What Determines the Fermi Wave Vector of Composite Fermions

We report the observation of a pronounced asymmetry in the magnetic field positions of the commensurability resistance minima of fully spin-polarized composite fermions (CFs) with respect to the field at $\nu \quad =$ 1/2 in two-dimensional (2D) electron and hole systems. The asymmetry is observed across a wide range of 2D densities and modulation periods. We can explain the asymmetry quantitatively if we assume that the CFs are fully spin-polarized and their density is equal to the density of the minority carriers in the lowest, spin-resolved Landau level (LL), namely the density of electrons when $\nu $ \textless 1/2 and of holes when $\nu $ \textgreater 1/2. Our results provide direct evidence that CFs are formed by pairing up of the minority carriers in the lowest spin-resolved LL with flux quanta. They further indicate that the CF commensurability minima are not observed at $\nu $ and (1 - $\nu )$, as expected from a simple particle-hole symmetry principle, pointing to a subtle breaking of this symmetry.