The Hall viscosity has been proposed as a topological property of incompressible fractional quantum Hall states and can be evaluated as Berry curvature. This paper reports on the Hall viscosities of composite-fermion Fermi seas at $\ensuremath{\nu}=1/m$, where
m is even for fermions and odd for bosons. A well-defined value for the Hall viscosity is not obtained by viewing the
1/m composite-fermion Fermi seas as the $n\ensuremath{\rightarrow}\ensuremath{\infty}$ limit of the Jain $\ensuremath{\nu}=n/(nm\ifmmode\pm\else\textpm\fi{}1)$ states, whose Hall viscosities $(\ifmmode\pm\else\textpm\fi{}n+m)\ensuremath{\hbar}\ensuremath{\rho}/4$ ($\ensuremath{\rho}$ is the two-dimensional density) approach $\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$ in the limit $n\ensuremath{\rightarrow}\ensuremath{\infty}$. A direct calculation shows that the Hall viscosities of the composite-fermion Fermi sea states are finite and also relatively stable with system size variation, although they are not topologically quantized in the entire $\ensuremath{\tau}$ space. I find that the $\ensuremath{\nu}=1/2$ composite-fermion Fermi sea wave function for a square torus yields a Hall viscosity that is expected from particle-hole symmetry and is also consistent with the orbital spin of
1/2 for Dirac composite fermions. I compare my numerical results with some theoretical conjectures.
There is increasing experimental evidence for fractional quantum Hall effect at filling factor $\ensuremath{\nu}=2+3/8$. Modeling it as a system of composite fermions, we study the problem of interacting composite fermions by a number of methods. In our variational study, we consider the Fermi sea, the Pfaffian paired state, and bubble and stripe phases of composite fermions, and find that the Fermi sea state is favored for a wide range of transverse thickness. However, when we incorporate interactions between composite fermions through composite-fermion diagonalization on systems with up to 25 composite fermions, we find that a gap opens at the Fermi level, suggesting that inter-composite fermion interaction can induce fractional quantum Hall effect at $\ensuremath{\nu}=2+3/8$. The resulting state is seen to be distinct from the Pfaffian wave function.
Field theories of the composite-fermion (CF) metal model it as a Fermi sea of composite fermions coupled to an emergent gauge field. Within a random phase approximation, these theories predict that the Landau damping of the gauge field resulting from its coupling to the low-energy, long-wavelength CF particle-hole excitations modifies the electrons' density-density correlation function related to the static structure factor S(q) at wave vector q. This produces a nonanalytic correction ∝q^{3}lnq to S(q) (with the magnetic length ℓ_{B}=1). Thanks to the recently developed quaternion formulation for Jain-Kamilla projection of CF wave functions, the evaluation of S(q) from the accurate microscopic theory of composite fermions has now become possible for systems containing as many as N=900 CFs, which enables a reliable determination of the small-q behavior of S(q). We study CF metals corresponding to electrons at Landau level filling factors ν=1/2 and 1/4, and for completeness, also of bosons at ν=1 and 1/3. In the q→0 limit, our microscopic calculation reveals a q^{3} term in S(q) of the CF metals rather than q^{3}lnq. This behavior is well predicted by a model of a noninteracting Fermi sea of dipolar CFs, which also obtains its coefficient accurately.