Percolative Mott insulator-metal transition in doped Sr$_2$IrO$_4$

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.