Dynamical Response and Confinement of the Electrons at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ Interface

With infrared ellipsometry and transport measurements we investigated the electrons at the interface between ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$. We obtained a sheet carrier concentration of $N_{\mathrm{s}}\approx 5–9\times {10}^{13}{\mathrm{cm}}^{-2}$, an effective mass of $m^{*}=3.2\pm 0.4m_e$, and a strongly frequency dependent mobility. The latter are similar as in bulk ${\mathrm{SrTi}}_{1-x}{\mathrm{Nb}}_x{\mathrm{O}}_3$ and therefore suggestive of polaronic correlations. We also determined the vertical concentration profile which has a strongly asymmetric shape with a rapid initial decay over the first 2 nm and a pronounced tail that extends to about 11 nm.

Figure 1

(a) Spectra of ${ϵ}_1$ (10 K) and ${ϵ}_2$ (200 K) for LS-5 (dashed lines) and bare ${\mathrm{SrTiO}}_3$ (solid lines). Insets: Magnification of the differences. Corresponding spectra of $\Delta {ϵ}_{1,2}={ϵ}_{1,2}-{ϵ}_{1,2}(\mathrm{STO})$ for LS-5 (b), LS-3 (c), LS-50 (d), and LS-50-ov (e) showing the Drude response. Top panels show the $T$ dependence of $\Delta {ϵ}_1$. Middle and bottom panels show $\Delta {ϵ}_1$ and $\Delta {ϵ}_2$ as obtained from experiment (symbols) and model calculations (lines), respectively.

Figure 2

Comparison of the sheet carrier concentration $N_s$ (a) and mobility $\mu$ (b) as deduced from IR (full symbols) and transport (TR, open symbols) measurements. The values deduced from the IR data were calculated using $m^{*}=3.2m_e$ as discussed in the text. Error bars represent 1 standard deviation.

Figure 3

(a) Difference spectra of the ellipsometric angle, $\Delta \Psi =\Psi (\mathrm{LS}\mathrm{\text{−}}5)-\Psi (\mathrm{STO})$, showing the Berreman mode in the vicinity of the highest LO phonon of STO. (b) Simulations of $\Delta \Psi$ with a rectangular concentration profile of the conducting layer. Shown from top to bottom (shifted for clarity) are the changes with respect to the thick solid line ($d=11\mathrm{nm}$, $n=5\times {10}^{13}{\mathrm{cm}}^{-3}$, $\mu =33{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$) upon variation of $n$ (dashed, $2.2\times {10}^{13}{\mathrm{cm}}^{-3}$, thin solid $13\times {10}^{13}{\mathrm{cm}}^{-3}$), of $\mu$ (dashed $10{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$, thin solid $80{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$), and $d$ (dashed 6 nm, thin solid 17 nm). (c) Comparison between the data of LS-5 at 10 K (circles) and calculations assuming a rectangular (dashed line) and a graded profile (solid lines) of the conducting layer. The corresponding data for LS-3 are shown as squares. (d) Depth profile of $n$ as obtained from the fit (solid line) in (c). Error bars represent 1 standard deviation.