Poor electronic screening in lightly doped Mott insulators observed with scanning tunneling microscopy

The effective Mott gap measured by scanning tunneling microscopy (STM) in the lightly doped Mott insulator $(\rm{Sr}_{1 -x}\rm{La}_x)_2\rm{IrO}_4$ differs greatly from values reported by photoemission and optical experiments. Here, we show that this is a consequence of the poor electronic screening of the tip-induced electric field in this material. Such effects are well known from STM experiments on semiconductors, and go under the name of tip-induced band bending (TIBB). We show that this phenomenon also exists in the lightly doped Mott insulator $(\rm{Sr}_{1 -x}\rm{La}_x)_2\rm{IrO}_4$ and that, at doping concentrations of $x\leq 4 \%$, it causes the measured energy gap in the sample density of states to be bigger than the one measured with other techniques. We develop a model able to retrieve the intrinsic energy gap leading to a value which is in rough agreement with other experiments, bridging the apparent contradiction. At doping $x \approx 5 \%$ we further observe circular features in the conductance layers that point to the emergence of a significant density of free carriers in this doping range, and to the presence of a small concentration of donor atoms. We illustrate the importance of considering the presence of TIBB when doing STM experiments on correlated-electron systems and discuss the similarities and differences between STM measurements on semiconductors and lightly doped Mott insulators.