Frequency dependent conductivity in the integer quantum Hall effect

Physics – Condensed Matter – Disordered Systems and Neural Networks

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4 pages LaTeX (annalen.cls), 3 ps-figures included. Proceedings of Localisation 1999, Hamburg, Germany; to appear in Annalen d

Scientific paper

Frequency dependent electronic transport is investigated for a two-dimensional disordered system in the presence of a strong perpendicular static magnetic field. The ac-conductivity is calculated numerically from Kubo's linear response theory using a recursive Green's function technique. In the tail of the lowest Landau band, we find a linear frequency dependence for the imaginary part of $\sigma_{xx}(\omega)$ which agrees well with earlier analytical calculations. On the other hand, the frequency dependence of the real part can not be expressed by a simple power law. The broadening of the $\sigma_{xx}$-peak with frequency in the lowest Landau band is found to exhibit a scaling relation from which the critical exponent can be extracted.

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