Novel Metal-Insulator Transition at the ${\mathrm{SmTiO}}_3/{\mathrm{SrTiO}}_3$ Interface

We report on a metal-insulator transition (MIT) that is observed in an electron system at the ${\mathrm{SmTiO}}_3/{\mathrm{SrTiO}}_3$ interface. This MIT is characterized by an abrupt transition at a critical temperature, below which the resistance changes by more than an order of magnitude. The temperature of the transition systematically depends on the carrier density, which is tuned from $\sim 1\times {10}^{14}$ to $3\times {10}^{14}{\mathrm{cm}}^{-2}$ by changing the ${\mathrm{SmTiO}}_3$ thickness. An analysis of the transport properties shows non-Fermi-liquid behavior and mass enhancement as the carrier density is lowered. We compare the MIT characteristics with those of known MITs in other material systems and show that they are distinctly different in several aspects. We tentatively conclude that both long-range Coulomb interactions and the fixed charge at the polar interface are likely to play a role in this MIT. The strong dependence on the carrier density makes this MIT of interest for field-tunable devices.

Figure 1

Schematic of the ${\mathrm{SmTiO}}_3/{\mathrm{SrTiO}}_3$ interface, showing the formal charges carried by the layers. The polar discontinuity corresponds to a fixed charge at the interface, which can be compensated by $\mathrm{½}$ mobile electrons per interface unit cell, or $\sim 3\times {10}^{14}{\mathrm{cm}}^{-2}$. The ${\mathrm{SmTiO}}_3$ surface has a similar polar problem and various ways of potentially resolving it (adsorbates, nonstoichiometry, etc.) [15]. For thick ${\mathrm{SmTiO}}_3$, interfaces have the full $3\times {10}^{14}{\mathrm{cm}}^{-2}$ mobile charge density, but for thin ${\mathrm{SmTiO}}_3$, the carrier density is reduced. It is likely that this is due to the proximity to the polar surface. A significant fraction of the mobile electrons, specifically those that are located in $d_{xz,yz}$ orbitals, spread out far into the ${\mathrm{SrTiO}}_3$ [17, 18]. The degree to which the electron gas spreads is determined by a number of boundary conditions, including the carrier density and field-dependent permittivity of ${\mathrm{SrTiO}}_3$. The ${\mathrm{SrTiO}}_3$ thickness thus affects the spatial distribution.

Figure 2

(a) $R_s$ as a function of the temperature for heterostructures with various ${\mathrm{SmTiO}}_3$ (3, 5, 7, and 20 u.c.) and ${\mathrm{SrTiO}}_3$ (20, 60, and 80 nm) thicknesses, respectively, as indicated in the legend. (b) Calculated $d{R}_s/dT$ as a function of the temperature for the same structures. The arrow indicates the resistance anomaly at 110 K, which is observed for all samples. The dashed line is a fit to a power law, $T^n$, behavior of the 20 u.c. ${\mathrm{SmTiO}}_3$ sample, which determined $n\sim 5/3$. The limited temperature range above $T_{\mathrm{MIT}}$ for the other samples precluded similar fits.

Figure 3

$T_{\mathrm{MIT}}$ as a function of $n_s$ for the samples shown in Fig. 2. The dotted line is a guide to the eye. The labels indicate the samples, with the first number referring to the ${\mathrm{SmTiO}}_3$ thickness in number of unit cells and the second number to the ${\mathrm{SrTiO}}_3$ thickness in nanometers. We note that for the sample with 20 u.c. of ${\mathrm{SmTiO}}_3$, which does not show an abrupt MIT, the temperature of the weak upturn in the resistance is shown instead.

Figure 4

(a) ${(e{R}_H)}^{-1}$ as a function of the temperature. Data below 50 K are not shown, as the resistances became too high for reliable Hall measurements for all samples except the one with 20 u.c. of ${\mathrm{SmTiO}}_3$ (note the very large error bars at low temperatures). (b) $H\text{cot}({\theta }_H)$ as a function of $T^2$. The lines are a fit to $T^2$ behavior that is used to obtain $H\alpha$, according to Eq. (1).