Electron-Electron Interactions and the Hall-Insulator

Abstract

Using the Kubo formula, we show explicitly that a non-interacting electron system can not behave like a Hall-insulator, {\it ie.,} a DC resistivity matrix ${\rho }_{xx}\to \infty$ and ${\rho }_{xy}=$finite in the zero temperature limit, as has been observed recently in experiment. For a strongly interacting electron system in a magnetic field, we illustrate, by constructing a specific form of correlations between mobile and localized electrons, that the Hall resistivity can approximately equal to its classical value. A Hall-insulator is realized in this model when the density of mobile electrons becomes vanishingly small. It is shown that in non-interacting electron systems, the zero-temperature frequency-dependent conductacnce generally does not give the DC conductance.

11 pages, RevTeX3.0

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