Composite fermi liquids in the lowest Landau level

Understand

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 $\phi_B=-2\pi\nu$.