Two-dimensional electron liquid state at ${\text{LaAlO}}_3{\text{-SrTiO}}_3$ interfaces

Using tunneling spectroscopy we have measured the spectral density of states of the mobile, two-dimensional electron system generated at the ${\text{LaAlO}}_3{\text{-SrTiO}}_3$ interface. As shown by the density of states the interface electron system differs qualitatively, first, from the electron systems of the materials defining the interface and, second, from the two-dimensional electron gases formed at interfaces between conventional semiconductors.

Figure 1

(Color online) Illustration of the experimental configuration. A metallic state is formed at the interface between the ${\text{SrTiO}}_3$ substrate and a 4 uc thick layer of ${\text{LaAlO}}_3$. Scanning tunneling microscopy and spectroscopy are performed by monitoring the tunneling current $I_{\text{t}}$ between the tip and the sample as a function of $V_{\text{s}}$, the voltage at the sample relative to the tip.

Figure 2

(Color online) Scanning probe microscopy images of ${\text{LaAlO}}_3{\text{-SrTiO}}_3$ heterostructures. (a) Topographic FM-SFM image of the ${\text{LaAlO}}_3$ film. (b) Profile taken along the line indicated in (a). (c) Topographic STM image acquired on the ${\text{LaAlO}}_3{\text{-SrTiO}}_3$ heterostructure recorded with a scanning speed of 5 nm/s, a bias voltage $V_{\text{s}}=2\text{V}$, and a current set point of 10 pA. (d) Profile taken along the line indicated in (c). All data were taken at 4.7 K. For further detail see Ref. 24.

Figure 3

(Color online) Comparison of the measured differential conductance and DFT calculated state densities. (a) $\text{NDC}\left(V_{\text{s}}\right)=\left(\partial I_{\text{t}}/\partial V_{\text{s}}\right)/\left(I_{\text{t}}/V_{\text{s}}+ϵ\right)\left(V_{\text{s}}\right)$ characteristics with $ϵ=1\text{pA}/\text{V}$ measured at several sites located far away from topographic steps. The measurements were performed at 4.7 K with fixed tip-sample separations. The different colors reflect different tip-sample separations [purple (light gray): $I_{\text{t},\text{stab}}=70\text{pA}$, $V_{\text{s},\text{stab}}=2.4\text{V}$; blue (dark gray): $I_{\text{t},\text{stab}}=12\text{pA}$, $V_{\text{s},\text{stab}}=1\text{V}$; and red (medium gray): $I_{\text{t},\text{stab}}=12\text{pA}$, $V_{\text{s},\text{stab}}=0.8\text{V}$]. The data were averaged over an interval of 75 mV. The purple (light gray) characteristic was measured on a different sample than the red (medium gray), and blue (dark gray) ones. (b) $\text{Ti}3d$ DOS of the interface ${\text{TiO}}_2$ layer calculated using LDA for a supercell with a 4 uc thick ${\text{LaAlO}}_3$ layer. (c) $\text{Ti}3d$ DOS of the interface ${\text{TiO}}_2$ layer calculated using $\text{LDA}+U$. In (a)–(c) the positions of characteristic features in the NDC are marked with gray lines.

Figure 4

(Color online) Illustration of the configuration of 2D electron systems in standard semiconductor interfaces and at the ${\text{LaAlO}}_3{\text{-SrTiO}}_3$ interface. (a) At the interface between the semiconductors an electron gas is generated at a potential well created by band bending, which typically has a width of tens of nanometers as determined by the electronic screening length $s$. The electron states can be approximated by the states of free electrons in this potential well. (b) At the oxide interface the potential well is provided by the Coulomb potential of the titanium ions in the ${\text{TiO}}_6$ octahedra and, to a smaller extent, by band bending. These potential wells are narrower than those at semiconductor interfaces; the “resonant” electron states are well approximated by the $\text{Ti}3d$ $t_{2\text{g}}$ states, which form a 2D electron system extended parallel to the interface. Due to the electronic correlations of the oxide lattices, the mobile electrons form an electron liquid.