Topological phases in polar oxide nanostructures

Topology provides a framework for an understanding of emergent phenomena in various fields such as the appearance of new results in the field of ferroelectrics. A historical introduction and a primer on the concepts of topology are followed by a discussion of experimental and theoretical methods that elucidate the exotic textures that appear in polar oxide nanostructures and superlattices. The complex interplay of several fundamental processes occurring on different energy scales leads to ground states that compete with one another and have large and/or novel responses with respect to external stimuli.