Variational Study of the Nematic State of the Two Dimensional Electron Gas in a Magnetic Field

We have studied the nematic state of the two dimensional electron gas (2DEG) at halffilled Landau level (LL). Our motivation comes from experiments in which anisotropic transport in the 2DEG under high magnetic field and at low temperature was observed. Based on a model of the nematic state proposed by Oganesyan, Fradkin and Kivelson, we investigate this state and compare it with other competing states proposed by other groups. First, we investigate at what LL the nematic state becomes energetically favorable as compared to the isotropic state. Our studies indicate that this occurs at the second excited LL. Moreover, we compare the energy of the nematic state with that of the stripe state obtained within the Hartree-Fock approximation (HF) and we conclude that, for the samples studied experimentally, the nematic state might be more stable. In our study we have used two different methods which both have advantages and disadvantages. The first method used is the Fermi-hyper-netted chain (FHNC) which provides results valid in the thermodynamic limit (infinite size system), however, it is accurate only for a low density system. The second method used is the Monte Carlo method (MC) which can be used on a finite-size system and, thus, the issue arises of how to extrapolate in the thermodynamic limit (finite-size effect). The results obtained from both methods are in good agreement and indicate that the nematic state might be a viable candidate to explain the experimental findings. In order to compare our results for the nematic state to those obtained for the stripe state, we needed to include the kinetic energy contribution beyond the familiar hw_c/2 term in the case of the nematic state which comes from the deformed geometry of the Fermi sea. For the stripe state we have carried out a HF calculation for a more realistic potential for a 2DEG which includes the effects of the finite confinement of the electron wave function along the z-direction.