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We report the growth and polarization switching properties of epitaxial ferroelectric–superconducting heterostructure PbZr0.52Ti0.48O3 (PZT) (100 nm)/YBa2Cu3O7−δ (YBCO) (100 nm) thin films for non-volatile ferroelectric random access memory elements. The epitaxial nature of the heterostructure is verified using the reciprocal space mapping data with the superconducting phase transition temperature (Tc) of nearly 25 K far below the Tc of as-grown YBCO under the same condition. The significant remanent polarization (Pr) ∼ 45 µC/cm2 at 1 kHz can switch from one state to another using 1 μs pulse. The devices meet the basic criteria of memory elements, such as high resistance ∼10 GΩ at 8 V, a butterfly-like capacitance–voltage (C/V) loop, significant polarization, a sharp change in the displacement current, long-time charge retention, and small fatigue at room temperature.