Dynamical Correlations in a Half-Filled Landau Level

TL;DR

This paper develops a self-consistent field theory for Chern-Simons fermions at half-filling, incorporating correlations beyond RPA to analyze dynamical responses in quantum Hall systems, revealing a density response vanishing quadratically and a linearly wave-vector-dependent conductivity.

Contribution

It introduces a self-consistent approach that includes correlations beyond RPA for studying dynamical responses in the half-filled Landau level.

Findings

Zero-frequency density response vanishes as wave vector squared.

Longitudinal conductivity shows linear wave vector dependence.

Calculated conductivities are higher than experimental values.

Abstract

We formulate a self-consistent field theory for the Chern-Simons fermions to study the dynamical response function of the quantum Hall system at $\nu=1/2$. Our scheme includes the effect of correlations beyond the random-phase approximation (RPA) employed to this date for this system. The resulting zero-frequency density response function vanishes as the square of the wave vector in the long-wavelength limit. The longitudinal conductivity calculated in this scheme shows linear dependence on the wave vector, like the experimentals results and the RPA, but the absolute values are higher than the experimental results.