Energetics of point defects in the two-dimensional Wigner crystal

The ground-state Coulomb energy and zero-point vibrational energy are calculated numerically for the perfect two-dimensional (2D) Wigner crystal and for a 2D Wigner crystal containing interstitials and vacancies. In the limit of large systems, only the vacancy and the interstitial with threefold rotational symmetry are stable. The scaling of the interaction between like defects with interdefect separation is studied and compared with the predictions of elasticity theory. Each type of point defect lowers the zero-point vibrational energy of the system. The role of point defects in the zero-temperature melting transition is discussed in light of these results.