Anisotropic multicarrier transport at the (111) ${\mathbf{LaAlO}}_3/{\mathbf{SrTiO}}_3$ interface

The conducting gas that forms at the interface between ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$ has proven to be a fertile playground for a wide variety of physical phenomena. The bulk of previous research has focused on the (001) and (110) crystal orientations. Here we report detailed measurements of the low-temperature electrical properties of (111) LAO/STO interface samples. We find that the low-temperature electrical transport properties are highly anisotropic in that they differ significantly along two mutually orthogonal crystal orientations at the interface. While anisotropy in the resistivity has been reported in some (001) samples and in (110) samples, the anisotropy in the (111) samples reported here is much stronger and also manifests itself in the Hall coefficient as well as the capacitance. In addition, the anisotropy is not present at room temperature and at liquid nitrogen temperatures, but only at liquid helium temperatures and below. The anisotropy is accentuated by exposure to ultraviolet light, which disproportionately affects transport along one surface crystal direction. Furthermore, analysis of the low-temperature Hall coefficient and the capacitance as a function of back gate voltage indicates that in addition to electrons, holes contribute to the electrical transport.

Figure 1

(a) Schematic representation of the Ti $d_{xy}$, $d_{yz}$, and $d_{xz}$ orbitals in a cubic crystal viewed along the [111] direction. (b) Schematic representation of the surface of the (111) LAO/STO sample chip, showing the four Hall bars. The electrical connections for longitudinal and Hall resistance measurements used for the two Hall bars that are discussed in detail in the text are as marked. Also shown are the crystal directions determined from x-ray measurements.

Figure 2

(a) $6\mu \mathrm{m}\times 6\mu \mathrm{m}$ AFM topography scan of the LAO/STO sample surface. The $x$ axis corresponds to the $\left[1\overline{1}0\right]$ direction and the $y$ axis to the $\left[\overline{1}\overline{1}2\right]$ direction. (b) Low temperature resistance vs temperature sweeps for the two crystal directions.

Figure 3

(a) Longitudinal sheet resistance $R_{\square }$ of the $\left[1\overline{1}0\right]$ and $\left[\overline{1}\overline{1}2\right]$ direction Hall bars as a function of the back gate voltage $V_g$. The sweep direction is marked by arrows. The green and blue curves show the average of the up and down sweeps for the two samples. (b) Logarithmic plot of $R_{\square }$ vs $V_g$ at two different sweep rates for the $\left[1\overline{1}0\right]$ sample. The black/(blue) curve corresponds to a 16/(24) hour long sweep of the back gate with its averaged curve in green/(red). Data taken at 4.4 K.

Figure 4

Symbols, measured Hall coefficient $R_H$ of $V_g$ for the two crystal orientations; solid lines are fits to the two-band model described in the text. All measurements were performed at 4.4 K.

Figure 5

(a) Schematic of the capacitance measurement apparatus. The current pre-amplifier acts as a virtual ground connected to the 2DEG. (b) Capacitance of control sample, fabricated on chip with the hall bars, as a function of $V_g$, at 4.4 K. Averaged measured capacitance of the two Hall bars. (c) All measurements were performed at 4.4 K.

Figure 6

Comparison of $R_{\square }$, $R_H$, and $C$ as a function of $V_g$ before and after UV irradiation. Red represents data or fits before UV irradiation; black represents data or fits after UV irradiation. (a), (b), and (c) are for the $\left[1\overline{1}0\right]$ direction; (d), (e), and (f) are for the $\left[\overline{1}\overline{1}2\right]$ direction. Parameters for the fits to Eq. (1) after UV irradiation are given in Table 2. All measurements were performed at 4.4 K.

Figure 7

Model diagram of the measurement $R_S$ corresponds to the sheet resistance of the 2DEG, $C_T$ corresponds to measured capacitance, and $G$ the conductance of the STO substrate.

Figure 8

Real and imaginary components of the admittance as a function of the frequency $f=\omega /2\pi$ of the $\left[1\overline{1}0\right]$ Hall bar at 4.4 K, measured as shown in Fig. 7 for $V_g=X$ V. The black curves are fits to Eq. (S(B1)) with parameters $R_s=25.4k\mathrm{\Omega }/\square$, $G=1E-15S$ and $C=63.5pF$.

Figure 9

Solid symbols: Capacitance obtained by simultaneously fitting the real and imaginary components of the measured admittance to Eq. (B2) at each value of $V_g$, for both Hall bars at 4.4 K. Solid lines are the measured quadrature component divided by $\omega$.