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

Abstract

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.

Universal behavior of magnetoresistance in quantum dot arrays with different degrees of disorder

“…At low temperatures the dephasing length increases, and the fitted value L * φ should saturate at the typical cluster size, ξ c . Interestingly, the values of ξ c ∼ 60-80 nm, compatible with our experimental results for all the samples, have the same order of magnitude as the localization length ξ * , which can be roughly estimated from the density of QDs using equation (9). The 'hopping' localization length, ξ , given by equation ( 3) also has the same order of magnitude.…”

“…The physical reason for clustering in QD arrays is a very interesting issue, which we are not able to approach in this paper. Specific clustering in strongly correlated systems of electrons in magnetic fields was predicted in [7][8][9]. The main properties of non-uniform many electron states essentially depend on interaction potentials and properties of electron wavefunctions in magnetic field.…”

“…In our case, the shapes of quantum dots change as a result of heat treatment of the samples, and one can expect that such changes influence the details of interaction potentials. In principle, they can even be non-monotonic, bringing the system closer to the model [9]. However, this is just a speculation.…”