  We study superconducting properties in multilayer thin films consisting of
superconducting La$_{1.85}$Sr$_{0.15}$CuO$_4$ (LSCO) and Mott insulator
Sr$_2$IrO$_4$ (SIO) and report enhanced superconductivity in optimized sample.
These multilayer heterostructures show an increase in superconducting
transition temperature ($T_C$) as compared to the single layer LSCO films. The
temperature dependence of SIO single layer is also investigated under thermal
activation, Arrhenius-type behaviour, and variable-range hopping mechanisms for
different temperature regimes. The decrease in $T_C$ beyond an optimum
thickness of LSCO in these multilayers is analyzed in the framework of a model
based on the assumption of induced superconductivity in SIO-LSCO interface due
to the doping of La and/or oxygen deficiencies into SIO layers
