Novel types of superconductivity is a very active area of research. Heterostructures are a promising and recent avenue for finding these. This thesis explores a theoretical model of a ferroelectric heterostructure to investigate whether dipole-mediated electron interactions can induce superconductivity. Two models were analyzed: a static case where the dipole aligns instantaneously with the net electric field and a dynamic case where the dipole has inertia and oscillates. The static model showed that under small lattice constants, dipole mediated interactions can overcome Coulomb repulsion between electrons, though such conditions are challenging to achieve. The dynamic model, analyzed using Floquet theory, revealed resonance effects that amplify electron motion. While definitive superconductivity was not established, experimental validation through pressure-tuned lattice constants and resonance conditions could validate the model’s predictions. Future research could extend this framework to quantum mechanical dipoles and more complex materials, enhancing the understanding of superconductivity in engineered heterostructures.

There has been interesting research on the superconducting diode recently. A possible structure for this is the Superconductor/Ferroelectric/Superconductor (S/FE/S) Josephson junction. Our goal is to simulate a S/FE/S junction with a magnetic field and see if this leads to a superconducting diode effect. First this junction and its properties are studied through a numerical simulation. Then a magnetic field is applied and we look at how this affects the junction. For our simulation we use the Velocity Verlet method. We start by simulating a normal RCSJ. The results agree with what we expect from the theory, however there is small but noticeable error which we attribute to the numerical method. Next a S/FE/S junction is simulated. The polarisation of the ferroelectric only affects the RCSJ when it oscillates at a frequency which is close to the plasma frequency. If we apply a magnetic field we see small gaps for the retrapping current however these are close to the numerical error thus they are to small too be detected by our simulation.