Majorana Fermions in One-Dimensional Structures at LaAlO3/SrTiO3 Oxide Interfaces

We study one-dimensional structures that may be formed at the LaAlO3/SrTiO3 oxide interface by suitable top gating. These structures are modeled via a single-band model with Rashba spin-orbit coupling, superconductivity and a magnetic field along the one-dimensional chain. We first discuss the conditions for the occurrence of a topological superconducting phase and the related formation of Majorana fermions at the chain endpoints, highlighting a close similarity between this model and the Kitaev model, which also reflects in a similar condition the formation of a topological phase. Solving the model in real space, we also study the spatial extension of the wave function of the Majorana fermions and how this increases with approaching the limit condition for the topological state. Using a scattering matrix formalism, we investigate the stability of the Majorana fermions in the presence of disorder and discuss the evolution of the topological phase with increasing disorder.