Abstract
Topological defects such as dislocations are predicted to determine the two-dimensional (2D) melting transition1,2,3,4. 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 membranes5,6,7,8.
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Acknowledgements
We acknowledge discussions with F. Guinea and A.I. Buzdin. The Laboratorio de Bajas Temperaturas is associated with the ICMM of the CSIC. This work was supported by the Spanish MICINN (Consolider Ingenio Molecular Nanoscience CSD2007-00010 program, MAT2008-06567-C02 and FIS2008-00454), the Comunidad de Madrid through program ‘Science and Technology at Millikelvin’, the Aragon Regional Government and NES and ECOM programs of the ESF.
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I.G. carried out and designed the experiments, analysed data and wrote the paper. H.S. designed the experimental set-up, supervised the experiment and analysis, and wrote the paper. A.F.-P., R.C., J.S., J.M.D.T. and M.R.I. carried out the growth and characterization of the samples, carried out the critical current measurements and contributed to the manuscript text. J.M.D.T. and M.R.I. proposed to study the samples with STS. S.V. supervised the experiment and analysis, and wrote the paper.
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Guillamón, I., Suderow, H., Fernández-Pacheco, A. et al. Direct observation of melting in a two-dimensional superconducting vortex lattice. Nature Phys 5, 651–655 (2009). https://doi.org/10.1038/nphys1368
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DOI: https://doi.org/10.1038/nphys1368
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