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

TL;DR

This paper compares Dirac composite fermion and bimetric theories for quantum Hall states near half filling, showing their equivalence near a nematic phase transition and analyzing the nematic mode dispersion.

Contribution

It demonstrates the equivalence of two theoretical frameworks near the nematic transition and derives the nematic mode dispersion from Dirac brackets.

Findings

The two theories are equivalent near the nematic phase transition.

The single mode approximation is reliable near the transition.

The nematic mode dispersion is quadratic at low momenta with a magnetoroton minimum.

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.