The application of topology to the band theory of electrical conduction has lead to an explosion of activity around topological insulators, semimetals, and superconductors. A time-periodic modulation of material properties, as done in solid-state, trapped-atom, and photonic experiments, allows us not only to tailor the topological properties of the bands, but also to create new types of topological phases, with new types of edge states. A suitable toy model for these novel topological phases is the so-called quantum walk. The PhD student would use quantum walks to discover new topological phases, and have a possibility to join in theoretical work directly connected to experimental efforts to realize these phases on trapped atoms (collaboration with University of Bonn) or photonic experiments (collaboration with University of Paderborn).
Good working knowledge of quantum mechanics, basic programming skills, basic solid state physics