Polar catastrophe and electronic reconstructions at the ${\text{LaAlO}}_3/{\text{SrTiO}}_3$ interface: Evidence from optical second harmonic generation

The so-called “polar catastrophe,” a sudden electronic reconstruction taking place to compensate for the interfacial ionic polar discontinuity, is currently considered as a likely factor to explain the surprising conductivity of the interface between the insulators ${\text{LaAlO}}_3$ and ${\text{SrTiO}}_3$. We applied optical second harmonic generation, a technique that a priori can detect both mobile and localized interfacial electrons, to investigating the electronic polar reconstructions taking place at the interface. As the ${\text{LaAlO}}_3$ film thickness is increased, we identify two abrupt electronic rearrangements: the first takes place at a thickness of 3 unit cells, in the insulating state; the second occurs at a thickness of 4–6 unit cells, i.e., just above the threshold for which the samples become conducting. Two possible physical scenarios behind these observations are proposed. The first is based on an electronic transfer into localized electronic states at the interface that acts as a precursor of the conductivity onset. In the second scenario, the signal variations are attributed to the strong ionic relaxations taking place in the ${\text{LaAlO}}_3$ layer.

Figure 1

(Color online) Sheet resistance versus temperature for two LAO/STO conducting samples having LAO thickness $d=4\text{u}\text{.c}\text{.}$, one from set 1 (solid line, blue) and the other from set 2 (dashed line, red). In both a metallic behavior is evident with a small resistance increase for the sample of set 1 at low temperatures.

Figure 2

(Color online) Schematic of the homodyne SHG experiment. The sample is irradiated with laser pulses at frequency $\omega$ (drawn in red/gray). The SH light ($2\omega$, in green/light gray) generated in reflection by the upper surface of the sample (including the interface) is made to interfere with the SH generated by a reference quartz crystal (R) illuminated by the reflected beam at the fundamental frequency (for clarity, in the figure the two beams are shown as being spatially separated; in reality, they are almost perfectly collinear and superimposed). The latter is moved along the beam path (with displacement $L$), so as to modulate the phase difference of the two SH terms by exploiting air dispersion. A filter (F) stops the reflected light of frequency $\omega$ before detection. The incidence angle is $64°$. The input/output polarizations $s$ and $p$ used in our experiments are also shown, with $s$ denoting an optical electric field parallel to the sample surface $xy$ and $p$ a field lying in the incidence plane $yz$.

Figure 3

Example of the SHG signal intensity (dots) detected for increasing input pulse energy (sample of set 1 with $d=6\text{u}\text{.c}\text{.}$); the line is a quadratic best fit.

Figure 4

(Color online) Two examples of SH interference fringes observed in our HSHG experiments ($sp$ polarizations) for samples of set 1 having LAO thickness $d=3\text{u}\text{.c}\text{.}$ (lower curve, red dots) and $d=4\text{u}\text{.c}\text{.}$ (upper curve, blue dots).

Figure 5

(Color online) Panels [(a)–(b)]: Amplitude of the SHG effective nonlinear susceptibilities (a) ${\chi }_{sp}^{\left(2\right)}$ and (b) ${\chi }_{pp}^{\left(2\right)}$ measured as a function of LAO thickness $d$ for samples of set 1 (blue squares) and set 2 (red circles). Different data points with the same $d$ refer to different samples. The dashed horizontal line gives the average SHG amplitude of the STO substrates $\left(d=0\right)$. The dot-dashed vertical line corresponds to the measured threshold thickness (i.e., between 3 and 4 u.c.) for the onset of conductivity. Inset of panel (b): imaginary component of ${\chi }_{pp}^{\left(2\right)}$ (data of set 2 are rescaled by a factor 4 for clarity). Panel (c): Sheet conductivity measured for most of our samples; note that all four samples with $d=3\text{u}\text{.c}\text{.}$ were found to be insulating, in the absence of external fields. Panel (d): HSHG $sp$ signal for a $d=3\text{u}\text{.c}\text{.}$ sample of set 2 in its insulating (red squares) and conductive (blue circles) state, respectively obtained by applying $-100$ and $+100\text{V}$ to a back gate (Ref. 3). All data were taken at room temperature.

Figure 6

(Color online) Complex effective SHG nonlinear susceptibility ${\chi }_{sp}^{\left(2\right)}={\chi }_{sp}^{\prime }+i{\chi }_{sp}^{″}$ panels (a) and (b) and ${\chi }_{pp}^{\left(2\right)}={\chi }_{pp}^{\prime }+i{\chi }_{pp}^{″}$ panels (c) and (d) of the LAO/STO heterostructure for samples of set 1 [(a) and (c)] and set 2 [(b) and (d)] having different LAO thicknesses $d$. The polar angle of each point corresponds to the argument (or phase) of the complex susceptibility, as measured by HSHG (defined to zero for $d=0$). The numbers typed next to the data points give the thicknesses of the LAO films in u.c. The two arrows in each panel (solid-line green and dashed-line red) indicate the two abrupt electronic transitions discussed in the text.