Fermi Surface Geometry from Charge Fluctuations in Three-Dimensional Metals

TL;DR

This paper demonstrates that charge fluctuations in 3D metals encode detailed information about Fermi surface shape and quantum geometry, linking topological invariants to measurable fluctuation terms.

Contribution

It reveals how the subleading logarithmic term of bipartite charge fluctuations encodes Fermi surface geometry and topology in three-dimensional metals.

Findings

Logarithmic term relates to Fermi surface curvature and quantum metric tensor.

Topological bounds depend on Euler characteristic and Chern number.

Charge fluctuations reveal quantum geometric and topological properties.

Abstract

For three-dimensional non-interacting multi-band metals, we show that important information about the shape and the quantum geometry of Fermi surfaces is encoded in the subleading logarithmic term of bipartite charge fluctuations. This logarithmic term is related to the dimensionless $|\mathbf{q}|^3$-coefficient of the structure factor in momentum space, and both quantities can be expressed as Fermi surface integrals of the Fermi surface curvature tensor and the quantum metric tensor. When the real-space partition surface is a quadric (i.e., sphere or ellipsoid), the logarithmic coefficient satisfies a topological bound depending only on the Euler characteristic and the Chern number of the Fermi surface, illustrating a non-trivial interplay between topology and quantum topology in multi-band metals.