existence of a kinetic heterogeneity in the relaxation dynamics and mobility of the system.

In fact, the kinetic heterogeneity can be visualized in our system. Typical charge configuration at $T=0.033$, as shown in Fig. 7, exhibits local striped patterns (ordered domains) and interfacial regions due to mismatch between adjacent domains. For a fixed quenching temperature, the average size of these local domains reaches a certain length scale when the system equilibrates. After equilibration, the system structurally rearranges itself going from one configuration to another with local domains of similar length scale. Figure 8 shows the trajectories of moving positive charges over a time interval of 500 MC steps for $T=0.033$ (corresponding to Fig. 7). We can see that there exist local regions with actively moving charges and other regions with relatively immobile charges. Among the active regions, we can find those charges moving along partially filled diagonal channels. We also find some extended interfacial regions where no discernible local order can be identified, that exhibit relatively high mobility. Enhancement of particle diffusion is probably due to the motions of charges along the partially filled diagonals as well as those fluidized motions in the extended interfacial regions. These fastly moving regions 