Anisotropy in two-dimensional electronic quantum Hall systems at half-filled valence Landau levels

Abstract

Strongly correlated electronic systems in two dimensions have constantly been a source of new discoveries. For example, the integer and fractional quantum Hall (QH) effects have emerged when such systems have been subjected to strong perpendicular magnetic fields. Recently, in the transitional regions between QH plateaus, strong magneto-transport anisotropies have been observed below ca. 100 mK. In this paper, we explain the emergence of broken rotational symmetry at half-filled valence Landau levels in terms of quantum liquid crystalline states with nematic order. Quantum Monte Carlo simulations indicate that while isotropic states are stable in the lowest and first excited Landau level, there are regions of instability towards liquid crystalline states in higher Landau levels. A possible connection of the recently discovered magneto-transport anisotropy in low magnetic fields and these liquid crystalline states is discussed.