Direct Visualization of Ambipolar Mott Transition in Cuprate ${\mathrm{CuO}}_2$ Planes

Identifying the essence of doped Mott insulators is one of the major outstanding problems in condensed matter physics and the key to understanding the high-temperature superconductivity in cuprates. We report real space visualization of Mott insulator-metal transition in ${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{\mathrm{CuO}}_{2+y}$ cuprate films that cover both the electron- and hole-doped regimes. Tunneling conductance measurements directly on the copper-oxide (${\mathrm{CuO}}_2$) planes reveal a systematic shift in the Fermi level, while the fundamental Mott-Hubbard band structure remains unchanged. This is further demonstrated by exploring the atomic-scale electronic response of ${\mathrm{CuO}}_2$ to substitutional dopants and intrinsic defects in a sister compound ${\mathrm{Sr}}_{0.92}{\mathrm{Nd}}_{0.08}{\mathrm{CuO}}_2$. The results may be better explained in the framework of self-modulation doping, similar to that in semiconductor heterostructures, and form a basis for developing any microscopic theories for cuprate superconductivity.

Figure 1

(a) XRD spectra for ${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{\mathrm{CuO}}_{2+y}$ films ($\sim 60$ unit cells) at varied $x$. Inset: the schematic crystal structure of SLCO. (b) Out-of-plane lattice constant $c$ as a function of $x$. (c),(d) Integrated differential phase contrast-STEM images of $n(p)\text{−}\mathrm{SLCO}/\mathrm{SrTi}{\mathrm{O}}_3$ heterostructures, with the interfaces marked by the horizontal dashes. In contrast to $n$-SLCO without apical oxygen, an excess of oxygens (marked by the red and green arrows) register at the apical sites of Cu and change alternately in intensity and shape in $p$-SLCO cuprates, while the planar oxygens (orange arrows) in the ${\mathrm{CuO}}_2$ planes exhibit no spatial variation. (e),(f) STM topographies ($80\times 80{\AA }^2$) of $n$-type ($x=0.076$) and $p$-type ($x=0.167$) SLCO films. Tunneling conditions are (e) $V=-1.0\mathrm{V}$, $I=10\mathrm{pA}$, and (f) $V=-0.3\mathrm{V}$, $I=50\mathrm{pA}$.

Figure 2

(a) Spatially averaged differential conductance $dI/dV$ spectra of SLCO films under various doping levels. Gray solid lines and short bars indicate $E_F$ and the midgap energy $E_i$ throughout. For each $dI/dV$ spectrum, the tunneling junction is stabilized to the starting voltage from the negative side and $I=100\mathrm{pA}$ except for $x=0.132$ and 0.167 ($I=200\mathrm{pA}$). (b),(c) Representative $dI/dV$ spectra taken at equal separations (1 nm) in $n$-SLCO ($x=0.100$, $V=-1.6\mathrm{V}$, $I=100\mathrm{pA}$) and $p$-SLCO ($x=0.206$, $V=1.8\mathrm{V}$, $I=200\mathrm{pA}$). Inserted are schematic energy bands of cuprates, only showing the CTB (green) and UHB (unfilled). (d) Statistically measured onset energies of CTB and UHB (top), charge-transfer gap ${\mathrm{\Delta }}_{\mathrm{CT}}$ (middle), and $E_F$ shift relative to $E_i$ (bottom) versus the La dopant.

Figure 3

(a) STM topography of SNCO films ($40\times 40{\AA }^2$, $V=1.5\mathrm{V}$, $I=20\mathrm{pA}$). (b) Tunneling spectra acquired along a trajectory of 26.5 Å on ${\mathrm{CuO}}_2$. The blue and black dashes mark the UHB and CTB onsets, respectively. (c),(d) Atomic-resolution topography ($20\times 20{\AA }^2$, $V=-1.4\mathrm{V}$, $I=20\mathrm{pA}$) of a single ${\mathrm{Nd}}_{\mathrm{Sr}}$ dopant and $dI/dV$ spectra along a trajectory of 16.4 Å from ${\mathrm{Nd}}_{\mathrm{Sr}}$ (bottom curve). (e),(f) STM topography ($20\times 20{\AA }^2$, $V=1.0\mathrm{V}$, $I=20\mathrm{pA}$) of an intrinsic ${\mathrm{O}}_A$ acceptor and $dI/dV$ spectra along a trajectory of 12.2 Å from its center (bottom curve). (g),(h) STM topography ($20\times 20{\AA }^2$, $V=1.5\mathrm{V}$, $I=20\mathrm{pA}$) of a Cu vacancy (${\mathrm{V}}_{\mathrm{Cu}}$) and $dI/dV$ spectra along a trajectory of 12.8 Å from its center (bottom curve). The set point is stabilized at $V=1.5\mathrm{V}$ and $I=50\mathrm{pA}$. Orange dots denote the top Cu atoms.

Figure 4

(a) Local DOS spectra along the white arrow of the inserted STM topography ($62\times 62{\AA }^2$, $V=0.4\mathrm{V}$, $I=20\mathrm{pA}$). Every curve is the mean of 16 $dI/dV$ spectra inside the color-coded square. For clarity, the curves have been vertically offset by 0.05 nS. (b) Correlations between UHB onsets (top), ${\mathrm{\Delta }}_{\mathrm{CT}}$ (bottom), and CTB onsets. (c) Maps of UHB onsets, CTB onsets, and ${\mathrm{\Delta }}_{\mathrm{CT}}$.