Dynamics of disordered quantum Hall crystals

Abstract

Charge density waves are thought to be common in two-dimensional electron systems in quantizing magnetic fields. Such phases are formed by the quasiparticles of the topmost occupied Landau level when it is partially filled. One class of charge density wave phases can be described as electron solids. In weak magnetic fields (at high Landau levels) solids with many particles per unit cell - bubble phases - predominate. In strong magnetic fields (at the lowest Landau level) only crystals with one particle per unit cell - Wigner crystals - can form. Experimental identification of these phases is facilitated by the fact that even a weak disorder influences their dc and ac magnetotransport in a very specific way. In the ac domain, a range of frequencies appears where the electromagnetic response is dominated by magnetophonon collective modes. The effect of disorder is to localize the collective modes and to create an inhomogeneously broadened absorption line, the pinning mode. In recent microwave experiments pinning modes have been discovered both at the lowest and at high Landau levels. We present the theory of the pinning mode for a classical two-dimensional electron crystal collectively pinned by weak impurities. We show that long-range Coulomb interaction causes a dramatic line narrowing, in qualitative agreement with the experiments.

6 pages, 3 figures. To be presented at EP2DS-15, Nara, Japan. One typo corrected

References in corpus (10)

• Charge Density Wave in Two-Dimensional Electron Liquid in Weak Magnetic Field
• The Ground State of a Two-Dimensional Electron Liquid in a Weak Magnetic Field
• Correlation lengths of Wigner crystal order in two dimensional electron system at high magnetic field
• Dynamical response of a weakly pinned two-dimensional Wigner crystal
• Dynamical response of a pinned two-dimensional Wigner crystal
• Microwave resonances of the bubble phases in 1/4 and 3/4 filled higher Landau levels
• Dynamical properties of the pinned Wigner crystal
• Some generic aspects of bosonic excitations in disordered systems
• Low-frequency dynamics of disordered XY spin chains and pinned density waves: from localized spin waves to soliton tunneling
• New collective states of 2D electrons in high Landau levels

Cited by in corpus (4)

• Crossover between localized states and pinned Wigner crystal in high-mobility n-GaAs/AlGaAs heterostructures near filling factor $\nu =1$
• Melting of Wigner crystal in high-mobility $n$-GaAs/AlGaAs heterostructures at filling factors $0.18>\nu >0.125$: Acoustic studies
• Magnetotransport in low-density $p$-Si/SiGe heterostructures: From metal through hopping insulator to Wigner glass
• Wigner crystal in a two-dimensional electron system in the vicinity of filling factor 1/5: Acoustic studies