Drude, Hall and Maximal Conductivities: A Unified Complex Model


By adopting a complex formulation of Ohm’s law, we arrive at combined equations connecting the conductivities of conductors. The horizontal resistivity is equal to the inverse of Drude’s conductivity δo( ), and the vertical resistivity (ρy) is equal to the Hall’s conductivity ( δH). At high magnetic field, the horizontal conductivity becomes exceedingly small, whereas the vertical conductivity equals to Hall’s conductivity. The Hall’s conductivity is shown to represent the maximal conductivity of conductors. Drude’s and Hall’s conductivities are related by δoHωC , where ωC is the cyclotron frequency, and is the relaxation time. The quantization of Hall’s conductivity is attributed to the fact that the magnetic flux enclosed by the conductor is carried by electrons each with h/e, where h is the Planck’s constant and e is the electron’s charge. The Drude’s conductance is found to be equal to Hall's conductance provided the magnetic flux enclosed by the conductor is a multiple of h/e.

Share and Cite:

A. Arbab, "Drude, Hall and Maximal Conductivities: A Unified Complex Model," Journal of Modern Physics, Vol. 3 No. 9, 2012, pp. 1040-1045. doi: 10.4236/jmp.2012.39137.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] P. Drude, Physikalische Zeitschrift, Vol. 1, 1900, p. 161.
[2] N. W. Ashcroft and N. D. Mermin, Solid State Physics, Prentice Hall, 1976.
[3] E. Hall, “On a New Action of the Magnet on Electric Currents,” American Journal of Mathematics, Vol. 2, No. 3, 1879, pp. 287-292. doi:10.2307/2369245
[4] A. I. Arbab, “The Complex Quantum Harmonic Oscillator Model,” Europhysics Letters, Vol. 98, No. 3, 2012, p. 30008. doi:10.1209/0295-5075/98/30008
[5] K. V. Klitzing, G. Dorda and M. Pepper, “New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance,” Physical Review Letters, Vol. 45, No. 6, 1980, pp. 494-497. doi:10.1103/PhysRevLett.45.494
[6] F. London, “Superfuids,” Wiley, New York, 1950.
[7] L. Onsager, “Magnetic Flux through a Superconducting Ring,” Physical Review Letters, Vol. 7, 1961, p. 50. doi:10.1103/PhysRevLett.7.50
[8] A. I. Arbab, “On the Electric and Magnetic Properties of Conductors,” Advanced Studies in Theoretical Physics, Vol. 5, No. 9-12, 2011, pp. 595-604.
[9] A. I. Arbab, H. M. Widatallah and M. A. H. Khalafalla (Unpublished).
[10] L. D. Landau, “Paramagnetism of Metals,” Z. Phys., Vol. 64, 1930, pp. 629-637.
[11] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science, Vol. 306, No. 5696, 2004, pp. 666-669.

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.