Thermopower in oxide heterostructures: The importance of being multiple-band conductors

We combine transport experiments, advanced ab initio calculations, and model analysis to determine the thermoelectric power in the two-dimensional electron gas formed at the paradigmatic oxide interface SrTiO${}_3$/LaAlO${}_3$. We demonstrate that contrary to popular expectation, quantum confinement does not enhance the thermoelectric power of the electron gas at this interface with respect to its corresponding three-dimensional case. Our analysis directly relates the thermopower behavior to band structure characteristics typical of the oxide heterostructure (i.e., on-site and intersite band splitting), furnishing general interpretive prescriptions to search for oxide heterostructures with improved thermoelectric capabilities.

Figure 1

Calculated STO/LAO Ti $t_{2g}$ bands for (left) the metallic, fully compensated interface (charged by $Q=1/2$ el/unit area, equivalent to $n_s=3.2\times {10}^{14}$ cm${}^{-2}$), and (right) the undoped, insulating interface. They represent two physical situations of a LAO thickness larger and smaller, respectively, than the threshold value necessary for the occurrence of the insulating metal transition. The zero is set to the Fermi energy on the left and to the band bottom on the right. $\Delta t_{2g}$ is the on-site $d_{xy}-(d_{xz},d_{yz})$ orbital splitting, $m_l=0.7m_e$, and $m_h=8.8m_e$ light and heavy electron masses.

Figure 2

2DEG sheet resistivity (${\rho }_s$), STO bulk resistivity ($\rho$), and Seebeck coefficient ($S$) measured (EXPT, left panels) and calculated (BBT, right) for a 5 u.c. STO/LAO interface (solid black lines) and several $n$-doped STO bulk samples. The Hall-measured concentrations are $n_s=2.4\times {10}^{13}$ cm${}^{-2}$ for the STO/LAO sample and $n_{3\text{D}}={10}^{21}$ cm${}^{-3}$ (long-dashed), $3\times {10}^{20}$ cm${}^{-3}$ (dash-dotted), and $2\times {10}^{19}$ cm${}^{-3}$ (dotted) for the STO samples. For the interface, two calculated values (2DEG${}_0$) and (2DEG${}_{1/2}$) are reported, corresponding to the band structure of the insulating and fully compensated interfaces, respectively. The 2DEG thickness establishing the 2D-3D equivalence is indicated as $L_{\text{eq}}$.

Figure 3

Total and band-by-band $t_{2g}$ conductivity (left panels) and thermopower (right panels) in the $x$ direction as a function of the total charge of the well $Q$, calculated using the multiband model described in Sec. 2c for the cases illustrated schematically in the right panels. From top to bottom: (a) the 3D case; (b) the 2D $t_{2g}$-degenerate case; (c) the 2D case plus a $d_{xy}-(d_{xz},d_{yz})$ band splitting of 0.1 eV; (d) the 2D case with intersite $d_{xy}$ bands split according to the ab initio calculated STO/LAO band structure for $Q=1/2$.