Reentrant melting of scarred odd crystals by self-shear

TL;DR

The study addresses how confinement-induced geometrical frustration and topological defects in active matter modify collective flows and induce novel mechanical responses. The authors use dense 2D granular spinners in a circular arena to create and tune confinement-induced grain boundary scars and control net chiral activity via the ratio of counterclockwise to clockwise spinners, characterized by $ ext{chi} = (N^{\otimes}-N^{\odot})/N$. They find that grain boundary scars decouple the topologically protected edge flow from the bulk, and that increasing chiral activity triggers spontaneous self-shear, leading to parity-violating radial stresses $\sigma_{rr}$ that drive a reentrant melting transition at fixed areal density $\phi$. Simulations and coarse-grained analyses reveal that GB scars weaken edge-bulk coupling through reduced resistive torque $\tau_{\text{res}}$, and that the density modulation $\phi_A(r)$ and vorticity $\omega(r)$ together mediate a density-driven crystallization–melting cycle. The results demonstrate that geometrical frustration and odd elasticity can be harnessed to engineer controlled flows and phase behavior in confined active solids.

Abstract

Spatial confinement can induce geometrical frustration in condensed phases, giving rise to topological defects that confer materials with new and exotic properties. Here, we experimentally uncover the remarkable effect of confinement-induced defect strings termed `grain boundary scars' on the behavior of dense two-dimensional assemblies of granular spinners, a canonical odd elastic solid. We show that the spatial arrangement of these scars fundamentally reshapes the flows triggered by chiral activity. Specifically, they cause the topologically protected edge flows - a ubiquitous feature of confined spinner assemblies - to decouple from the bulk. Strikingly, increasing the net chiral activity of the system by tuning the ratio of counterclockwise to clockwise spinners caused spontaneous self-shearing. The resulting odd radial stresses led to a chiral activity-mediated reentrant melting transition at a fixed areal spinner density. Our findings open new avenues for exploiting geometrical frustration to elicit novel responses from odd elastic solids.

Figures (3)

