Properties of the Composite Fermion Wigner Crystal

In two dimensional electron systems at small filling factor the ground state is a Wigner crystal. Wigner crystals can also be observed for systems near integer fillings, where electrons or holes in the partially filled Landau Level form a Wigner crystal. Recent experimental evidence (PRL 105, 126803 (2010)) suggests that a Wigner crystal of composite fermions forms near the filling factor of $v=\frac{1}{3}$. Motivated by these results, we calculate the shear modulus of the composite fermion Wigner crystal in the vicinity of several fillings of the form $v=\frac{1}{3},\frac{2}{5},\frac{3}{7}$, following the procedure of Maki-Zotos, using the effective two-body real space interactions between composite fermions calculated by Lee, Scarola, and Jain. We discuss the differences from the electron Wigner crystal, and also the experimental implications of our results.