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

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Based on the Kosterlitz-Thouless-Halperin-Nelson-Young theory of two-dimensional melting and the analogy between Laughlin states and the two-dimensional one-component plasma, we investigate the possibility of liquid crystalline states in a single Landau level (LL). We introduce many-body trial wave functions that are translationally invariant but possess twofold (i.e., nematic), fourfold (tetratic), or sixfold (hexatic) broken rotational symmetry at respective filling factors ν = 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 simulations, we determine that, for a considerable variety of interaction potentials, the anisotropic states are energetically unfavorable for the lowest and first excited LL#x2019;s (with index L = 0, 1), whereas the nematic is favorable at the second excited LL (L = 2). © 2004 The American Physical Society.

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