Dirac Composite Fermions and Emergent Reflection Symmetry about Even Denominator Filling Fractions

TL;DR

This paper introduces relativistic Dirac composite fermion theories for quantum Hall states at even denominator fillings, explaining observed reflection symmetry and connecting to Jain sequence states.

Contribution

It proposes a new class of relativistic composite fermion theories involving Dirac fermions and flux attachment, elucidating reflection symmetry in quantum Hall states.

Findings

Reproduces Jain sequence states near $ u=1/2n$

Shows reflection symmetry relates these states at mean field level

Argues for Dirac fermions tuning to criticality in the lowest Landau level

Abstract

Motivated by the appearance of a `reflection symmetry' in transport experiments and the absence of statistical periodicity in relativistic quantum field theories, we propose a series of relativistic composite fermion theories for the compressible states appearing at filling fractions $\nu=1/2n$ in quantum Hall systems. These theories consist of electrically neutral Dirac fermions attached to $2n$ flux quanta via an emergent Chern-Simons gauge field. While not possessing an explicit particle-hole symmetry, these theories reproduce the known Jain sequence states proximate to $\nu=1/2n$, and we show that such states can be related by the observed reflection symmetry, at least at mean field level. We further argue that the lowest Landau level limit requires that the Dirac fermions be tuned to criticality, whether or not this symmetry extends to the compressible states themselves.