Anisotropic Quantum Hall Liquid States with No Translational Invariance in the Lowest Landau Level

Abstract

Strongly correlated two-dimensional electron systems in a high perpendicular magnetic field have displayed remarkable new physics leading to the discovery of phenomena such as the integer and the fractional quantum Hall effect, to mention a few. Laughlin’s theoretical model and the composite fermion’s (CFs) approach provide a good description of the liquid electronic phases in the lowest Landau level (LLL) at relatively large filling factors. Other electronic phases at smaller filling factors of the LLL likely represent electronic Wigner solid states. It is believed that no other phases with intermediate order stabilize at the liquid–solid transition region. The current study deals with filling factor 1/6 in the LLL, a state which is very close to the critical filling factor where the liquid–solid transition takes place. With the assumption that the underlying signs of crystalline order are starting to appear at this transitional regime, we focus our attention and study the properties of a hybrid electronic phase that lacks translational invariance. To describe such a state, we consider a wave function that lies entirely in the LLL but, unlike a typical quantum Hall liquid phase, does not possess translational invariance. Although inspired by Laughlin’s approach, the wave function we introduce differs from Laughlin’s or CFs wave functions that describe translationally invariant uniform electronic phases. We perform quantum Monte Carlo simulations in a standard disk geometry to gain a better understanding of the properties of this wave function that may be considered as a precursor to the more conventional Wigner crystal phase.