Electron-Electron Interactions and the Hall-Insulator

TL;DR

This paper demonstrates that non-interacting electrons cannot exhibit Hall-insulator behavior, while strongly interacting electrons can, especially when mobile electron density is very low, highlighting the importance of interactions in quantum Hall phenomena.

Contribution

The paper explicitly shows that non-interacting electrons cannot behave as Hall-insulators and constructs a model illustrating how strong interactions lead to Hall-insulator behavior.

Findings

Non-interacting electrons cannot produce Hall-insulator behavior.

Strong interactions enable Hall-insulator characteristics at low mobile electron density.

Zero-temperature frequency-dependent conductance does not always reflect DC conductance in non-interacting systems.

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 $\rho_{xx}\rightarrow\infty$ 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.