Electromagnetic response of composite Dirac fermions in the half-filled Landau level

TL;DR

This paper computes the electromagnetic response of the Son-Dirac composite fermion theory at half-filled Landau level, showing that including a dipole term ensures consistency and distinguishes it from previous models.

Contribution

It introduces a detailed RPA analysis of the Son-Dirac theory, emphasizing the importance of a dipole correction for physical accuracy and consistency.

Findings

Spurious interband transitions are suppressed with the dipole correction.

The theory remains valid at all frequencies to leading order in momentum.

The dipole term alters the Fermi-liquid response at low frequencies and momenta.

Abstract

An effective field theory of composite Dirac fermions was proposed by Son [Phys. Rev. X 5, 031027 (2015)] as a theory of the half-filled Landau level with explicit particle-hole symmetry. We compute the electromagnetic response of this Son-Dirac theory on the level of the random phase approximation (RPA), where we pay particular attention to the effect of an additional composite-fermion dipole term that is needed to restore Galilean invariance. We find that once this dipole correction is taken into account, spurious interband transitions and collective modes that are present in the response of the unmodified theory either cancel or are strongly suppressed. We demonstrate that this gives rise to a consistent theory of the half-filled Landau level valid at all frequencies, at least to leading order in the momentum. In addition, the dipole contribution modifies the Fermi-liquid response at small frequency and momentum, which is a prediction of the Son-Dirac theory within the RPA that distinguishes it from a separate description of the half-filled Landau level by Halperin, Lee, and Read within the RPA.