Theoretical Physics Seminar: Jaakko Nissinen (Aalto University)

Geometric aspects of 3+1d crystalline topological insulators and the chiral anomaly in topological Weyl superfuids

Topological responses have usually universally quantized coefficients and protected boundary modes. They arise from topological invariants encoded by characteristic classes, theta and Chern-Simons terms, and are related by the concept of anomaly inflow from a higher dimensional theory. In this talk we discuss two examples of “almost topological” responses in three-dimensions, both with additional geometric fields entering the response. First, I will discuss the three-dimensional quantum Hall effect and electric polarization in topological crystalline insulators in terms of so called elasticity tetrads. We show in what sense the mixed response with elasticity tetrads and electro-magnetic fields is geometrical and topological, as well as how gauge invariance is maintained by the anomaly inflow, even in the presence of dislocations defects. Secondly, time permitting, I will discuss how anomalous momentum transport in topological Weyl superfluids (and superconductors) in the presence of textures and superflow can be given a consistent interpretation as the chiral Nieh-Yan gravitational anomaly experienced by Weyl fermions on an emergent curved spacetime with torsion and curvature. The coefficient of this anomaly term is not universally quantized and seems to be determined by the underlying non-relativistic Fermi-liquid and Galilean symmetries.