566 (1983).
A. Zettl and G. Grüner, Solid State Commun. 46, 501 (1983); Phys. Rev. B 29, 755 (1984).
R. M. Fleming and C. C. Grimes, Phys. Rev. Lett. 42, 1423 (1979).
G. Mozurkewich and G. Grüner, Phys. Rev. Lett. 51, 2206 (1983).
N. P. Ong, G. Verma and K. Maki, Phys. Rev. Lett. 52, 663 (1984); L. P. Gor'kov, Pis'ma Zh. Eksp. Teor. Fiz. 38, 76 (1983) [JETP Lett. 38, 87 (1983)].
S. N. Coppersmith and P. B. Littlewood (unpublished).
We are grateful to Daniel Fisher for pointing this out to us.
X-ray diffraction measurements on ${NbSe}_{3}$ _ indicate that the second harmonic amplitude is less than 5% of the fundamental [R. M. Fleming (private communication)].

[c1] For reviews, see G. Grüner, Physica D 8, 1 (1983); and N. P. Ong, Can. J. Phys. 60, 757 (1982).

[c2] H. Fukuyama and P. A. Lee, Phys. Rev. B 17, 535 (1978).

[c3] P. A. Lee and T. M. Rice, Phys. Rev. B 19, 3970 (1979).

[c4] L. Sneddon, M. C. Cross and D. S. Fisher, Phys. Rev. Lett. 49, 292 (1982).

[c5] D. S. Fisher, Phys. Rev. Lett. 50, 1486 (1983); and (unpublished).

[c6] L. Sneddon, Phys. Rev. B 29, 719, 725 (1984).

[c7] R. A. Klemm and J. R. Schrieffer, Phys. Rev. Lett. 51, 47 (1983).

[c8] G. Grüner, A. Zawadowski and P. M. Chaikin, Phys. Rev. Lett. 46, 511 (1981).

[c9] G. Grüner, A. Zettl and W. G. Clark, Phys. Rev. B 26, 5773 (1982).

[c10] G. X. Tessema and N. P. Ong, Phys. Rev. B 27, 1417 (1983); ibid. 31, 1055 (1985).

[c11] S. E. Brown, G. Mozurkewich and G. Grüner, Phys. Rev. Lett. 52, 2277 (1984).

[c12] M. Sherwin and A. Zettl (unpublished); P. Bak, T. Bohr, M. H. Jensen, and P. V. Christiansen (unpublished).

[c13] M. Azbel and P. Bak, Phys. Rev. B 30, 3722 (1984).

[c14] R. Fleming, L. F. Schneemeyer and R. J. Cava, Phys. Rev. B 31, 1181 (1985).

[c15] An anisotropic medium can be accounted for by using scaled variables (see Refs. 2 and 7).

[c16] A. Schmid and W. Hauger, J. Low Temp. Phys. 11, 667 (1973).

[c17] These results lead to scaling between the high-field dc nonlinear conductivty and the high-frequency linear conductivity in the form σ ( ω / $ω_{c}$ ) α j (E)/E, as established experimentally.

[c18] S. N. Coppersmith (unpublished); L. Sneddon, Phys. Rev. Lett. 52, 65 (1984).

[c19] See, for example, S. N. Coppersmith and D. S. Fisher, Phys. Rev. B 28, 2566 (1983).

[c20] A. Zettl and G. Grüner, Solid State Commun. 46, 501 (1983); Phys. Rev. B 29, 755 (1984).

[c21] R. M. Fleming and C. C. Grimes, Phys. Rev. Lett. 42, 1423 (1979).

[c22] G. Mozurkewich and G. Grüner, Phys. Rev. Lett. 51, 2206 (1983).

[c23] N. P. Ong, G. Verma and K. Maki, Phys. Rev. Lett. 52, 663 (1984); L. P. Gor'kov, Pis'ma Zh. Eksp. Teor. Fiz. 38, 76 (1983) [JETP Lett. 38, 87 (1983)].

[c24] S. N. Coppersmith and P. B. Littlewood (unpublished).

[c25] We are grateful to Daniel Fisher for pointing this out to us.

[c26] X-ray diffraction measurements on ${NbSe}_{3}$ _ indicate that the second harmonic amplitude is less than 5% of the fundamental [R. M. Fleming (private communication)].

Physical Review B

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‘‘Inductive’’ response from nonlinear mixing in sliding charge-density waves

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