arXiv:1410.7782v1Long-range correlations in two-dimensional (2D) systems are significantly altered by disorder potentials. Theory has predicted the existence of disorder-induced phenomena, such as Anderson localization or the emergence of a Bose glass. More recently, it has been shown that when disorder breaks 2D continuous symmetry, long-range correlations can be enhanced. Experimentally, developments in quantum gases have allowed the observation of the effects of competition between interaction and disorder. However, experiments exploring the effect of symmetry-breaking disorder are lacking. Here, we create a 2D vortex lattice at 0.1 K in a superconducting thin film with a well-defined 1D thickness modulation - the symmetry-breaking disorder - and track the field-induced modification using scanning tunnelling microscopy. We find that the 1D modulation becomes incommensurate with the vortex lattice and drives an order-disorder transition, behaving as a scale-invariant disorder potential. We show that the transition occurs in two steps and is mediated by the proliferation of topological defects. The resulting critical exponents determining the loss of positional and orientational order are far above theoretical expectations for scale-invariant disorder and follow instead the critical behaviour describing dislocation unbinding melting. Our data show that randomness disorders a 2D crystal, with enhanced long-range correlations due to the presence of a 1D modulation.This work was supported by the Spanish MINECO (FIS2011-23488, MAT2011-27553-C02, MAT 2012-38318-C03, Consolider Ingenio Molecular Nanoscience CSD2007-00010), the Comunidad de Madrid through program Nanobiomagnet (S2009/MAT-1726) and by the Marie Curie Actions under the project FP7-PEOPLE-2013-CIG-618321 and contract no. FP7-PEOPLE-2010-IEF-273105.Peer Reviewe
