  Design of epitaxial interfaces is a pivotal way to engineer artificial
structures where new electronic phases can emerge. Here we report a systematic
emergence of interfacial superconducting state in epitaxial heterostructures of
LaTiO3 and KTaO3. The superconductivity transition temperature increases with
decreasing the thickness of LaTiO3. Such behavior is observed for both (110)
and (111) crystal oriented structures. For thick samples, the finite resistance
developing below the superconducting transition temperature increases with
increasing LaTiO3 thickness. Consistent with previous reports, the (001)
oriented heterointerface features high electron mobility of 250 cm2/Vs and
shows no superconducting transition down to 40 mK. Our results imply a
non-trivial impact of LaTiO3 on the superconducting state and indicate how
superconducting KTaO3 interfaces can be integrated with other oxide materials.
