Freezing and Melting of a Colloidal Adsorbate on a 1D Quasicrystalline Substrate

Using Monte Carlo simulations and an extended Landau-Alexander-McTague theory, we demonstrate that colloids in a one-dimensional quasicrystalline potential order in triangular and rhombic-$\alpha$ crystalline phases. Increasing the strength of the potential further, a new type of light-induced melting is discovered that has its origin in the nonperiodicity of the potential. In contrast to reentrant melting in periodic potentials, the quasicrystalline potential melts the crystalline phases even when they already exist at zero potential.

Figure 1

Reciprocal lattice vectors of four possible phases in a laser potential modulated with the wave vectors ${\mathbf{G}}_{\alpha }=\tau G_0{\mathbf{e}}_x$ and ${\mathbf{G}}_{\beta }=(1/\tau )G_0{\mathbf{e}}_x$. In the pentagonal and triangular phase the lengths of the lattice vectors are $G_j=G_0$ ($j=1,\dots ,5$ or $1,\dots ,3$). In the rhombic phases ${\mathbf{G}}_1$ equals either ${\mathbf{G}}_{\alpha }$ or $-{\mathbf{G}}_{\beta }$; ${\mathbf{G}}_2$ and ${\mathbf{G}}_3$ are chosen such that the colloidal density is the same as in the triangular lattice.

Figure 2

The order parameters $\rho ({\mathbf{G}}_2)$ characterizing the crystalline ordering of the colloids as a function of the strength $V$ of the 1D quasicrystalline potential and the reduced inverse Debye length $\kappa a_s$. Inset: resulting phase diagram.

Figure 3

Snapshots of particle positions in a one-dimensional quasicrystalline potential indicated in the lower part of each figure. The inverse screening length $\kappa a_s=14$ is chosen such that the colloidal system is solid for zero potential. For $V=10k_{B}T$ (a) the rhombic-$\alpha$ phase occurs; for $V=1000k_{B}T$ (b) the rhombic ordering has melted into a modulated liquid.

Figure 4

(a) Phase diagram showing the regions of a stable triangular (dark gray) and rhombic-$\alpha$ (light gray) phase. In all other regions of the parameter space, only the modulated liquid phase is stable. (b)–(d) Phase diagrams for rigid crystals with $c=1$ (b), intermediate systems with $c={10}^{-2}$ (c), and soft systems with $c={10}^{-4}$ (d).