Quantum dislocations: the fate of multiple vacancies in two-dimensional solid 4He

Abstract

Defects are believed to play a fundamental role in the supersolid state of 4He. We havestudied solid 4He in two dimensions (2D) as a function of the number of vacanciesnv, up to 30, inserted in the initial configuration atρ = 0.0765 Å − 2, close to the melting density, with the exact zero-temperature shadow path integral groundstate method. The crystalline order is found to be stable also in the presenceof many vacancies and we observe two completely different regimes. For smallnv,up to about 6, vacancies form a bound state and cause a decrease of the crystalline order. At largernv, the formation energy of an extra vacancy at fixed density decreases by one order ofmagnitude to about 0.6 K. It is no longer possible to recognize vacancies in the equilibratedstate because they mainly transform into quantum dislocations and crystalline order isfound almost independently of how many vacancies have been inserted in the initialconfiguration. The one-body density matrix in this latter regime shows a non-decayinglarge distance tail: dislocations, that in 2D are point defects, turn out to be mobile, theirnumber is fluctuating, and they are able to induce exchanges of particles across the systemmainly triggered by the dislocation cores. These results indicate that the notionof the incommensurate versus the commensurate state loses meaning for solid 4He in 2D, because the number of lattice sites becomes ill defined when the system is notcommensurate. Crystalline order is found to be stable also in 3D in the presence of up to100 vacancies.