Thermally Activated Deviations from Quantum Hall Plateaus

Abstract

The Hall conductivity ${\sigma }_{\mathrm{xy}}$ of a two-dimensional electron system is quantized in units of $e^2/h$ when the Fermi level is located in the mobility gap between two Landau levels. We consider the deviation of ${\sigma }_{\mathrm{xy}}$ from a quantized value caused by the thermal activation of electrons to the extended states for the case of a long range random potential. This deviation is of the form ${\sigma }_{\mathrm{xy}}^{\ast }\exp (-\Delta /T)$. The prefactor ${\sigma }_{\mathrm{xy}}^{\ast }$ is equal to $e^2/h$ at temperatures above a characteristic temperature $T_2$. With the temperature decreasing below $T_2$, ${\sigma }_{\mathrm{xy}}^{\ast }$ decays according to a power law: ${\sigma }_{\mathrm{xy}}^{\ast }=\frac{e^2}{h}(T/T_2{)}^{\gamma }$. Similar results are valid for a fractional Hall plateau near filling factor $p/q$ if $e$ is replaced by the fractional charge $e/q$.

4 pages in PostScript (figures included)

References in corpus (2)

• Explanation for the Resistivity Law in Quantum Hall System
• Universal Prefactor of Activated Conductivity in the Quantum Hall Effect

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• Diagrammatic Approach for the High-Temperature Regime of Quantum Hall Transitions
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