Emergent reflection symmetry from nonrelativistic composite fermions

A recent experimental study [Pan et al., arXiv:1902.10262] has shown that fractional quantum Hall effect gaps are essentially consistent with particle-hole symmetry in the lowest Landau level. Motivated by this result, we consider a clean two-dimensional electron system from the viewpoint of composite fermion mean-field theory. In this paper, we show that while the experiment is manifestly consistent with a Dirac composite fermion theory proposed recently by Son, it can equally well be explained within the framework of nonrelativistic composite fermions, first put forward by Halperin, Lee, and Read.

Figure 1

(a) A schematic for the response of Dirac composite fermion theory to an applied gate voltage. Energy levels shown with green, red, and blue colors represent negative, positive, and zero energy Landau levels, respectively. The number of filled Landau levels is $p+\frac{1}{2}$ for either sign of the effective magnetic field. Taking into account the contribution of the massive Dirac partner, one gets $p$ filled Landau levels for $b>0$ and $p+1$ Landau levels for $b<0$. This is identical to the response of the HLR theory depicted in (b) as explained in Sec. 3.