Liquid crystalline states for two-dimensional electrons in strong magnetic fields

Abstract

Based on the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory of two-dimensional melting and the analogy between Laughlin states and the two-dimensional one-component plasma (2DOCP), we investigate the possibility of liquid crystalline states in a single Landau level (LL). We introduce many-body trial wavefunctions that are translationally invariant but posess 2-fold (i.e. {\em nematic}), 4-fold ({\em tetratic}) or 6-fold ({\em hexatic}) broken rotational symmetry at respective filling factors $\nu =1/3$, 1/5 and 1/7 of the valence LL. We find that the above liquid crystalline states exhibit a soft charge density wave (CDW) which underlies the translationally invariant state but which is destroyed by quantum fluctuations. By means of Monte Carlo (MC) simulations, we determine that, for a considerable variety of interaction potentials, the anisotropic states are energetically unfavorable for the lowest and first excited LL's (with index $L=0,1$), whereas the nematic is favorable at the second excited LL ($L=2$).

arXiv comment7 figures, submitted to PRB, high-quality figures available upon request

References in corpus (11)

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Cited by in corpus (9)

• Theory of Nematic Fractional Quantum Hall State
• Anisotropic magnetoresistance and piezoelectric effect in GaAs Hall samples
• Unified hydrodynamics theory of the lowest Landau level
• Interaction-dependent anisotropy of fractional quantum Hall states
• Universal behavior of magnetoresistance in quantum dot arrays with different degree of disorder
• Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations
• Competition between Pomeranchuk instabilities in the nematic and hexatic channels in a two-dimensional spinless Fermi fluid
• Toward a new theory of the fractional quantum Hall effect: The many-body spectra and energy gaps at $\nu <1$
• Toward a new theory of the fractional quantum Hall effect