The half-filled Landau level: the case for Dirac composite fermions

TL;DR

This paper provides numerical evidence that at half-filling in the fractional quantum Hall effect, composite fermions form a particle-hole symmetric Fermi sea consistent with Dirac particles, challenging previous models.

Contribution

It demonstrates that composite fermions at $ u=1/2$ are particle-hole symmetric and behave as massless Dirac particles, supported by DMRG simulations and suppression of $2k_F$ backscattering.

Findings

Evidence for a Fermi sea of composite fermions at $ u=1/2$

Particle-hole symmetry of the state

Suppression of $2k_F$ backscattering indicating Dirac nature

Abstract

One of the most spectacular experimental findings in the fractional quantum Hall effect is evidence for an emergent Fermi surface when the electron density is nearly half the density of magnetic flux quanta ($\nu = 1/2$). The seminal work of Halperin, Lee, and Read (HLR) first predicted that at $\nu = 1/2$ composite fermions--bound states of an electron and a pair of vortices--experience zero net magnetic field and can form a "composite Fermi liquid" with an emergent Fermi surface. In this paper we use infinite cylinder DMRG to provide compelling numerical evidence for the existence of a Fermi sea of composite fermions for realistic interactions between electrons at $\nu = 1/2$. Moreover, we show that the state is particle-hole symmetric, in contrast to the construction of HLR. Instead, our findings are consistent if the composite fermions are massless Dirac particles, at finite density, similar to the surface state of a 3D topological insulator. Exploiting this analogy we devise a numerical test and successfully observe the suppression of $2k_F$ backscattering characteristic of Dirac particles.