Fractional quantum Hall systems near nematicity: bimetric theory, composite fermions, and Dirac brackets

Abstract

We perform a detailed comparison of the Dirac composite fermion and the recently proposed bimetric theory for a quantum Hall Jain states near half filling. By tuning the composite Fermi liquid to the vicinity of a nematic phase transition, we find that the two theories are equivalent to each other. We verify that the single mode approximation for the response functions and the static structure factor becomes reliable near the phase transition. We show that the dispersion relation of the nematic mode near the phase transition can be obtained from the Dirac brackets between the components of the nematic order parameter. The dispersion is quadratic at low momenta and has a magnetoroton minimum at a finite momentum, which is not related to any nearby inhomogeneous phase.

13 pages, 1 figure

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• Density-curvature response and gravitational anomaly
• Theory of Nematic Fractional Quantum Hall State
• Particle-hole symmetry and electromagnetic response of a half-filled Landau level
• Exact Electromagnetic Response of Landau Level Electrons
• Shape of the magnetoroton at $\nu =1/3$ and $\nu =7/3$ in real samples
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• Electrons and composite Dirac fermions in the lowest Landau level

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