  The crystal structure of bulk SrTiO$_3$(STO) transitions from cubic to
tetragonal at around 105K. Recent local scanning probe measurements of
LaAlO$_3$/SrTiO$_3$ (LAO/STO) interfaces indicated the existence of spatially
inhomogeneous electrical current paths and electrostatic potential associated
with the structural domain formation in the tetragonal phase of STO. However,
how these effects impact the electron conduction in LAO/STO devices has not
been fully studied. Here we report a study of temperature dependent electronic
transport in combination with the polarized light microscopy of structural
domains in mesoscopic scale LAO/STO devices. By reducing the spatial size of
the conductive interface to be comparable to the size of a single tetragonal
domain of STO, the anisotropy of interfacial electron conduction in
relationship to the domain wall and its direction was characterized in the
temperature range $T$=10-300K. It was found that the four-point resistance
measured with current parallel to the domain wall in device is larger than the
resistance measured perpendicular to the domain wall. This observation is
qualitatively consistent with the current diverting effect from a more
conductive domain wall within the sample. Among all the samples studied, the
maximum resistance ratio found is at least 10 and could be as large as 10$^5$
at $T$=10K. This electronic anisotropy may have implications on other oxide
hetero-interfaces and the further understanding of electronic/magnetic
phenomena found in LAO/STO.
