Topology of the Fermi sea: ordinary metals as topological materials

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 number, i.e. the Euler characteristic (χ_F), serves to classify metals. Here I will survey three recent proposals that relate χ_F to experimental observables, which are: (i) nonlinear responses [1], (ii) equal-time density correlations [2], and (iii) Andreev state transport along a Josephson pi-junction [3]. Moreover, from the quantum information perspective, we show that multipartite entanglement in real space probes the Fermi sea topology in momentum space [2]. This series of works provide a new perspective to study topology and universality in gapless quantum matters.

[1] C. L. Kane, Phys. Rev. Lett. 128, 076801 (2022)

[2] P. M. Tam, M. Claassen, C. L. Kane, Phys. Rev. X 12, 031022 (2022)

[3] P. M. Tam and C. L. Kane, arXiv:2210.08048