Particle-Hole Symmetry and the Composite Fermi Liquid

Abstract

The half-filled Landau level is widely believed to be described by the Halperin-Lee-Read theory of the composite Fermi liquid (CFL). In this paper, we develop a theory for the particle-hole conjugate of the CFL, the Anti-CFL, which we argue to be a distinct phase of matter as compared with the CFL. The Anti-CFL provides a possible explanation of a recent experiment [Kamburov et. al., Phys. Rev. Lett. 113, 196801 (2014)] demonstrating that the density of composite fermions in GaAs quantum wells corresponds to the electron density when the filling fraction $\nu <1/2$ and to the hole density when $\nu >1/2$. We introduce a local field theory for the CFL and Anti-CFL in the presence of a boundary, which we use to study CFL - Insulator - CFL junctions, and the interface between the Anti-CFL and CFL. We show that the CFL - Anti-CFL interface allows partially fused boundary phases in which "composite electrons" can directly tunnel into "composite holes," providing a non-trivial example of transmutation between topologically distinct quasiparticles. We discuss several observable consequences of the Anti-CFL, including a predicted resistivity jump at a first order transition between uniform CFL and Anti-CFL phases. We also present a theory of a continuous quantum phase transition between the CFL and Anti-CFL. We conclude that particle-hole symmetry requires a modified view of the half-filled Landau level, in the presence of strong electron-electron interactions and weak disorder, as a critical point between the CFL and the Anti-CFL.

29 pages, 8 figures. v2 includes additional discussion of Landau level mixing (Sec. VII D) and paired composite fermion states

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• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Theory of a continuous Mott transition in two dimensions
• Composite Dirac liquids: parent states for symmetric surface topological order
• Continuous transitions between composite Fermi liquid and Landau Fermi liquid: a route to fractionalized Mott insulators

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