Band inversion driven by electronic correlations at the (111) ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface

Quantum confinement at complex oxide interfaces establishes an intricate hierarchy of the strongly correlated $d$ orbitals which is widely recognized as a source of emergent physics. The most prominent example is the (001) ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ (LAO/STO) interface, which features a dome-shaped phase diagram of superconducting critical temperature and spin-orbit coupling (SOC) as a function of electrostatic doping, arising from a selective occupancy of $t_{2g}$ orbitals of different character. Here we study (111)-oriented LAO/STO interfaces, where the three $t_{2g}$ orbitals contribute equally to the subband states caused by confinement, and investigate the impact of this unique feature on electronic transport. We show that transport occurs through two sets of electronlike subbands, and the carrier density of one of the sets shows a nonmonotonic dependence on the sample conductance. Using tight-binding modeling, we demonstrate that this behavior stems from a band inversion driven by on-site Coulomb interactions. The balanced contribution of all $t_{2g}$ orbitals to electronic transport is shown to result in strong SOC with reduced electrostatic modulation.

Figure 1

(a) Band diagram of the LAO/STO interface before electronic reconstruction. $\mathrm{\Delta }E$: critical potential buildup. $\varphi$: valence-band offset. (b) Top view of three consecutive (111) ${\mathrm{Ti}}^{4+}$ layers. The red shaded area represents the unit-cell cross section of a bilayer. The three $t_{2g}$ orbitals are shown to evidence their equivalent projection onto the 2DES plane. (c) Left: stacking of ionic planes across the interface. The bottommost ${\mathrm{Ti}}^{4+}$ plane is considered to react with oxygen to form ${\mathrm{TiO}}^{2+}$. Right: resulting electric field across the interface before the electronic reconstruction takes place. (d) Electrostatic potential as a function of the number of unit cells.

Figure 2

(a) Carrier density ($n$) and mobility ($\mu$) as a function of temperature ($T$) measured for the pristine state. Inset: schematic representation of the measurement configuration. (b) Superconducting critical temperature ($T_{\mathrm{c}}$) as a function of sample conductance (${\sigma }_{\mathrm{tot}}$) for different thicknesses of the LAO film. (c) Carrier densities and (d) mobilities as a function of ${\sigma }_{\mathrm{tot}}$.

Figure 3

(a),(b) Band structure along $k_y$ at low and high filling, respectively. Dashed gray line indicates the renormalized Fermi level. Color indicates the orbital character. Stoke indicates the band subset. Inset shows the hexagonal Brillouin zone as well as the $k_x$ ($\mathrm{\Gamma }K$) and $k_y$ (($\mathrm{\Gamma }M$) directions. (c),(d) Corresponding Fermi surfaces. (e) Evolution of the carrier density pertaining to the first ($n_1$) and second ($n_2$) subset of bands as a function of renormalized Fermi level and respective sample conductance.

Figure 4

(a) Variation of conductance $\mathrm{\Delta }\sigma$ as a function of the $B$ field for different levels of electrostatic doping. Black dots: $B_{\min }$. Black lines: fit to the HLN equation. (b) Extracted characteristic lengths $l_{\mathrm{i},\mathrm{so}}$.