Abstract: The study of topological phases of matter and the invariants that define them has become a central pursuit of condensed matter physics. In particular, crystalline systems are known to host a large set of topological invariants, but the physical response properties associated to them are still not fully understood. In this talk we describe how to construct a topological response theory that makes detailed predictions about a set of crystalline topological invariants; we focus on two of them, the 'discrete shift', and a quantized charge polarization. We show that these invariants can be extracted from a lattice model by measuring the fractional charge at lattice defects such as disclinations and dislocations. To illustrate our method, we study the Hofstadter model of spinless electrons in a background magnetic field, and show that these invariants lead to new 'Hofstadter butterflies' which significantly expand the known phase diagram of the model.
Location: ATL 2324