Quantum nematic as ground state of a two-dimensional electron gas in a magnetic field

We study the ground state of a nematic phase of the two-dimensional electron gas at filling fraction ν=1 2 using a variational wave function having Jastrow pair correlations of the form Πi<j (zi - zj) 2 and an elliptical Fermi sea. Using the Fermi-hypernetted-chain approximation, we find that below a critical value of the broken-symmetry parameter, the nematic phase is energetically favorable as compared to the isotropic state for the second excited Landau level. We also find that below a critical value of the layer "thickness" parameter λ (and in the actual materials), the quantum nematic is energetically favorable relative to the stripe ordered Wigner crystal phase. © 2007 The American Physical Society

Variational Monte Carlo calculation of the nematic state of the two-dimensional electron gas in a magnetic field

We use a Jastrow-Slater wave function with an elliptical Fermi sea to describe the nematic state of the two-dimensional electron gas in a magnetic field and the Monte Carlo method to calculate a variational energy upper bound. These energy upper bounds are compared with other upper bounds describing stripe-ordered ground states, which are obtained from optimized Hartree-Fock calculations, and with those which correspond to an isotropic ground state. Our findings support the conclusions drawn in our previous study, where the Fermi-hypernetted chain approximation was used instead of the Monte Carlo method. Namely, the nematic state becomes energetically favorable relative to the stripe-ordered Wigner crystal phase for the second excited Landau level and below a critical value of the layer "thickness" parameter, which is very close to its value in the actual materials. © 2008 The American Physical Society

Effective Interaction Potentials in the Uppermost Landau Level

We consider a quantum Hall system of electrons confined to the uppermost Landau level and assume that the lower Landau levels are full and inert causing no Landau level mixing. While it is known that the problem of electrons interacting with the Coulomb interaction in a higher Landau level is mathematically equivalent to the problem of electrons in the lowest Landau level interacting with an effective interaction, the way the effective interaction can be calculated is not unique. We focus on the details of two different calculations of such effective interaction potentials in the uppermost Landau level and discuss the influence of one or another form of the effective potential on the stability of various correlated electronic phases in the quantum Hall regime