Imaging the dynamics of single vortices on grain boundaries in YBa$_2$Cu$_3$O$_{6+x}$ thin films

We use a scanning Hall probe microscope with single vortex resolution to study the dynamics of single vortices on grain boundaries in YBa$_2$Cu$_3$O$_{6+x}$ thin films with ~10 kHz bandwidth. In the presence of an applied current, we observe individual vortices hopping between pinning sites. Detecting the motion of individual vortices allows us to probe the very- low-voltage regime of the current -voltage ($I-V$) characteristic, at voltage levels of $2\cdot10^{-15}$ V. By scanning the grain boundary we show local $I-V$ curves and investigate the statistical processes at the onset of vortex motion.