Composite fermi liquids in the lowest Landau level

Abstract

We study composite fermi liquid (CFL) states in the lowest Landau level (LLL) limit at a generic filling $\nu =\frac{1}{n}$. 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 ${\varphi }_B=-2\pi \nu$. We illustrate this point with the CFL of fermions at filling fractions $\nu =1/2q$ and (single and two-component) bosons at $\nu =1/(2q+1)$. 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 $\nu =1/2$. Nevertheless, we show that the existing LLL theory of the composite fermi liquid for bosons at $\nu =1$ does have an emergent particle-hole symmetry. We interpret this particle-hole symmetry as a transformation between the empty state at $\nu =0$ and the boson integer quantum hall state at $\nu =2$. 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 $\nu =1$.

16 pages, 1 figure, new version with minor changes

References in corpus (8)

• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• A controlled expansion for certain non-Fermi liquid metals
• Emergent particle-hole symmetry in the half-filled Landau level
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Emergent Fermi sea in a system of interacting bosons

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