Mott transition and collective charge pinning in electron doped ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$

We studied the in-plane dynamic and static charge conductivity of electron doped ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ using optical spectroscopy and DC transport measurements. The optical conductivity indicates that the pristine material is an indirect semiconductor with a direct Mott gap of 0.55 eV. Upon substitution of $2\%$ La per formula unit the Mott gap is suppressed except in a small fraction of the material (15%) where the gap survives, and overall the material remains insulating. Instead of a zero energy mode (or Drude peak) we observe a soft collective mode (SCM) with a broad maximum at $40\mathrm{meV}$. Doping to $10\%$ increases the strength of the SCM, and a zero-energy mode occurs together with metallic DC conductivity. Further increase of the La substitution doesn't change the spectral weight integral up to 3 eV. It does however result in a transfer of the SCM spectral weight to the zero-energy mode, with a corresponding reduction of the DC resistivity for all temperatures from 4 to 300 K. The presence of a zero-energy mode signals that at least part of the Fermi surface remains ungapped at low temperatures, whereas the SCM appears to be caused by pinning a collective frozen state involving part of the doped electrons.

Figure 1

Left: doping dependence of the optical conductivity from 0 to 0.15 eV at 300 K and 9 K. The dashed curves represent extrapolations of the optical conductivity obtained from fitting reflectivity $R\left(\omega \right)$ with a Drude-Lorentz parametrization. The shaded areas correspond to the noise level of the original reflectivity data (see Fig. 7). The dark lines are the result of binning the data in intervals of 0.3 meV. Full symbols correspond to the conductivity values measured in DC transport (see Fig. 2). Right: doping dependence in the range of 0 to 1 eV at 9 K.

Figure 2

Temperature dependence of the resistivity for different doping compositions.

Figure 3

Left: doping dependence of optical conductivity in the whole measured range. Right: temperature and doping dependence of the real part of optical conductivity below 1 eV. The spectral features are labeled according to Ref. [22]. Tight-binding calculations for the undoped material at 30 K using the parameters A (same parameters as Ref. [6]) and B (best fit to the optical data) of Table 3 of Appendix pp2 are shown as orange (A) and dark khaki (B, best fit). The result of model A (B) has been scaled down by a factor 5 (2.5) to match the vertical range of the data shown. The dark-khaki curve for $y=0.18$ was calculated with the same band parameters as the dark-khaki curve of the top panel (parameter set B) but the self-consistent solution of the band structure gives a smaller Hubbard gap due to the electron doping.

Figure 4

Top: Effective electron number per Ir atom as a function of energy for different dopings. Bottom: Doping dependence of the coherent $(K^{*}$, black squares) and total $(K$, red circles) free carrier spectral weight. Calculated values are shown for the band parameters reported in Table 3.

Figure 5

Zoom of the optical conductivity in the SCM region of sample $y=0.1$.

Figure 6

Temperature dependence of Hall density (a) and Hall mobility (b) for the $y=0.1$ and the $y=0.18$ sample.

Figure 7

Reflectivity spectra at 4 K and 300 K for different doping levels. Left panel shows an expanded scale from 0 to 150 meV to highlight the range of the optical phonons. At 0.7 eV the reflectance and ellipsometry data were merged. For the latter only 300 K data could be measured, the whole measured data indicated in the right panel. These data were used for the Kramers-Kronig analysis at all other temperatures using the method detailed in this section.

Figure 8

Comparison for the $y=0.1$ sample of the Kramers-Kronig output for the optical conductivity with and without an overall vertical shift of the reflectance spectra by $\pm 2\%$. Since our cryostat design with integrated gold evaporator (used for signal calibration) does not involve any mechanical motion of the sample when comparing sample and reference, the systematic error is in fact below $0.5\%$.

Figure 9

Top: The solid black curve is the real part of the optical conductivity ${\sigma }_1\left(\omega \right)$ at 9 K below 1 eV. The Drude-Lorentz fit is indicated by the dashed red line. The color coded shaded areas correspond to the Drude (green) and Lorentz (all other colors) oscillators. Bottom: Drude (top panel) Lorentz (bottom panel) decomposition below 0.4 eV of the doped samples.

Figure 10

Atomic force microscopy (a) and near-field infrared optics (b) for a pristine sample and two samples with different doping levels.

Figure 11

Top panels: Band structure (top) and optical conductivity corresponding to model A (left) and ${\mathrm{A}}^{\prime }$ (right) of Table 3. Different colors are used to distinguish the different bands more easily, but they have no additional meaning. Bottom panels: Band structure (top) and optical conductivity corresponding to model B (left) and ${\mathrm{B}}^{\prime }$ (right) of Table 3. Labels $(k_1,k_2)$ along the top refer to the actual $\sqrt{2}\times \sqrt{2}$ unit cell in two dimensions containing 2 Ir atoms. Labels $(k_x,k_y)$ along the bottom refer to the undistorted unit cell in two dimensions containing 1 Ir atom and with $k_x,k_y$ along the Ir-O bond direction.