Topological Order Parameters in Oxides

With the now vast collection of materials hosting topological phases, the next goal is to provide design routes for their control with strain and fields. In particular, oxides are an enticing class of materials in which to investigate on-demand topological phases since they already host highly-tunable orders such as ferroelectricity, ferromagnetic and superconductivity. In this talk, I will discuss how the conventional order parameters in oxides such as ferroelectric mode distortions and octahedral rotations can be used tune topological order. I will provide two cases studies looking at higher-order topological phases in perovskite oxides, and the interplay between real and reciprocal space topological in hexagonal manganites using first principles calculations and phenomenology theory. Finally, I will discuss the prospects of these materials as hosts for Majorana fermions and their potential as robust elements in topological quantum computers.