Research Assistant, PhD candidate, Baylor University
A numerical study of the Anderson localization in a 2D complex plasma crystal
In condensed matter, a crystal without impurities at zero temperature acts like a perfect conductor for a travelling electron. As the amount of lattice disorder reaches a critical value, the electron wavefunction experiences a transition from extended to a localized state, called Anderson localization. The existence of such transition in 2D materials has been the subject of heated debate over the past few decades due to a disagreement between theoretical prediction and experimental observation. Here, we present a numerical study of the Anderson localization in a 2D complex plasma crystal, which is used as a macroscopic analogue of a disordered 2D material. The goal of this research is to establish if Anderson localization can be experimentally observed in a 2D complex plasma crystal and to determine how spatial defects influence the dynamical behavior of strongly coupled Coulomb systems.
Complex plasma crystals exhibit characteristic distance and time scales which are easily observable by video microscopy. As such, these strongly coupled many-particle systems are ideal for the study of localization phenomena in the classical regime. In this work, we investigate the transport properties of the dusty plasma crystal by analyzing the diffusion of coplanar lattice waves travelling within the medium. The results from our simulations are compared to the predictions of a novel mathematical method, called the spectral approach to delocalization. The spectral approach determines (with probability 1) the existence of extended states in infinite disordered lattices of any dimension without the use of boundary conditions or scaling. Thus, the comparison between theoretical and numerical results is used to evaluate the effect of physical boundaries and system size. We further discuss the interplay between disorder-driven behavior and interparticle interaction in the strongly coupled dusty plasma system.
Abstract: Mach cones composed of shear waves were observed experimentally in a two-dimensional screened-Coulomb crystal. Highly charged microspheres suspended in a plasma and interacting with a repulsive Yukawa potential arranged themselves in a triangular lattice with hexagonal symmetry. Mach cones were excited by applying a force from the radiation pressure of a moving laser beam. They had a single-cone structure, which is explained by the almost dispersionless character of shear waves. The cone's opening angle obeyed the Mach-cone-angle relation. Results are compared to a molecular-dynamics simulation.
Pub.: 17 Apr '02, Pinned: 27 Jun '17
Abstract: Nonlinear mixing and harmonic generation of compressional waves were studied in a 2D Yukawa (screened Coulomb) triangular lattice. The lattice was a monolayer of highly charged polymer microspheres levitated in a plasma sheath. Two sinusoidal waves with different frequencies were excited in the lattice by pushing the particles with modulated Ar+ laser beams. Waves at the sum and difference frequencies and harmonics were observed propagating in the lattice. Phonons interacted nonlinearly only above an excitation-power threshold due to frictional damping, as predicted by theory.
Pub.: 05 Mar '04, Pinned: 27 Jun '17
Abstract: The propagation of a nonlinear low-frequency mode in two-dimensional (2D) monolayer hexagonal dusty plasma crystal in presence of external magnetic field and dust-neutral collision is investigated. The standard perturbative approach leads to a 2D Korteweg-de Vries (KdV) soliton for the well-known dust-lattice mode. However, the Coriolis force due to crystal rotation and Lorentz force due to magnetic field on dust particles introduce a linear forcing term, whereas dust-neutral drag introduce the usual damping term in the 2D KdV equation. This new nonlinear equation is solved both analytically and numerically to show the competition between the linear forcing and damping in the formation of quasilongitudinal soliton in a 2D strongly coupled complex (dusty) plasma. Numerical simulation on the basis of the typical experimental plasma parameters and the analytical solution reveal that the neutral drag force is responsible for the usual exponential decay of the soliton, whereas Coriolis and/or Lorentz force is responsible for the algebraic decay as well as the oscillating tail formation of the soliton. The results are discussed in the context of the plasma crystal experiment.
Pub.: 15 Oct '14, Pinned: 27 Jun '17
Abstract: We report complex plasma experiments, assisted by numerical simulations, providing an alternative qualitative link between the macroscopic response of polycrystalline solid matter to small shearing forces and the possible underlying microscopic processes. In the stationary creep regime we have determined the exponents of the shear rate dependence of the shear stress and defect density, being α=1.15±0.1 and β=2.4±0.4, respectively. We show that the formation and rapid glide motion of dislocation pairs in the lattice are dominant processes.
Pub.: 26 Jul '14, Pinned: 27 Jun '17
Abstract: In this paper we introduce the spectral approach to delocalization in infinite disordered systems and provide a physical interpretation in context of the classical model of Edwards and Thouless. We argue that spectral analysis is an important contribution to localization problems since it avoids issues related to the use of boundary conditions. Applying the method to 2D and 3D numerical simulations with various amount of disorder W shows that delocalization occurs for W<=0.6 in 2D and for W<=5 for 3D.
Pub.: 09 Jul '16, Pinned: 27 Jun '17
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