Emergence of liquid crystalline order in the lowest Landau level of a quantum Hall system with internal anisotropy

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It has now become evident that interplay between internal anisotropy parameters (such as electron mass anisotropy and/or anisotropic coupling of electrons to the substrate) and electron-electron correlation effects can create a rich variety of possibilities especially in quantum Hall systems. The electron mass anisotropy or material substrate effects (for example, the piezoelectric effect in GaAs) can lead to an effective anisotropic interaction potential between electrons. For lack of knowledge of realistic ab-initio potentials that may describe such effects, we adopt a phenomenological approach and assume that an anisotropic Coulomb interaction potential mimics the internal anisotropy of the system. In this work we investigate the emergence of liquid crystalline order at filling factor ν = 1/6 of the lowest Landau level, a state very close to the point where a transition from the liquid to the Wigner solid happens. We consider small finite systems of electrons interacting with an anisotropic Coulomb interaction potential and study the energy stability of an anisotropic liquid crystalline state relative to its isotropic Fermi-liquid counterpart. Quantum Monte Carlo simulation results in disk geometry show stabilization of liquid crystalline order driven by an anisotropic Coulomb interaction potential at all values of the interaction anisotropy parameter studied.

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