It has long been known that the quantum ground state of a metal is characterized by an abstract manifold in momentum space called the Fermi sea. Fermi sea can be distinguished topologically in much the same way that a ball can be distinguished from a donut by counting the number of holes. The associated topological invariant, i.e. the Euler characteristic (χ_F), serves to classify metals. In this talk, I will survey two recent proposals to relate χ_F to experimental observables, namely (i) the equal-time density correlation [1], and (ii) the transport of Andreev states along a planar Josephson junction [2]. Furthermore, from the quantum information perspective, I will highlight how the multipartite entanglement in real space probes the Fermi sea topology in momentum space [1]. Our works not only provide a new connection between topology and entanglement in gapless quantum matters, but also suggest accessible experimental platforms to extract the topology in metals.
Host: Meng Cheng (m.cheng@yale.edu)