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 ${\left({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x\right)}_2{\mathrm{IrO}}_4$ 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 ${\left({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x\right)}_2{\mathrm{IrO}}_4$ and that, at doping concentrations of $x\le 4\%$, 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.

Figure 1

Equipotential lines in STM experiments showing different screening of electric fields in different materials. (a) When STM experiments are performed on samples with a gapped density of states at the Fermi energy, the electric field can penetrate the sample due to the poor electronic screening. (b) In standard STM experiments on metals, the electric field generated by the tip is largely screened within the first atomic layer and there is no significant field penetration.

Figure 2

(a) Topograph of a typical surface with $x=2\%$ doping. The setup conditions are $V_{\mathrm{s}}=-1.1\mathrm{V},I_{\mathrm{s}}=-200$ pA. La dopants (e.g., in the red square) are identified as dark atoms surrounded by a square of brighter conductance, as previously reported in Ref. [26]. (b) Raw tunneling $dI/dV$ spectra measured on ${\left({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x\right)}_2{\mathrm{IrO}}_4$ samples. Each spectrum is the average of ${10}^4\text{–}{10}^5$ spectra measured in regions with different doping. (At zero doping, the samples are perfectly insulating prohibiting STM experiments even at 77 K.) (c) Qualitative explanation of TIBB illustrating why the measured gap exceeds the intrinsic gap. When a bias voltage $V_{\mathrm{b}}$ is applied between tip and sample, TIBB induces a voltage difference ${\phi }_{\mathrm{BB}}$ between the bottom of the sample (grounded) and its surface.

Figure 3

(a) Tip-sample geometry ($r$ and $h$ are not to scale) as used for the electric potential calculation. (b) $G\equiv dI/dV$ spectra measured at different tip-sample distances $h$ on a sample with 2.2% doping. The bias setup voltage $V_{\mathrm{s}}$ is fixed to 1.5 V and the current $I_{\mathrm{s}}$ goes from 600 pA (light blue) to 10 pA (red). In the inset the same plot is shown on a logarithmic scale. (c) The same spectra as in panel (b), each normalized by its its setup junction resistance $I_{\mathrm{s}}/V_{\mathrm{s}}$. The gray line shows the standard deviation $\sigma \left(G\right)$ calculated for each energy, multiplied by a factor two. The inset shows the same plot with logarithmic scale. (d) Extracted intrinsic DOS $g_{\mathrm{s}}$ as a function of $E$ obtained from Eq. (9), after minimization of the model parameter $W_0$, yielding an intrinsic gap of 600 meV. The gray line shows the standard deviation $\sigma \left(g_{\mathrm{s}}\right)$ calculated for each energy, multiplied by a factor two. Since the rescaling of the curves causes different horizontal axes for each curve, we calculate $\sigma \left(g_{\mathrm{s}}\right)$ over extrapolated values of $g_{\mathrm{s}}$ at equally spaced energies. The inset shows the same plot with logarithmic scale. (e) Calculated ${\phi }_{\mathrm{BB}}(V_b,h=5\AA )$ function for different bias voltages. The dashed line represents the voltage corresponding to the work function difference $W_0$, at which no band bending is present. (f) Calculated apparent gap width in the sample DOS for different tip-sample distances. Within distances where typical STM experiments are performed the variation is relatively small compared to the difference with the real gap value.

Figure 4

Visualization of a tip-induced band bending bubble in ${\left({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x\right)}_2{\mathrm{IrO}}_4$ at $x\approx 5\%$. [(a)–(c)] Conductance layers of a field of view of $3\times 3{\mathrm{nm}}^2$ at $g$(−230 meV), $g$(40 meV), and $g$(250 meV). (d) Cross section in energy [($E,r$) plot] of the bubble along the red line in (a). The hyperbolic profile is due to the increasing diameter of the bubble with increasing energy. The arrows indicate the energies at which the conductance layers shown in panels (a)–(c) are extracted.

Figure 5

(a) Topograph of a sample with $\sim 5\%$ doping in a field of view of $17\times 17{\mathrm{nm}}^2$. The setup conditions are ($V_{\mathrm{s}}=460\mathrm{meV},I_{\mathrm{s}}=300\mathrm{pA}$). We count 180 La dopants, easily identified on the surface as bright squares. (b) Conductance layer at $g$(540 meV) in the same field of view. We observe $\sim 15$ circular bubbles of different sizes. The black line indicates the border of the phase separation between the pseudogap puddles (around clusters of dopant atoms) and the Mott areas [32]. (c) Hyperbolas extracted from all the bubbles appearing in the data set shown in (a) and (b). The gray lines are fits to the hyperbolas, added as guide to the eye. Most of the hyperbolas are only above or only below the sample chemical potential, but for a few of them both the positive and the negative energy parts are visible. The two green straight lines emphasize the increasing maximal bubbles' diameter with increasing donor depth below the surface. The vertical black lines indicate the grouping of hyperbolas starting at similar threshold potentials.