A topological superconductor features at its boundaries and vortices Majorana fermions, which are potentially applicable for topological quantum computations. The scarcity of the known experimentally verified physical systems with topological superconductivity, time-reversal invariant ones in particular, is giving rise to a strong demand for identifying new candidate materials. In this research, we study a heterostructure consisting of a transition metal oxide two-dimensional electron gas (2DEG) sandwiched by insulators near the paraelectric (PE) / ferroelectric (FE) phase transition. Its relevant characteristics is the combination of the transition metal spin-orbit coupling and the soft odd-parity phonons arising from the ferroelectric fluctuation; it gives rise to the fluctuating Rashba effect, which can mediate the pairing interaction for time-reversal invariant topological superconductivity. As the PE / FE phase transition can be driven by applying strain on the heterostructure, this system provides a tunable electron-phonon coupling. Through the first-principle calculations on the (001) [BaOsO3][BaTiO3]4, we find such electron-phonon coupling to be strong over a wide range of applied tensile bi-axial strain in the monolayer BaOsO3 sandwiched between the (001) BaTiO3, hence qualifying it as a good candidate material. Furthermore, the stability of topological superconductivity in this material is enhanced by its orbital physics that gives rise to the anisotropic dispersion.
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