• Figure 1: Chiral activity drives reentrant melting of spinner crystals. (A) Top left panel: Picture of 3D-printed clockwise $(\otimes)$ and counterclockwise $(\odot)$ rotating spinner; arrows show the spin direction. Right panel: Representative image of a dense packing of spinners, interacting via transverse forces, for net chiral activity, $\chi = 0$, and area fraction, $\phi = 0.72$. The zoomed-in view shows circles and dots marked on the $\odot$ and $\otimes$ spinners, respectively, to track their rotation. (B) The panels show spinners colored as per the magnitude of the hexagonal bond-order parameter, $\langle |\psi_6| \rangle$, for $\phi = 0.72$ at different $\chi$ values. The dashed circle delineates the bulk from the boundary and has a cutoff radius, $r_c = 0.7R$, where $R$ is the system's radius. This cutoff corresponds to an $r$ where layering due to confinement is negligible (Fig. \ref{['Figure3']}C). The averaged areal spinner density of the bulk, $\phi_\text{Bulk}$, is also indicated. (C) shows the variation in $\langle|\psi_6|\rangle$ on increasing $\chi$ for different $\phi$ values. Here, $\langle\rangle$ denotes an average over all the spinners in the bulk and at all times. The error bars denote the standard error. (D) Strength of reentrance, $\Delta$ (shown in Fig. \ref{['Figure1']}C), versus $\phi$. (E) shows the annular radial density profile, $\phi_A(r)$, with $r/R$, for different $\chi$ values at $\phi = 0.72$. $\phi_A(r)$ for a packing of passive disks at the same $\phi$ is also shown. Here, $r$ is the outer radius of the annulus, with width $0.09d_p$, where $d_p$ is the particle diameter.
• Figure 2: Grain boundary (GB) scars cause spinner crystals to self-shear. All sub-figures are for $\phi = 0.72$. (A) Average angular velocity, $\omega(r)$, of spinners in annuli defined with respect to the system center versus $r/R$ for different values of $\chi$. There is a sharp drop in $\omega(r)$ at $r/R\approx 0.9$ (black vertical line) for $\chi>0$. The bulk and the edge rotate in opposite directions for $\chi = 0.6$ & 1. The orange- and green-shaded regions correspond to the edge and bulk flow, respectively. (B) Voronoi tesselation of the spinner assembly at $\chi = 1$. The colors represent the spinner coordination number. The drop in $\omega(r)$ occurs across the annulus harboring GB scars (grey-shaded annulus). The zoomed-in view shows the composition of a GB scar. Unlike conventional grain boundaries, which terminate at the system edge, these scars terminate within the system bausch2003grain. (C) The average number of dislocations per scar, $N_{\text{D}}$, for the experiment (red) and simulation (blue) at $\chi = 1$ for $\phi = 0.72$ and $\phi = 0.79$. The error bars represent the standard error. (D) shows $\phi_A(r)$ close to the edge for $\chi = 1$ in sectors with and without a GB scar, corresponding to the red- and blue-shaded regions in (B), respectively. (E) Resistive torque, $\tau_{\text{res}}$, obtained from simulations for different values of $\chi$ at $\phi = 0.72$. There is a clear minimum in $\tau_{\text{res}}$ at $r/R\approx 0.9$ (grey-shaded region). (F) shows the annular spinner spin velocity $\langle\Omega(r)\rangle$ versus $r/R$ for different $\chi$ values. (G) A snapshot of spinners near the confining boundary at $\chi=1$. Blue and red dots are scattered over the five- and seven-coordinated spinners, respectively, to highlight the scar, which is located in layer $L_4$. The direction of the force experienced (exerted) by the annulus from (on) its neighboring one is also shown. For instance, $\bf{F}_{12}$ is the force on layer $L_1$ due to $L_2$.
• Figure 3: An odd re-entrant melting transition. (A) Illustration of the microscopic mechanism that gives rise to odd radial stresses in spinner materials. The handedness of particle spin, edge, and bulk flows is represented by $(\odot)$ for counterclockwise and $(\otimes)$ for a clockwise motion. Panels (i)-(iii) are for $\otimes$ spinners. Panel (i): No flow ($\omega_\text{Edge} = \omega_\text{Bulk} = 0$). Here, edge spinners collide with bulk spinners from above and below with equal probability. During collisions, the transverse forces (black arrows) on average add up to zero along $\hat{r}$ and hence the radial stress $\sigma_{rr}=0$. Panel (ii): Edge and bulk flow have handedness opposite to particle spin. Edge spinners collide with bulk spinners more frequently from below since $^\odot \omega_\text{Edge}>^\odot \omega_\text{Bulk}$. The transverse forces now have a component along $\hat{r}$, and, hence, $\sigma_{rr}>0$. The bulk dilates. Panel (iii): Edge and bulk flow and particle spin have the same handedness and $^\otimes \omega_\text{Edge}>^\otimes \omega_\text{Bulk}$. $\sigma_{rr}$ now points inwards, compressing the bulk. Panel (iv): For $0<\chi<1$, although $^\otimes \omega_\text{Edge}>^\otimes \omega_\text{Bulk}$, transverse forces in many inter-spinner collisions have a component along $\hat{r}$ unlike in Panel (iii) where it is predominantly along $-\hat{r}$. Thus, the stress $|\sigma'_{rr}|$ is always smaller than the $\chi = 1$ case. $\sigma'_{rr} = 0$ for $\chi = 0$. (B), (C), and (D) are for $\phi = 0.72$. (B) shows the vorticity obtained from a coarse-grained velocity field for different $\chi$ values. The color bar denotes the magnitude and handedness of the vorticity. The black and the white arrows correspond to $\sigma_{rr}$ along $\hat{r}$ and $-\hat{r}$, respectively. (C) shows the peak height, $P_H(r)$, of $\phi_A(r)$ for different $\chi$ values. The peak height is measured from the baseline shown in Fig. \ref{['Figure1']}D. The dashed vertical lines delineate the bulk from the edge. (D) shows the full width at half maximum (FWHM) in units of $d_P$ for peaks close to the edge. The peak width is a direct measure of the total $\sigma_{rr}$.