Phase Diagram of Electrostatically Doped ${\mathrm{SrTiO}}_3$

Electric double layer transistor configurations have been employed to electrostatically dope single crystals of insulating ${\mathrm{SrTiO}}_3$. Here we report on the results of such doping over broad ranges of temperature and carrier concentration employing an ionic liquid as the gate dielectric. The surprising results are, with increasing carrier concentration, an apparent carrier-density dependent conductor-insulator transition, a regime of the anomalous Hall effect, suggesting magnetic ordering, and finally the appearance of superconductivity. The possible appearance of magnetic order near the boundary between the insulating and superconducting regimes is reminiscent of effects associated with quantum critical behavior in some complex compounds.

Figure 1

Schematic diagrams of the sample and the operation of an EDLT: (Left) Upon application of a positive gate bias, anions are attracted to the gate electrode and cations are repelled, this creates an EDL at the sample surface. (Right) Schematics of top and side views of the sample design. A Pyrex glass cylinder was glued onto the STO wafer using a common epoxy to serve as an IL container. Oxygen-deficient ${\mathrm{SrTiO}}_{3\mathrm{\text{−}}\delta }$ was created below and around the $\mathrm{Ti}/\mathrm{Au}$ electrodes, but not across the channel.

Figure 2

Sheet resistance ($R_s$) vs temperature ($T$) on cooling, at various sheet carrier densities ($n_s$) (in units of ${10}^{13}{\mathrm{cm}}^{-2}$, obtained from the Hall effect at 180 K). When $n_s\geqq 3.3\times {10}^{14}{\mathrm{cm}}^{-2}$, the resistance is well below the quantum resistance $h/e^2=25.8\mathrm{k}\Omega$, and $d{R}_s/dT>0$ persists down to the base temperature of 0.35 K. Note that the resistance peak when $n_s=1.3\times {10}^{14}{\mathrm{cm}}^{-2}$ shifted upon the application of a magnetic field (see Fig. 5). An anomalous Hall effect was observed at this and nearby charge transfers. The inset shows the hysteretic behavior of the sharply rising curve with $n_s=1.4\times {10}^{12}{\mathrm{cm}}^{-2}$. Similar behavior was observed at other carrier concentrations. The arrows in the inset indicate the temperature sweep direction.

Figure 3

The onset of superconductivity at various values of $n_s$ (in units of ${10}^{13}{\mathrm{cm}}^{-2}$, taken at 0.5 K). Note that at higher carrier densities the transition was not observed at temperatures down to 350 mK. In the inset, the $B$ dependence of $R_s$ at $T=400\mathrm{mK}$ for $n_s=3.9\times {10}^{14}{\mathrm{cm}}^{-2}$ shows an increasing resistance until saturation above 0.3 T. This supports the observation of superconductivity.

Figure 4

Anomalous Hall effect. These data were obtained with $n_s=1.3\times {10}^{14}{\mathrm{cm}}^{-2}$ (at 180 K) over a temperature range from 15 to 90 K. The AHE effect was not observed at temperatures of 90 K and above, as shown in the inset (The inset shows the original data before the OHE subtraction and they exhibit no signature of AHE.) A similar effect was observed at neighboring values of $n_s$.

Figure 5

$R_s$ vs $T$ at various magnetic field up to 9 Tesla with $n_s=13\times {10}^{13}{\mathrm{cm}}^{-2}$ with the latter obtained at 180 K. The lower-right inset shows $R_s(B)$ at $n_s=2.0\times {10}^{13}{\mathrm{cm}}^{-2}$ and $T=95\mathrm{K}$, which is the onset temperature for the sharp rise in $R_s(T)$ shown in Fig. 2. It exhibits no change with field.

Figure 6

Phase diagram of STO: the plot of $T$ vs $n_s$ (taken at 180 K) shows the features found. The various dashed lines are simply guides to the eye. The dots represent temperatures and values of $n_s$ at which $R_s$ appeared to diverge. The vertically hatched regions correspond the approximate boundary where $d{R}_s/dT$ changes sign, and the diamonds denote the onset of superconductivity, which does not change much, over a significant range of values of $n_s$. The other crosshatched region denotes the range of temperatures and carrier concentrations over which an AHE was found.