Eur. Phys. J. B 78, 439-447 (2010)
https://doi.org/10.1140/epjb/e2010-10176-y

Superfluid density in a two-dimensional model of supersolid

¹ Laboratoire de Physique Statistique, École Normale Supérieure, UPMC Paris 06, Université Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France
² Institut Jean Le Rond D'Alembert, UMR 7190 CNRS-UPMC, 4 place Jussieu, 75005 Paris, France
³ Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avda. Diagonal las Torres 2640, Peñalolén, Santiago, Chile
⁴ INLN, CNRS-UNSA, 1361 route des Lucioles, 06560 Valbonne, France

Corresponding author: ^a josseran@lmm.jussieu.fr

Received: 28 February 2010
Revised: 27 October 2010
Published online: 6 December 2010

Abstract

We study in 2-dimensions the superfluid density of periodically modulated states in the framework of the mean-field Gross-Pitaevskiǐ model of a quantum solid. We obtain a full agreement for the superfluid fraction between a semi-theoretical approach and direct numerical simulations. As in 1-dimension, the superfluid density decreases exponentially with the amplitude of the particle interaction. We discuss the case when defects are present in this modulated structure. In the case of isolated defects (e.g. dislocations) the superfluid density only shows small changes. Finally, we report an increase of the superfluid fraction up to 50% in the case of extended macroscopical defects. We show also that this excess of superfluid fraction depends on the length of the complex network of grain boundaries in the system.