2006 International Journal of Modern Physics B  
Since 1999, experiments have shown a plethora of surprising results in the lowtemperature magnetotransport in intermediate regions between quantum Hall (QH) plateaus: the extreme anisotropies observed for half-filling, or the re-entrant integer QH effects at quarter filling of high Landau levels (LL); or even an apparent melting of a Wigner Crystal (WC) at filling factor ν = 1/7 of the lowest LL. A large body of seemingly distinct experimental evidence has been successfully interpreted in terms
more » ... nterpreted in terms of liquid crystalline phases in the two-dimensional electron system (2DES). In this paper, we present a review of the physics of liquid crystalline states for strongly correlated two-dimensional electronic systems in the QH regime. We describe a semi-quantitative theory for the formation of QH smectics (stripes), their zero-temperature melting onto nematic phases and ultimate anisotropic-isotropic transition via the Kosterlitz-Thouless (KT) mechanism. We also describe theories for QH-like states with various liquid crystalline orders and their excitation spectrum. We argue that resulting picture of liquid crystalline states in partially filled LL-s is a valuable starting point to understand the present experimental findings, and to suggest new experiments that will lead to further elucidation of this intriguing system. Keywords: Two-dimensional electronic system; quantum Hall effects; liquid crystals; topological phase transitions. 747 748 C. Wexler & O. Ciftja b The effect is exaggerated by the current distribution geometry; the intrinsic anisotropy is smaller: ρxx/ρyy ∼ 20. See S. Simon, Phys. Rev. Lett. 83, 4223 (1999). c At zero temperature, the existence of an ordered smectic phase is still unsettled. See A. H. MacDonald and M. P. A. Fisher, Phys. Rev. B 61, 5724 (2000); H. Yi, H. A. Fertig and R. Côté, Phys. Rev. Lett. 85, 4156 (2000).
doi:10.1142/s0217979206033632 fatcat:2oyh5gobmna6jmefbo47tafyfi