Large phonon-drag enhancement induced by narrow quantum confinement at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface

The thermoelectric power of the two-dimensional electron system (2DES) at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface is explored below room temperature, in comparison with that of Nb-doped ${\mathrm{SrTiO}}_3$ single crystals. For the interface, we find a region below $T=50$ K where thermopower is dominated by phonon drag, whose amplitude is hugely amplified with respect to the corresponding bulk value, reaching values $\sim \mathrm{mV}$/K and above. The phonon-drag enhancement at the interface is traced back to the tight carrier confinement of the 2DES, and represents a sharp signature of strong electron-acoustic phonon coupling at the interface.

Figure 1

(a) Seebeck coefficient $S$ measured for the three interfaces as a function of temperature. (b) Seebeck coefficient for the three Nb-doped single crystals. (c) Sheet resistance $\left(R_{\mathrm{sheet}}\right)$, 2D carrier density $\left(n_{2\mathrm{D}}\right)$, and Hall mobility $\left(\mu \right)$ for the interfaces. (d) Resistivity $\left(\rho \right)$, 3D carrier density $\left(n_{3\mathrm{D}}\right)$, and Hall mobility $\left(\mu \right)$ for the Nb-doped ${\mathrm{SrTiO}}_3$ single crystals.

Figure 2

Seebeck coefficient measured for interface sample A as a function of temperature for three values of the back-gate voltage $V_g$.

Figure 3

(a)–(c) Model calculation of phonon drag vs temperature at varying gas thickness $t$ (indicated for each line in nm). Each panel corresponds to different values of effective masses and charge densities, also reported on each panel. (d) Diffusive Seebeck coefficient (dashed lines) and total (diffusive plus phonon-drag) Seebeck coefficient (full lines) for the three sets of calculations and $t=1$ nm. Green curves are for case (a), red curves for (b), and blue curves for (c). (e) Sheet resistance; (f) electron mobility.

Figure 4

Left panel: $z$-localized squared wave functions with varying localization length, normalized to unity. Right: corresponding Fourier transforms. Each wave function is built as a sum of Gaussian functions, centered in the middle of a perovskite unit cell, further interpolated by a Gaussian envelope of varying thickness.