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

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