Towards Two-Dimensional Metallic Behavior at ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ Interfaces

Using a low-temperature conductive-tip atomic force microscope in cross-section geometry we have characterized the local transport properties of the metallic electron gas that forms at the interface between ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$. At low temperature, we find that the carriers do not spread away from the interface but are confined within $\sim 10\mathrm{nm}$, just like at room temperature. Simulations taking into account both the large temperature and electric-field dependence of the permittivity of ${\mathrm{SrTiO}}_3$ predict a confinement over a few nm for sheet carrier densities larger than $\sim 6\times {10}^{13}{\mathrm{cm}}^{-2}$. We discuss the experimental and simulations results in terms of a multiband carrier system. Remarkably, the Fermi wavelength estimated from Hall measurements is $\sim 16\mathrm{nm}$, indicating that the electron gas in on the verge of two dimensionality.

Figure 1

CTAFM images in cross section geometry collected at 300 (a) and 8 K (b). Corresponding conductance profiles (c),(d). The inset in (d) shows the same data in logarithmic scale.

Figure 2

(a) Carrier density profile at 10 K for $n_{2\mathrm{D}}=3.3\times {10}^{14}{\mathrm{cm}}^{-2}$. Calculations are performed either with $\chi$ constant (as approximated by Siemons et al. [18]) or with a more realistic variation of $\chi$ with the electric field; see the inset in (c). (b) Dependence of the local electric field with the distance from the LAO/STO interface. The inset shows the corresponding potential profile. (c) Dependence of the dielectric constant with the distance. The electric-field dependence of $\chi$ is shown in the inset.

Figure 3

Dependence of the critical thickness $\xi$ and the maximum interfacial electric field with the sheet carrier density.