Composite fermi liquids in the lowest Landau level

TL;DR

The paper proposes a lowest Landau level composite Fermi liquid described as a quantum vortex liquid of charge-neutral fermions forming a Fermi surface with a Berry phase $φ_B=-2πν$, eliminating the Chern-Simons term and producing distinct transport without Landau-level mixing. This Berry-phase CFL, applicable to fermions at ν=1/2 and bosons at ν=1 as well as spinful cases, yields concrete predictions for thermal and spin Hall responses that differ from Halperin–Lee–Read theory. It further reveals an emergent particle-hole symmetry for bosons at ν=1, unifies bosonic Jain and Pfaffian-like states within Read’s LLL framework, and connects to 3D bosonic topological insulators via bulk–boundary dualities and symmetry-enforced constraints. A no-go theorem shows that, under SU(2) and particle-hole symmetry, a fully gapped symmetric topological order cannot exist at ν=1, illustrating symmetry-enforced gaplessness and deep links to SPT boundary phenomena.

Abstract

We study composite fermi liquid (CFL) states in the lowest Landau level (LLL) limit at a generic filling $ν= \frac{1}{n}$. We begin with the old observation that, in compressible states, the composite fermion in the lowest Landau level should be viewed as a charge-neutral particle carrying vorticity. This leads to the absence of a Chern-Simons term in the effective theory of the CFL. We argue here that instead a Berry curvature should be enclosed by the fermi surface of composite fermions, with the total Berry phase fixed by the filling fraction $φ_B=-2πν$. We illustrate this point with the CFL of fermions at filling fractions $ν=1/2q$ and (single and two-component) bosons at $ν=1/(2q+1)$. The Berry phase leads to sharp consequences in the transport properties including thermal and spin Hall conductances, which in the RPA approximation are distinct from the standard Halperin-Lee-Read predictions. We emphasize that these results only rely on the LLL limit, and do not require particle-hole symmetry, which is present microscopically only for fermions at $ν=1/2$. Nevertheless, we show that the existing LLL theory of the composite fermi liquid for bosons at $ν=1$ does have an emergent particle-hole symmetry. We interpret this particle-hole symmetry as a transformation between the empty state at $ν=0$ and the boson integer quantum hall state at $ν=2$. This understanding enables us to define particle-hole conjugates of various bosonic quantum Hall states which we illustrate with the bosonic Jain and Pfaffian states. The bosonic particle-hole symmetry can be realized exactly on the surface of a three-dimensional boson topological insulator. We also show that with the particle-hole and spin $SU(2)$ rotation symmetries, there is no gapped topological phase for bosons at $ν=1$.

Figures (1)

• Figure 1: Cancelation of the Chern-Simons term by integrating out composite fermions deep in the fermi sea. Final theory: a composite fermi surface with Berry phase $\phi_B=-2\pi/n$.