Anisotropy in a high Landau level due to effective electron-electron interactions

Abstract

Quantization of Hall resistivity in strongly correlated two-dimensional electronic systems at high magnetic fields generally indicates the stabilization of novel electronic quantum liquid phases of matter. This is the nature of the integer and fractional quantum Hall states that stabilize at integer and fractional odd-denominator (not always, though) filling factors of the Landau level. Away from certain filling factors that represent quantum Hall liquid states, different phases, some of them with unusually high magneto-transport anisotropy have been known to stabilize specially in high Landau levels. In this work, we try to understand this anisotropic behaviour in terms of effective electron-electron interaction potentials. To this effect, we implement a full projection of the original Coulomb interaction potential in the suitable Landau level. We find out that, in high Landau levels, thus for relatively weak magnetic fields, a semi-classical description of the interaction potential between electrons appear to be an adequate choice. The features of this semi-classical interaction potential in this limit suggest ways how the energetic balance between density waves and/or liquid crystalline phases might be sensitively affected.