Metal-insulator transition of the LaAlO${}_3$-SrTiO${}_3$ interface electron system

We report on a metal-insulator transition in the LaAlO${}_3$-SrTiO${}_3$ interface electron system, of which the carrier density is tuned by an electric gate field. Below a critical carrier density $n_c$ ranging from 0.5 to $1.5\times {10}^{13}/{\mathrm{cm}}^2$, LaAlO${}_3$-SrTiO${}_3$ interfaces, forming drain-source channels in field-effect devices, are nonohmic. The differential resistance at zero channel bias diverges within a 2$\%$ variation of the carrier density. Above $n_c$, the conductivity of the ohmic channels has a metal-like temperature dependence, while below $n_c$ conductivity sets in only above a threshold electric field. For a given thickness of the LaAlO${}_3$ layer, the conductivity follows a ${\sigma }_0\propto (n-n_c)/n_c$ characteristic. The metal-insulator transition is found to be distinct from that of the semiconductor 2D systems.

Figure 1

Sketch of the sample structure (top view).

Figure 2

(a) $J(E)$ characteristics of a measurement bridge in a LaAlO${}_3$-SrTiO${}_3$ interface with a 4-uc-thick LaAlO${}_3$ layer (4 K, no applied magnetic field). The bridge was 60 $\mu$m long and 10 $\mu$m wide. At $V_G=-61.2$ V, the $J(E)$ characteristic changes from linear to nonlinear behavior with a much smaller conductivity. At $V_G=-62.1$ V, the differential conductivity at $J~0$ equals $~$10${}^{-7}$ S. (b) $J(E)$ characteristics of (a) plotted in the small current regime. For $V_G⩽-62.1$ V a hysteresis emerges near zero bias and conductivity sets in only above a threshold field $E_{\mathrm{th}}$. This hysteresis is caused by the long RC time in this regime and shrinks to zero on increasing the time constant of the measurement. Because in the insulating regime the voltage $V$ along the bridge is no longer small compared to $V_G$, the respective $J(E)$ characteristics are asymmetric. The color code is the one of (a).

Figure 3

Threshold electric field $E_{\mathrm{th}}$ as shown by Fig. 2 plotted as function of the reduced carrier density $\delta n=(n-n_c)/n_c$. The inset shows the respective $J(E)$ curves.

Figure 4

(a) Conductivities of 10- and 25-$\mu$m-wide channels in 4-uc LaAlO${}_3$-SrTiO${}_3$ interfaces measured as function of the carrier density varied by $V_G$ (in zero magnetic field). For ${\sigma }_0\lesssim e^2/h$, the current-voltage characteristics are nonlinear. Only data points derived from $J(E)$ curves that are reversible for the whole bias range are plotted. (b) Conductivities of LaAlO${}_3$-SrTiO${}_3$ interfaces plotted as function of the reduced carrier density. The scaling curve only includes data points in the ohmic regime. For $\delta n=0$, ${\sigma }_0$ becomes minute (inset).

Figure 5

Magnetoconductance of the 25-$\mu$m sample shown in Fig. 4a measured at 4.2 K. Due to the large Hall voltage in the depleted state, the conductance is symmetrized using $[\sigma (H)+\sigma (-H)]/2$. From high to low carrier density, the corresponding reduced carrier densities, $\delta n$, are 2.96, 0.23, and 0.03, respectively.

Figure 6

Conductivities of all seven devices in LaAlO${}_3$-SrTiO${}_3$ interface samples measured as function of the carrier density as controlled by $V_G$ (in zero magnetic field). For clarity, not all data are shown. The critical carrier density $n_c$ ranges from $0.5\times {10}^{13}/{\mathrm{cm}}^2$ to $1.5\times {10}^{13}/{\mathrm{cm}}^2$. Except for the data of the devices with 8-uc-thick LaAlO${}_3$ layers (sample E to sample G), all data of devices with 4-uc-thick LaAlO${}_3$ layers (sample A to sample D) have the same characteristic.

Figure 7

Conductivities of LaAlO${}_3$-SrTiO${}_3$ interface samples plotted as function of the reduced carrier density. The curve includes data points in the ohmic regime only. Sample A to sample D have 4-uc-thick LaAlO${}_3$ layers, while sample E to sample G have 8-uc-thick LaAlO${}_3$ layers.

Figure 8

Normalized conductivities of LaAlO${}_3$-SrTiO${}_3$ interface samples plotted as function of the reduced carrier density. The conductivity is normalized by ${\sigma }_1$. The values of ${\sigma }_1$ are shown in Table . Sample A to sample D have 4-uc-thick LaAlO${}_3$ layers, while sample E to sample G have 8-uc-thick LaAlO${}_3$ layers.