  Despite many efforts to rationalize the strongly correlated electronic ground
states in doped Mott insulators, the nature of the doping induced insulator to
metal transition is still a subject under intensive investigation. Here we
probe the nanoscale electronic structure of the Mott insulator
Sr$_2$IrO$_{4-\delta}$ with low-temperature scanning tunneling microscopy and
find enhanced local density of states (LDOS) inside the Mott gap at the
location of individual apical oxygen site defects. We visualize paths of
enhanced conductance arising from the overlapping of defect states which
induces finite LDOS at the Fermi level. By combining these findings with the
typical spatial extension of isolated defects of about 2~nm, we show that the
insulator to metal transition in Sr$_2$IrO$_{4-\delta}$ is of percolative
nature.
