A lanthanum aluminate ( LaAlO.sub.3) substrate on which thin films of layered perovskite copper oxide superconductors are formed. Lanthanum aluminate, with a pseudo-cubic perovskite crystal structure, has a crystal structure and lattice constant that closely match the crystal structures and lattice constants of the layered perovskite superconductors. Therefore, it promotes epitaxial film growth of the superconductors, with the crystals being oriented in the proper direction for good superconductive electrical properties, such as a high critical current density. In addition, LaAlO.sub.3 has good high frequency properties, such as a low loss tangent and low dielectric constant at superconductive temperatures. Finally, lanthanum aluminate does not significantly interact with the superconductors. Lanthanum aluminate can also used to form thin insulating films between the superconductor layers, which allows for the fabrication of a wide variety of superconductor circuit elements.