Dynamics of electrons in quantum Hall bubble phases

Abstract

In Landau levels $N>1,$ the ground state of the two-dimensional electron gas (2DEG) in a perpendicular magnetic field evolves from a Wigner crystal for small filling ${\ensuremath{\nu}}^{*}$ of the partially filled Landau level, into a succession of bubble states with increasing number of guiding centers per bubble as ${\ensuremath{\nu}}^{*}$ increases, to a modulated stripe state near ${\ensuremath{\nu}}^{*}=0.5.$ In this work, we show that these first-order phase transitions between the bubble states lead to measurable discontinuities in several physical quantities such as the density of states and the magnetization of the 2DEG. We discuss in detail the behavior of the collective excitations of the bubble states and show that their spectra have higher-energy modes besides the pinned phonon mode. The frequencies of these modes, at small wave vector k, have a discontinuous evolution as a function of filling factor that should be measurable in, for example, microwave absorption experiments.