Topology of the Fermi Sea

Explore the topological nature of the Fermi sea in metals through this insightful lecture by Charles Kane from the University of Pennsylvania. Delve into the concept of the Euler characteristic, a topological invariant that characterizes the Fermi sea, and discover its implications in quantized non-linear response and correlation functions. Examine how the Euler characteristic manifests in density correlation functions and non-linear response functions for Fermi gases of various dimensions. Critically analyze the impact of electron interactions and learn about proposed experiments on cold atomic gas systems and 2D electronic materials. Investigate the connection between the Euler characteristic and multipartite entanglement in Fermi gases, and understand how this generalizes known results in conformal field theory. Conclude by exploring the role of the Euler characteristic in distinguishing topological Fermi liquid phases in interacting 3D systems.