Inverse melting and re-entrant transformations of the vortex lattice in amorphous Re₆Zr thin film

"Inverse melting" refers to a rare phenomenon where an increase in temperature can induce a transition from a liquid to a solid. The vortex lattice in Type II superconductors is one system where inverse melting has been theoretically predicted. Here, we report the inverse melting of vortices in an amorphous Re₆Zr thin film with moderate vortex pinning under the application of a magnetic field. By imaging the vortex state using a scanning tunnelling microscope, we show that at low fields and temperatures, the vortices form a "pinned liquid", that is characterised by low mobility of the vortices and vortex density that is spatially inhomogeneous. As the temperature or magnetic field is increased, the vortices get ordered, eventually forming a nearly perfect vortex solid before melting again into a liquid. Complementing direct imaging with transport measurements, we show that these transformations leave distinct signatures in the magnetotransport properties of the superconductor.