A Dirac Fermion Hierarchy of Composite Fermi Liquids

Composite Fermi liquids (CFLs) are compressible states that can occur for 2D interacting fermions confined in the lowest Landau level at certain Landau level fillings. They have been understood as Fermi seas formed by composite fermions which are bound states of electromagnetic fluxes and physical fermions due to the celebrated work by Halperin, Lee and Read [Phys. Rev. B 47, 7312 (1993)]. At half filling, an explicitly particle hole symmetric theory based on Dirac fermions [Phys. Rev. X 5, 031027 (2015)] was proposed by Son as an alternative low energy description. In this work, we propose an effective theory, which generalizes Son’s Dirac fermion theory, by internal gauge flux attachment, from half filling to all fillings that CFLs for fermions can occur. We also numerically investigated the Berry curvature of CFL model wave functions at fillings not being one half, and observed that it is uniformly distributed on the Fermi sea except at the center where an additional π phase was found. The numerical results support the idea of internal gauge flux attachment.