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Abstract
Topological defects such as dislocations are predicted to determine the two-dimensional (2D) melting transition. In 2D superconducting vortex lattices, macroscopic measurements provide evidence for melting close to the transition to the normal state. However, the direct observation at the scale of individual vortices of the melting sequence has never been carried out. Here, we use scanning tunnelling spectroscopy (STS) to provide step-by-step imaging of a 2D system of vortices up to the melting transition in a W-based superconducting thin film. We show directly the transition into an isotropic liquid below the superconducting critical temperature. Before that, we find a hexatic phase, characterized by the appearance of free dislocations, and a smectic-like phase, possibly formed through partial disclination unbinding. These results represent a significant step in the understanding of the melting of 2D systems, with an impact across several research fields, such as liquid-crystal molecules or lipids in membranes. [PUBLICATION ABSTRACT]