Layer-by-Layer Evolution of a Two-Dimensional Electron Gas Near an Oxide Interface

We report the momentum-resolved measurement of a two-dimensional electron gas at the ${\mathrm{LaTiO}}_3/{\mathrm{SrTiO}}_3$ interface by angle-resolved photoemission spectroscopy (ARPES). Thanks to an advanced sample preparation technique, the orbital character of the conduction electrons and the electronic correlations can be accessed quantitatively as each unit cell layer is added. We find that all of these quantities change dramatically with distance from the interface. These findings open the way to analogous studies on other heterostructures, which are traditionally a forbidden field for ARPES.

Figure 1

Experimental constant-energy maps at $E_{\mathrm{F}}$ and schematics of the Fermi surfaces at the vacuum interface of the ${\mathrm{SrTiO}}_3(n)/{\mathrm{LaTiO}}_3/{\mathrm{SrTiO}}_3$ ($n=0–3$; sample $L1$ or $L1Sn$) sandwich structures. Notice the clear change of the Fermi surface, corresponding to the transition from Ti $3d_{xy}$ (orange) to $3d_{xz,yz}$ (blue) oriented states (${\mathrm{SrTiO}}_3$ lattice constant $a=3.905\AA$ and $\pi /a=0.805{\AA }^{-1}$). At the bottom, corresponding microscopic structures of the samples are illustrated by adding unit cell layers of ${\mathrm{LaTiO}}_3$ (red shade) and ${\mathrm{SrTiO}}_3$ (blue shade) on the ${\mathrm{SrTiO}}_3$ buffer layers [La (red), Sr (blue), Ti (black), and oxygen (yellow)].

Figure 2

(a)–(d) Constant-energy maps of the states at $E_{\mathrm{F}}$ in the Brillouin zone at ${\Gamma }_{11}=(2\pi ,2\pi )$ on samples $L1$ to $L1S3$. The circular (elliptic) contours are identified as the Fermi surfaces of the out-of-plane-oriented (in-plane-oriented) $d_{xy}$ ($d_{xz,yz}$) ellipsoidal pockets, respectively. (e)–(h) Energy dispersions along the horizontal dashed lines ($\Gamma X$ direction) in (a)–(d) display the shift of the band bottom as well as the orbital occupancy switching. The white dotted lines are guides to the eye and mimic the band dispersions. (Measurement temperature 20 K with $hv=99\mathrm{eV}$.)

Figure 3

(a) Surface layer occupancies of the Ti $3d$ orbitals ($d_{xy}$, filled circles; $d_{xz,yz}$, filled diamonds) and charge density ($\mathrm{per}{\mathrm{cm}}^2$ at the surface layer; open squares) of individual unit-cell layers near the interface. At the charge-donating ${\mathrm{LaTiO}}_3$ layer (${\mathrm{SrTiO}}_3$ $\mathrm{\text{thickness}}=0$) the $d_{xy}$ are the dominant states, while for increasing ${\mathrm{SrTiO}}_3$ thickness the electrons acquire more and more $d_{xz,yz}$ character. At $L1S2$ there is no longer a trace of the $d_{xy}$ states at $E_{\mathrm{F}}$. By taking into account the degeneracy between $d_{xz}$ and $d_{yz}$ orbitals, the total occupancy of the $d_{xz,yz}$ states is twice the value shown here. The overall surface charge density shows little variation ($<20\%$), comparable with the error bar of the measurement. Note that the error bars are largest for sample $L1S1$, where the contours have the worst definition. (b) Energy distribution curves in correspondence of ${\Gamma }_{11}$, showing the reduction in the quasiparticle weight for sample $L1S1$ and the absence of any intensity at $E_{\mathrm{F}}$ in the ${\mathrm{SrTiO}}_3$ buffer layer.