Crystallization of Chiral Active Brownian Particles at Low Densities

Abstract

Chiral active matter is a variant of active matter systems in which the motion of the constituent particles violates mirror symmetry. In this letter, we simulate two-dimensional chiral Active Brownian Particles, the simplest chiral model in which each particle undergoes circular motion, and show that the system crystallizes at low densities well below the melting point of the equilibrium counterpart. Crystallization is only possible if the orbital radius is long enough to align the circulating particles, but short enough for neighboring particles to avoid collisions. Of course, the system must be driven sufficiently far from equilibrium, since chirality cannot affect thermodynamic properties in classical equilibrium systems. The fluid-crystal phase diagram shows a re-entrant melting transition as a function of the radius of the circles. We show that at least one of the two transitions follows the same two-step melting scenario as in equilibrium systems.

Figures (5)

• Figure 1: (a)--(d) Snapshots of the stationary state of cABP for various values of $R=v_0/\Omega$ at $\varphi=0.4$, $v_0=1$, and $\tau_p=200$. (a) $R=10^3$, (b) $10^2$, (c) $1$, (d) $0.2$. (e) $S(\bm{q})$ for several $R$ values. The thick two broken lines indicate $q^{-3}$ and $q^2$. The thin vertical line shows the position of $q=2\pi/\sigma$. The system size is $N=10^4$.
• Figure 2: The heat map of the structure factor $S(\bm{q})$ for $\varphi=0.4$ and $\tau_p=10^2$ at (a) $R=0.299$ and (b) $R=0.294$. The color sidebar shows the intensity of the $S(\bm{q})$.
• Figure 3: (a) Snapshot of the particle configuration at $R=0.294$, $\tau_p=10^2$, and $\varphi=0.4$. The color of each particle represents the magnitude of its local hexatic order parameter $|\psi^i_6|$ (see the color bar). The inset shows a magnified view with particle trajectories superimposed to highlight their circular motion. (b) The configuration of the centers of mass of the orbits for the configuration in (a). The size of the circles representing the center positions is identical to that of the particles.
• Figure 4: (a) Phase diagram at $\varphi = 0.4$. The color of the dots represents $|\Psi_6|$. Blue and red arrows indicate the upper and lower phase boundaries, respectively, as estimated from a geometric argument (see text). (b) The dependence of $|\Psi_6|$ on $R$ at $\tau_p = 10^2$ (shown as the solid line in (a)). (c) and (d) present the same plots for $\varphi = 0.35$.
• Figure 5: (a) $g_6({\bm r})/g_0({\bm r})$ and (b) $g_0({\bm r})-1$ (bottom) along the direction of $y=0$ for several $R$ values near the first transition. (c), (d) Same as (a) and (b), but for $R$ near the second transition. The dashed lines in (a) and (b) represent the power laws $x^{-1/4}$ and $x^{-1/3}$, respectively.