Transport in 2D Complex Plasma Crystals

Abstract

In this chapter, we investigate numerically the transport properties of a 2D complex plasma crystal by examining the propagation of coplanar dust lattice waves. In the limit where the Hamiltonian interactions can be decoupled from the non-Hamiltonian effects, we identify two distinct regimes of wave transport: Anderson-type delocalization and long-distance excitation. We use the spectral approach to evaluate the contribution from the Anderson problem, i.e. to determine whether the initial lattice perturbation delocalized through nearest neighbor (short distance) interaction. The theoretical predictions are then compared against the results from a mulecular dynamics simulation. Any major deviations between the predicted and observed crystal dynamics are contributed to non-Hamiltonian effects. The benefit of our approach is twofold. First, the use of complex plasma system allows for tunability of the initial conditions and investigation of the transport problem at the kinetic level. In addition, the 2D dust crystal exhibit hexagonal symmetry, which makes it an ideal macroscopic analogue for materials, such as graphene. Second, the Hamiltonian part of the transport problem is analyzed using a theoretical approach, which determines delocalization in an infinite disordered system without the use of finite-size scaling or periodic boundary conditions. Thus, the comparison between theoretical and numerical results can be used to evaluate the effect of the actual physical boundaries and system size.

Here we focus on cases, where the wave did not spread far away from the initially perturbed dust particle, yet excitations are observed in remote parts of the lattice. In all simulations examined we established that long-distance excitations involve dust grains located around crystal defects. This makes sense physically since lattice defects consist of particles that are displaced from their position in the unperturbed lattice and are, therefore, in unstable equilibrium. In the decoupled Hamiltonian regime, the observed effects can be contributed to the dust lattice interaction with the plasma environment.

We start with a brief introduction to basic complex plasma physics concepts (Sect. 6.1). The use of the two-dimensional dust lattice as a macroscopic analogue for materials such as graphene is discussed in Sect. 6.2. Next, we provide an overview of transport problems in the classical regime and their application to non-Hamiltonian systems, such as the complex plasma crystals (Sect. 6.3). Section 6.4 presents the results from a series of numerical simulations, where an in-plane dust lattice wave is induced in a disordered 2D dust crystal. In Sect. 6.5 we analyze the dynamics of the crystal using the spectral approach and evaluate the contribution from non-Hamiltonian effects.

This chapter published as: Kostadinova, F. Guyton, A. Cameron, K. Busse, Liaw, C. D., Matthews, L. S., & Hyde, T. W. (2017). Transport properties of disordered 2D complex plasma crystal (recommended for publication in Contrib. To Plasma Phys.)