Impact of internal anisotropy on integer quantum Hall effect electronic phases

We study the integer quantum Hall effect state at filling factor one of the lowest Landau level in presence of an anisotropic Coulomb interaction potential between electrons where anisotropy is incorporated via a phenomenological parameter. Such a potential represents a nontrivial source of internal anisotropy to the original integer quantum Hall phase under consideration. The objective of the work is to gain insight on the impact of such an anisotropic interaction potential on the energy stability of the liquid state. We adopt a widely used model of electrons immersed on disk geometry. It is found that this particular choice of the anisotropic Coulomb potential leads to a problem that is amenable to an analytical calculation of the energy per particle of the system in the thermodynamic limit. The results suggest that any presence of internal anisotropy in the interaction potential increases the overall energy of the system relative to the value corresponding to an isotropic liquid Coulomb potential. This, in turn, implies that another liquid phase with broken rotational symmetry may become energetically favorable when the interaction potential has a sufficient degree of anisotropy.