Imaging Nanoscale Electronic Inhomogeneity in the Lightly Doped Mott Insulator ${\mathrm{C}\mathrm{a}}_{2-x}{\mathrm{N}\mathrm{a}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_2{\mathrm{C}\mathrm{l}}_2$

The spatial variation of electronic states was imaged in the lightly doped Mott insulator ${\mathrm{C}\mathrm{a}}_{2-x}{\mathrm{N}\mathrm{a}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_2{\mathrm{C}\mathrm{l}}_2$ using scanning tunneling microscopy or spectroscopy. We observed nanoscale domains with a high local density of states within an insulating background. The observed domains have a characteristic length scale of 2  nm ($\sim 4–5a$, $a$: lattice constant) with preferred orientations along the tetragonal [100] direction. We argue that such spatially inhomogeneous electronic states are inherent to slightly doped Mott insulators and play an important role for the insulator to metal transition.

Figure 1

(a) $15\mathrm{n}\mathrm{m}\times 15\mathrm{n}\mathrm{m}$ STM images of (001) cleavage planes of ${\mathrm{C}\mathrm{a}}_{1.92}{\mathrm{N}\mathrm{a}}_{0.08}{\mathrm{C}\mathrm{u}\mathrm{O}}_2{\mathrm{C}\mathrm{l}}_2$ single crystals taken at a sample bias ($V_{\mathrm{s}}$) of 200 mV, a tunneling current ($I_{\mathrm{t}}$) of 10 pA and at 7.0 K. (b) Crystal structure of ${\mathrm{C}\mathrm{a}}_{2-x}{\mathrm{N}\mathrm{a}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_2{\mathrm{C}\mathrm{l}}_2$. (c) Autocorrelation patterns of (a).

Figure 2

(a) $dI/dV$ spectra measured along the line shown in (b). Each spectrum is shifted vertically dependent on the position. For clarity, the spectra taken at apparently lower positions are colored blue; the spectra taken at apparently higher positions are colored red. (b) STM image with the trajectory along which the spectra in (a) were measured. The colors of the line in (b) identify the positions where the $dI/dV$ spectra with the same color in (a) were observed.

Figure 3

The averaged LDOS from the high (red, solid line) and the low (blue, broken line) domains are shown for a $x=0.08$ sample. The LDOS was estimated from the $dI/dV$ spectrum by calibrating the tip-sample distance. The vertical ticks located $\pm 10\mathrm{m}\mathrm{e}\mathrm{V}$ indicate the knees in the LDOS spectra. The inset shows the topographic image taken at $V_{\mathrm{s}}=200\mathrm{m}\mathrm{V}$ and $I_{\mathrm{t}}\sim 100\mathrm{p}\mathrm{A}$ with markers where the spectra were taken ($\mathrm{\text{red cross}}=\mathrm{\text{bright}}$; $\mathrm{\text{blue diamond}}=\mathrm{\text{dark}}$). Colors of markers correspond to the colors of spectra in the main panel.

Figure 4

Doping dependence of STM images and $dI/dV$ spectra of ${\mathrm{C}\mathrm{a}}_{2-x}{\mathrm{N}\mathrm{a}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_2{\mathrm{C}\mathrm{l}}_2$. The topographic images (a), (b), and (c) were from $x=0.06$ (insulator), $x=0.08$ (right at IMT), and $x=0.10$ (superconductor) samples, respectively. (a) was taken at $V_{\mathrm{s}}=300\mathrm{m}\mathrm{V}$, $I_{\mathrm{t}}\sim 100\mathrm{p}\mathrm{A}$, and $T=5.0\mathrm{K}$. (b) and (c) were taken at $V_{\mathrm{s}}=200\mathrm{m}\mathrm{V}$, $I_{\mathrm{t}}\sim 100\mathrm{p}\mathrm{A}$, and $T=4.7\mathrm{K}$. The image from $x=0.08$ (b) was taken on different surface from that of Fig. 3, demonstrating the reproducibility of main features. (d) and (e) are averaged differential conductance spectra collected from the bright and dark regions, respectively. The spectra are shifted vertically for clarity and the horizontal bars indicate zero. The vertical tick marks indicate the energies of the shoulder structures in the spectra.