Title: Geometry-Charge Responses in Topological Phases of Matter
Abstract: In the last several decades, it has become well appreciated that quantum system can exhibit topologically quantized electromagnetic responses. The most ubiquitous topological response is the quantum Hall response, which describes how a transverse current is driven by electric field, or, equivalently, how charge is bound to magnetic fluxes. More recently, it has also been shown that crystalline quantum systems can also host so called topological “geometry-charge” responses, where charge fluctuations are driven by distortions of the underlying crystal lattice. In this talk, I will discuss these geometry-charge responses, focusing on responses where charge is bound to disclination defects of a rotation invariant lattice. I will show that the disclination-charge responses can be encoded as topological terms that couple the electromagnetic gauge field to lattice curvature in an effective field theory. In addition to providing a mathematical framework for studying geometry-charge responses, the topological terms also show that the disclination-charge responses leads to surfaces that are anomalous with respect to spatial rotation symmetry. I will give concrete examples of these responses, and the associated anomalies, in various topological systems, including: higher-order topological insulators, topological crystalline insulators, and Dirac semimetals.