Metal--Insulator Transition in the Flux-Flow Resistivity of Optimally Doped YBa$_{2}$Cu$_{3}$O$_{6+x}$

We have made high resolution microwave measurements of the flux-flow resistivity of optimally doped YBa$_{2}$Cu$_{3}$O$_{6+x}$ in the mixed state at temperatures down to 1.2~K. We find that the effective resistivity of the vortex cores exhibits a metal--insulator transition, with a minimum at 13~K and a logarithmically growing form below 5~K, as has been seen in the low-temperature DC resistivity of under-doped cuprates in which superconductivity has been globally suppressed. Our work is the first report of a metal--insulator transition in optimally doped YBa$_{2}$Cu$_{3}$O$_{6+x}$, and the first to be seen in a system in which superconductivity has not been globally suppressed. The transition is seen in samples of the highest quality and in magnetic fields as low as 1~T.