Two-Dimensional Electron Gases at ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ Interfaces: Orbital Symmetry and Hierarchy Engineered by Crystal Orientation

Recent findings show the emergence of two-dimensional electron gases (2DEGs) at ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interfaces along different orientations; yet details on band reconstructions have remained so far unknown. Via x-ray linear dichroism spectroscopy, we demonstrate that crystal symmetry imposes distinctive 2DEG orbital hierarchies on (001)-and (110)-oriented quantum wells, allowing selective occupancy of states of different symmetry. Such orientational tuning expands the possibilities for electronic engineering of 2DEGs and opens up enticing opportunities to understand the link between orbital symmetry and complex correlated states at ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ quantum wells.

Figure 1

(a) and (b), scanning transmission electron microscopy (STEM) high-angle annular dark field (HAADF) images of ${\mathrm{LaAlO}}_3(8\mathrm{MLs})/{\mathrm{SrTiO}}_3(001)$ and a ${\mathrm{LaAlO}}_3(9\mathrm{MLs})/{\mathrm{SrTiO}}_3(110)$ samples, respectively. The (a) and (b) images were acquired in a Nion UltraSTEM200 and in a FEI Titan (60–300 kV), respectively, and have been Fourier filtered to reduce background noise. The zone axes are along [100] and [001], respectively. Green arrows point to the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface, easily distinguished due to the different intensities between individual La and Sr atomic columns. The scale bar corresponds to a length of 2 nm. The panels on the right hand side show the schematic structure of both interfaces.

Figure 2

Schematics of the interaction of linearly polarized light with $d$ orbitals for normal incidence of x rays on (001)-oriented samples (a) and (110)-oriented samples (b); same schematics for the case of grazing incidence on (001) samples (c) and (110) samples (d). The color shading code is shown in the box. Simulations of XLD signal ($I_a-I_b$) for ${\mathrm{Ti}}^{4+}$ in tetragonal crystal field with positive (e) and negative (f) distortion parameters. The corresponding orbital hierarchy is shown, as related to the relative orientation of light polarization and orbitals.

Figure 3

(a) Normalized XAS spectra of sample ${\mathrm{LaAlO}}_3(8\mathrm{MLs})/{\mathrm{SrTiO}}_3(001)$ measured at normal incidence are shown. XAS curves are plotted for $E_a\parallel [100](I_a)$ and $E_b\parallel [010](I_b)$ polarizations. The XLD spectra ($I_a-I_b$) are also shown. (b) Normalized XAS and XLD spectra of sample ${\mathrm{LaAlO}}_3(9\mathrm{MLs})/{\mathrm{SrTiO}}_3(110)$. Here, the polarizations are $E_a\parallel [001]$ and $E_b\parallel$ [0–10].

Figure 4

Normalized XAS spectra measured at grazing incidence are plotted for bare ${\mathrm{SrTiO}}_3$ surfaces as well as ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interfaces for orientation along (a) [001] and (b) [110]. The ${\mathrm{LaAlO}}_3$ thickness is 8 MLs for (001) and 9 MLs for (110) interfaces. The corresponding XLD spectra are shown for (001)- and (110)-oriented samples in (c) and (d), respectively. Note that (d) also includes the XLD for ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ with thickness 2 MLs. Red lines, corresponding to XLD simulations using ctm4xas, are shifted for clarity. Finally, the energy splittings for (001)- and (110)-oriented samples are sketched in (e).