Square Lattice Formation in a Monodisperse Complex Plasma

We present the first observations of a square lattice formation in a monodisperse complex plasma system, a configurational transition phenomenon that has long been an experimental challenge in the field. The experiments are conducted in a tabletop L-shaped dusty plasma experimental device in a dc glow discharge Argon plasma environment. By a careful control of the vertical potential confining the charged particles as well as the strength of the ion wake charge interactions with the dust particles, we are able to steer the system toward a crystalline phase that exhibits a square lattice configuration. The transition occurs when the vertical confinement strength is slightly reduced below a critical value leading to a buckling of the monodisperse hexagonal 2D dust crystal to form a narrowly separated bilayer state (a quasi-2D state). Some theoretical insights into the transition process are provided through molecular dynamics simulations carried out for the parameters relevant to our experiment.

Figure 1

(a) The schematic of the experimental setup. (b) A schematic vertical view of confinement ring with dust particles. (c) Side view of dust crystal at $P=4.8$ Pa and $V=406\mathrm{V}$.

Figure 2

Local structural arrangement displayed by the order parameter [${\mathrm{\Psi }}_n(j)$] of the particles in the monodisperse complex plasma experiment at discharge voltages (a) $V=400\mathrm{V}$, and (b) $V=396\mathrm{V}$ at a constant pressure of $P=4.8\mathrm{Pa}$. The particles with red color have ${\mathrm{\Psi }}_6>0.6$, black has ${\mathrm{\Psi }}_8>0.6$, and the blue color corresponds to defects. The rectangles of Figs. 2 and 2 mark the area having different structural arrangements. (c) Top enlarged view of region IV of Fig. 2 shows the $2\square$ structure in complex plasma observed in our experiments. (d) A typical sketch of unit cells of a bilayer square structure ($2\square$). All the particles in Fig. 2 are identical and their colors distinguish particles of two different layers. The shaded regions mark the unit cells of the corresponding lattices.

Figure 3

(a) Side view of the particles at $P=4.8\mathrm{Pa}$ and $V=400\mathrm{V}$. The particles in the dotted box represents the quasi-2D layer. (b) Histogram of particle’s position in $z$ direction corresponding to experimental condition mentioned in (a).

Figure 4

A hysteresis behavior in the system with discharge voltage as a control parameter. The $Y$ axis represents the number of particles in the region of interest having ${\mathrm{\Psi }}_8>0.6.$

Figure 5

Snapshot of particle positions resulting from MD simulations for experimentally relevant parameters at ${\tilde{\mathrm{\Omega }}}_h=0.026$ (a) ${\tilde{\mathrm{\Omega }}}_v=1.07$ and (b) ${\tilde{\mathrm{\Omega }}}_v=0.97$. Black color represents particle having ${\mathrm{\Psi }}_8>0.6$, red particles have ${\mathrm{\Psi }}_6>0.6$, and blue particles are defects. The parameters are $\kappa =5.7$ and $\mathrm{\Gamma }=3563$.

Figure 6

The evolution of the average interlayer separation (normalized with $a$) with discharge voltage. For comparison, we also show the normalized average interlayer separation at different confinement frequency (${\tilde{\mathrm{\Omega }}}_v$) found in the MD simulation.