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

TL;DR

This paper explores the theoretical possibility of liquid crystalline phases in two-dimensional electron systems under strong magnetic fields, using trial wavefunctions and Monte Carlo simulations to analyze their stability across different Landau levels.

Contribution

It introduces new many-body wavefunctions with broken rotational symmetry and assesses their energetic favorability in various Landau levels using Monte Carlo methods.

Findings

Nematic states are energetically favorable in the second excited Landau level.

Liquid crystalline states exhibit a soft charge density wave that quantum fluctuations can destroy.

Anisotropic states are generally unfavorable in the lowest and first excited Landau levels.

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 ($L = 2$).