Title:
Proposal for Measurement of Euler characteristic of Fermi sea

Abstract:
A dramatic consequence of the role of topology in the structure of quantum matter is the existence of topological invariants that are reflected in quantized response functions. While much attention is paid on the topology associated with the twisting of wavefunctions, the base manifold, such as the Fermi sea of metals, may also exhibit a geometric topology.

In this talk, I will introduce the proposal of Kane for the measurement of the Euler characteristic of the Fermi sea of metals. It is associated with a nonlinear frequency-dependent D+1 terminal conductance that characterizes a D-dimensional Fermi gas. Motivated by the Landauer conductance in D=1, the author generalized it to D=2 case through a simple thought experiment and sharpened the argument by a semiclassical Boltzmann transport theory and further a more general quantum treatment.

Ref:
C. L. Kane. Quantized Nonlinear Conductance in Ballistic Metals. Physical Review Letters, 128(7):076801, February 2022.