Vacancy dynamics and magnetism in a two-dimensional Wigner crystal

The two-dimensional Wigner crystal (WC) occurs in the strongly interacting regime of the two-dimensional electron gas. Recently, the present authors showed from the semi-classical instanton calculation that the cooperative hopping processes of interstitial defect of the WC induce a large ferromagnetic polaron with a large energy scale. We extend this work to the vacancy defect of the WC and obtain its effective T=0 dynamics. In contrast to the interstitial defect, vacancy induces paramagnetic (or antiferromagnetic) tendencies around it. From this we speculate on the phases resulting from doping a small density of vacancies in the WC.