Modulation of superconducting transition temperature in LaAlO$_{3}$/SrTiO$_{3}$ by SrTiO$_{3}$ structural domains

The tetragonal domain structure in SrTiO$_{3}$ (STO) is known to modulate the normal-state carrier density in LaAlO$_{3}$/SrTiO$_{3}$ (LAO/STO) heterostructures, among other electronic properties, but the effect of STO domains on the superconductivity in LAO/STO has not been fully explored. Using a scanning SQUID susceptometer microscope to map the superconducting response as a function of temperature in LAO/STO, we find that the superconducting transition temperature is spatially inhomogeneous and modulated in a pattern that is characteristic of structural domains in the STO.