  Strontium titanate is a low-temperature, non-Bardeen-Cooper-Schrieffer
superconductor that superconducts to carrier concentrations lower than in any
other system and exhibits avoided ferroelectricity at low temperatures. Neither
the mechanism of superconductivity in strontium titanate nor the importance of
the structure and dielectric properties for the superconductivity are well
understood. We studied the effects of twin structure on superconductivity in a
5.5-nm-thick layer of niobium-doped SrTiO$_{3}$ embedded in undoped
SrTiO$_{3}$. We used a scanning superconducting quantum interference device
susceptometer to image the local diamagnetic response of the sample as a
function of temperature. We observed regions that exhibited a superconducting
transition temperature $T_{c}$ $\gtrsim$ 10% higher than the temperature at
which the sample was fully superconducting. The pattern of these regions varied
spatially in a manner characteristic of structural twin domains. Our results
emphasize that the anisotropic dielectric properties of SrTiO$_{3}$ are
important for its superconductivity, and need to be considered in any theory of
the mechanism of the superconductivity.
