Direct observation of melting in a two-dimensional superconducting vortex lattice

Abstract

Topological defects such as dislocations and disclinations are predicted to determine the twodimensional (2-D) melting transition [1][2][3] . In 2-D superconducting vortex lattices, macroscopic measurements evidence 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 performed. Here we provide step by step imaging through scanning tunneling spectroscopy of a 2-D system of vortices up to the melting transition in a focused-ion-beam nanodeposited 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, 1 characterized by the appearance of free dislocations, and a smectic-like phase, possibly originated through partial disclination unbinding. These results represent a significant step in the understanding of melting of 2-D systems, with impact across several research fields, such as liquid crystal molecules, or lipids in membranes [4][5][6][7] .The seminal ideas of Kosterlitz and Thouless , have been much discussed in connection with melting of many different 2-D hexagonal crystals. These include crystals formed from elongated rod-like entities such as superfluid vortices, lipids or liquid crystal molecules, as well as from more isotropic constituents, as electrons Wigner crystals, particles or bubbles, or electronic charge density arrangements [8][9][10] . Theoretically, it is found that the unbinding of dislocation pairs creates an intermediate phase in a 2-D hexagonal crystal, named the hexatic phase, which retains sixfold orientational order but has no long range translational order [1][2][3] . The hexatic phase, which appears between the 2-D crystalline phase and the isotropic liquid, has been since then subject of much research. Vortex lattices in superconducting thin films appear as an ideal system where the mechanism of the 2-D melting process can be investigated. Until now, work on the 2-D solid-liquid superconducting vortex lattice transition has focused on macroscopic studies of thermal properties or of critical currents around the melting transition [11][12][13][14][15] . The transition seems to be consistent with the theory of 2-D dislocation-unbinding melting behavior [1][2][3][16][17][18] . However, no local direct observation of melting has been provided. Here we track the modifications induced by temperature on a 2-D vortex system, from its formation up to the isotropic liquid state. Increasing temperature we first observe thermal de-pinning of vortices, which produces a more ordered hexagonal lattice. Melting process is then initiated with 2 the appearance of free dislocations, corresponding to the hexatic phase, from which a smectic-like phase emerges, before the isotropic liquid is formed.Our sample is an amorphous W-based thin film nano-deposited using focused-ion-beam, with a superconducting critical temperature at zero field T c = 4. 15 K 19, 20 . It is an extrem...

Experimental observation of thermal fluctuations in single superconducting Pb nanoparticles through tunneling measurements

“…[1][2][3] However, recent findings promoted by technological developments have revived the interest in this field. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] These advances can shed light on the evolution of the ground state with particle size or the role of (thermodynamic) fluctuations on the stability of the superconducting state. Many earlier reports [19][20][21][22][23] have addressed some of these questions.…”

Imaging superconducting vortex cores and lattices with a scanning tunneling microscope

“…In the same W-based thin films, authors further observe thermally induced vortex de-pinning by imaging the changes in zero field cooled vortex arrangements induced with increasing temperature at different magnetic fields [63]. For example, at 1T the thermal de-pinning of the lattice was observed at 1.5 K. To obtain this value, a sequence of 145 vortex lattice images was taken while increasing the temperature starting from 0.1K in steps of 0.1K.…”

Fingerprints of angulon instabilities in the spectra of matrix-isolated molecules

“…Angulons, on the other hand, are the eigenstates of the total angular momentum operator,L 2 , and therefore the transferred angular momentum is three-dimensional. While vortex instabilities have been subject to several experimental studies in the context of superfluid helium [4,5,[26][27][28][29][30][31], ultracold quantum gases [32][33][34][35][36], and superconductors [37][38][39][40], the transfer of angular momentum to a superfluid via the angulon instabilities has not yet been observed in experiment.In this Letter we provide evidence for the emergence of the angulon instabilities in experiments on CH 3 [41] and NH 3 [42] molecules trapped in superfluid helium nanodroplets. Spectroscopy of molecules matrix-isolated in 4 He has been an active area of research during the last two decades [6][7][8][9][10][11][12][13]43].…”