Semi-Classical Model of Strongly Correlated Coulomb Systems in Weak Magnetic Field

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The integer and fractional quantum Hall effects are two remarkable macroscopic quantum phenomena occurring in two-dimensional strongly correlated electronic systems at high magnetic fields and low temperatures. Quantization of Hall resistivity in the very high magnetic field regime at partial filling of the lowest Landau level indicates the stabilization of an electronic liquid quantum Hall phase of matter. Other interesting phases that differ from the quantum Hall phases take prominence in weaker magnetic fields when many more Landau levels are filled. These states manifest anisotropic magneto-transport properties and, under certain conditions, appear to mimic charge density waves and/or liquid crystalline phases. One way to understand such a behavior has been in terms of effective interaction potentials confined to the highest Landau level partially filled with electrons. In this work we show that, for weak magnetic fields, such a quantum treatment of these strongly correlated Coulomb systems resembles a semi-classical model of rotating electrons in which the time-averaged interaction potential can be expressed solely in terms of guiding center coordinates. We discuss how the features of this semi-classical effective potential may affect the stability of various strongly correlated electronic phases in the weak magnetic field regime. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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