The fractional quantum Hall nematics on the first Landau level in a tilted field

We investigated the behavior of fractional quantum Hall (FQH) states in a two-dimensional electron system with layer thickness and an in-plane magnetic field. Our comparisons across various filling factors within the first Landau level revealed a crucial observation. A slight in-plane magnetic field specifically enhances the nematic order of the $\nu = 7/3$ FQH state. For this particular filling, through calculating the energy gap, the Ising nematic order parameter, the pair-correlation function, and the static structure factor, we observed that as the in-plane magnetic field increases, the system first enters into an anisotropic FQH phase without closing the spectrum gap, then the FQH nematic (FQHN) phase after neutral gap closing. The system eventually enters a gapless one-dimensional charge density wave (CDW) phase for a large in-plane field. We thus provide a full phase diagram of the $\nu = 7/3$ state in a tilted magnetic field, demonstrating the existence of the FQHN, which aligns with recent resonant inelastic light scattering (RILS) experimental observations.