Two-loop study of the metal-insulator transition in the presence of weak magnetic scattering

C. S. Ting

doi:10.1103/PhysRevB.31.3765

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Two-loop study of the metal-insulator transition in the presence of weak magnetic scattering

C. S. Ting

Department of Physics, University of Houston, Houston, Texas 77004 and Institute for Theoretical Physics, University of California, Santa Barbara, California 93106

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Phys. Rev. B 31, 3765 – Published 15 March, 1985

DOI: https://doi.org/10.1103/PhysRevB.31.3765

Abstract

The scaling function β(g) for disordered noninteracting electrons, in which weak magnetic scatterings are assumed to exist, is studied in terms of two-loop conductivity diagrams. Our β(g), unlike the result obtained recently by Kawabata, does not depend on the ultraviolet cutoffs. Instead, it depends on (τ/ $τ_{m}$ $)^{1 / 2}$ where τ and $τ_{m}$ are, respectively, the elastic scattering time and the magnetic scattering time. This result implies that in β(g) there may be more than one scaling parameter present. In the limit of weak magnetic scattering, τ/ $τ_{m}$ ≪1, the conductivity can be shown to behave like σ= $σ_{0}$ ‖1- $n_{c}$ /n $‖^{s}$ with s≃0.5 near the metal-insulator transition and n the donor concentration. This result seems to be in agreement with recent experimental results on phosphorus-doped silicon.

References (17)

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[c1] T. F. Rosenbaum, K. Andres, G. A. Thomas and N. R. Bhatt, Phys. Rev. Lett. 45, 1723 (1980).

[c2] G. A. Thomas, Y. Ootuka, S. Katsumoto, S. Kobayashi and W. Sasaki, Phys. Rev. B 25, 1288 (1982).

[c3] M. A. Paalanen, T. F. Rosenbaum, G. A. Thomas and R. N. Bhatt, Phys. Rev. Lett. 48, 1284 (1982).

[c4] N. Nishida, M. Yamaguchi, T. Furubayashi, K. Morigaki, H. Ishimoto and K. Ono, Solid State Commun. 44, 305 (1982).

[c5] G. Hertel, D. J. Bishop, E. G. Spencer, J. M. Rowell and R. C. Dynes, Phys. Rev. Lett. 50, 743 (1983).

[c6] E. Abrahams, P. W. Anderson, D. C. Locciardello and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).

[c7] D. Vollhardt and P. Wölfle, Phys. Rev. Lett. 45, 842 (1980).

[c8] S. Hikami, Phys. Rev. B 24, 2671 (1981).

[c9] G. S. Grest and P. A. Lee, Phys. Rev. Lett. 50, 693 (1963).

[c10] B. L. Altshuler and A. G. Aronov, Solid State Commun. 46, 429 (1983).

[c11] S. Ikehata, T. Ema, S Kobayashi and W. Sasaki, J. Phys. Soc. Jpn. 50, 3655 (1981).

[c12] A. Kawataba, J. Phys. Soc. Jpn. 53, 318 (1984).

[c13] A. Abrikosov, L. Gor'kov, and I. Dzyaloshinkskii, Quantum Field Theoretical Methods in Statistical Physics (Pergamon, New York, 1965).

[c14] W. Cai and C. S. Ting, J. Phys. C (to be published).

[c15] A. Kawabata, J. Phys. Soc. Jpn. 49, 628 (1980).

[c16] K. B. Efetov, Zh. Eksp. Teor. Fiz. 82, 872 (1982) [Sov. Phys.—JETP 55, 514 (1983)].

[c17] C. S. Ting, Phys. Rev. 26, 678 (1982).

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Two-loop study of the metal-insulator transition in the presence of weak magnetic scattering

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