Interplay of Short-Range Interactions and Quantum Interference Near the Integer Quantum Hall Transition

Abstract

Short-range electron-electron interactions are incorporated into the network model of the integer quantum Hall effect. In the presence of interactions, the electrons, propagating along one link, experience exchange scattering off the Friedel oscillations of the density matrix of electrons on the neighboring links. As a result, the energy dependence of the transmission, ${\cal T}(\epsilon)$, of the node, connecting the two links, develops an anomaly at the Fermi level, $\epsilon=\epsilon_F$. We show that this interaction-induced anomaly in ${\cal T}(\epsilon)$ translates into the anomalous behavior of the Hall conductivity, $\sigma_{xy}(\nu)$, where $\nu$ is the filling factor (we assume that the electrons are {\em spinless}). At low temperatures, $T \to 0$, the evolution of the quantized $\sigma_{xy}$ with decreasing $\nu$ proceeds as $1\to 2 \to 0$, in apparent violation of the semicircle relation. The anomaly in ${\cal T}(\epsilon)$ also affects the temperature dependence of the peak in the diagonal conductivity, $\sigma_{xx}(\nu, T)$. In particular, unlike the case of noninteracting electrons,the maximum value of $\sigma_{xx}$ stays at $\sigma_{xx} = 0.5$ within a wide temperature interval.