Signatures of electronic nematicity in (111) ${\mathbf{LaAlO}}_{\mathbf{3}}/{\mathbf{SrTiO}}_{\mathbf{3}}$ interfaces

The two-dimensional conducting gas (2DCG) that forms at the interface between ${\mathrm{LaAlO}}_3$ (LAO) and ${\mathrm{SrTiO}}_3$ (STO) has been widely studied due to the multitude of in situ tunable phenomena that exist at the interface. Recently it has been shown that nearly every property of the 2DEG that forms at the interface of (111) oriented LAO/STO is strongly anisotropic with respect to the in-plane crystal direction. This in-plane rotational symmetry breaking points to the existence of an electronic nematic phase at the interface that can be modified by an in situ electrostatic back-gate potential. Here we show that the onset temperature of the anisotropy in the longitudinal resistance is $T\approx 22\mathrm{K}$, which does not match up with any known structural transition, and coincides with the onset of anisotropy in the Hall response of the system. Furthermore, below 22 K, charge transport is activated in nature with different activation energies along the two in-plane crystal directions. Such a response implies that the band edges along the two directions are different and provides further evidence of an electronic nematic state at the interface.

Figure 1

(a) Schematic of the first three monolayers at the LAO/STO interface with the $\left[\overline{1}\overline{1}2\right]$ and $\left[1\overline{1}0\right]$ direction labeled. The red atoms represent oxygen, and the blue atoms represent titanium. The titanium atoms are further labeled Ti 1/2/3 to indicate their distance away from the interface with Ti 1 being at the interface. (b) Averaged $R_{\square }$ vs $V_g$ for the $\left[\overline{1}\overline{1}2\right]/\left[1\overline{1}0\right]$ direction in red/black measured simultaneously at 4.4 K. The inset shows a schematic of the device configuration on each measured LAO/STO sample.

Figure 2

(a) $R_{\square }$ vs $T$ for the $\left[\overline{1}\overline{1}2\right]/\left[1\overline{1}0\right]$ directions in red/black measured simultaneously at $V_g=50\mathrm{V}$. Measurable anisotropy can be seen below $\sim 22\mathrm{K}$. (b) $R_{\square }$ vs $1/T$ for $V_g=50$ and 55 V superimposed with fits to activated behavior as described in the text. (c) Plots of the extracted activation temperatures $T_a$ vs $V_g$ for the $\left[\overline{1}\overline{1}2\right]/\left[1\overline{1}0\right]$ directions in red/black, respectively.

Figure 3

(a) The Hall coefficient $R_H$ vs temperature $T$ for the $\left[\overline{1}\overline{1}2\right]$ and $\left[1\overline{1}0\right]$ directions in red and black, respectively, measured simultaneously at $V_g=50\mathrm{V}$. (b) The ratio $r_H^{\mathrm{aniso}}=R_{H_{\left[1\overline{1}0\right]}}/R_{H_{\left[\overline{1}\overline{1}2\right]}}$ of the Hall coefficients along the two crystal directions vs $T$ for different $V_g$'s. (c) Schematic of a system with anisotropic band edges. The solid parabolic bands represent the $\left[\overline{1}\overline{1}2\right]/\left[1\overline{1}0\right]$ directions in red and black, respectively, the horizontal lines represent the Fermi energy at different values of $V_g$, and the orange dashed lines represent defect states at the interface.