Stability of the hexagonal lattice of charged colloids

We discuss the stability of the hexagonal lattice in charged colloidal systems using (i) an effective Yukawa potential characterized by a cutoff introduced to model many-body effects and (ii) the full Poisson-Boltzmann cellular theory. We analyze the hexagonal-to-square structural transition in terms of a simple shear mode, and we scan the phase diagram at T = 0. We find that a short enough cutoff destabilizes the hexagonal lattice, while the more complete Poisson-Boltzmann theory does not show this feature. By expanding the energy in terms of the order parameter of the transition, we identify the main structural differences between the two lattices and we show that the hexagonal lattice could be destabilized by a shoulder-like potential; however, electrostatic interaction is not expected to give rise to an effective potential of this kind.