Replica study of pinned bubble crystals

Abstract

In higher Landau levels ($N>1$), the ground state of the two-dimensional electron gas in a strong perpendicular magnetic field evolves from a Wigner crystal for small filling $\nu$ of the partially filled Landau level, into a succession of bubble states with increasing number of guiding centers per bubble as $\nu$ increases, to a modulated stripe state near $\nu =0.5$. In this work, we compute the frequency-dependent longitudinal conductivity of the Wigner and bubble crystal states in the presence of disorder. We apply an elastic theory to the crystal states which is characterized by a shear and a bulk modulus. We obtain both moduli from the microscopic time-dependent Hartree-Fock approximation. We then use the replica and Gaussian variational methods to handle the effects of disorder. Within the semiclassical approximation we get the dynamical conductivity as well as the pinning frequency as functions of the Landau level filling factor and compare our results with recent microwave experiments.

19 pages and 6 eps figures

References in corpus (14)

• Ground state phase diagram of 2D electrons in a high Landau level: - DMRG study
• Correlation lengths of Wigner crystal order in two dimensional electron system at high magnetic field
• Wigner Crystals in the lowest Landau level at low filling factors
• Pinned Wigner Crystals
• Microwave Resonance of 2D Wigner Crystal around integer Landau fillings
• Competition between quantum-liquid and electron-solid phases in intermediate Landau levels
• Microwave resonances of the bubble phases in 1/4 and 3/4 filled higher Landau levels
• Evidence for Two Different Solid Phases of Two Dimensional Electrons in High Magnetic Fields
• Evidence of a first order phase transition between Wigner crystal and Bubble Phases of 2D electrons in higher Landau levels
• Microscopic Theory of the Reentrant IQHE in the First and Second Excited LLs
• Dynamics of electrons in the quantum Hall bubble phases
• Wigner crystalization about $\nu$=3
• Quantum Depinning Transition of Quantum Hall Stripes
• Dynamical Conductivity of Disordered Quantum Hall Stripes

Cited by in corpus (6)

• Contrasting Energy Scales of the Reentrant Integer Quantum Hall States
• Skyrme and Wigner crystals in graphene
• De-Pinning Transition of Bubble Phases in a High Landau Level
• Anisotropic states of two-dimensional electrons in high magnetic fields
• Static and dynamic properties of crystalline phases of two-dimensional electrons in a strong magnetic field
• Dynamical matrix of two-dimensional electron crystals