Collective Excitations of Two-Dimensional Electron Solids and Correlated Quantum Liquids in High Magnetic Fields
A simple but rigorous approach will be presented for studying the nature of intra-Landau level collective excitations of interacting electrons fully polarized in a perpendicular magnetic field with partial filling of the lowest Landau level. A finite gap, due to correlations in the density fluctuations of the centers of cyclotron orbits, or no gap, due to crystalline-like correlations because of broken magnetic translational invariance are shown to exist rigorously in the long-wavelength limit of low-lying collective excitations in two condensed phases, i.e., an incompressible quantum liquid and a two-dimensional electron quantum solid, respectively.
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