Two-stage melting induced by dislocations and grain boundaries in Monolayers of Hard Spheres

Using event-driven Molecular Dynamics simulations, we find that the peculiar two-stage melting scenario of a continuous solid-hexatic transition and a first-order hexatic-liquid transition as observed for an exactly 2D system of hard disks [Bernard and Krauth, Phys. Rev. Lett. 107, 155704 (2011)] persists even for a quasi-2D system of hard spheres with out-of-plane particle motions as high as half the particle diameter. We explain this melting behavior, which is at odds with the KTHNY theory or a first-order fluid-solid transition, by the density-dependence of the dislocation core energy Ec. In the solid, Ec exceeds the critical value of 2.84 kT and melting occurs via dissociation of bound dislocation pairs, whereas in the hexatic phase Ec decreases to the critical value and a first-order grain-boundary induced melting transition preempts the KTHNY scenario.