Pomeranchuk Instability driven by Coulomb interaction in half-filled Landau levels

We study the Coulomb interaction driven Pomeranchuk instability as a mechanism for observed electronic nematic phases at high Landau levels. Such a mechanism will be signaled by the instability of the Fermi surface to quadripolar deformations: $F_2<-1$, where $F_2$ is the Fermi liquid parameter for the angular momentum $L=2$ channel. We compare the Fermi Liquid parameters for the lowest three half-filled Landau levels ($\nu=1/2, 5/2 and 9/2$). We calculate the Fermi liquid parameters by evaluating energies of eight independent particle-hole pair excitation configurations using a quantum Monte Carlo algorithm through correlated sampling. We used composite fermion many-body wave functions for $37$ electrons on a toroidal geometry that are interacting through the Coulomb potential. We find $F_2$ to become increasingly negative as we go to higher Landau levels. This is consistent with experimental observations.