Fine-grained topological structures hidden in Fermi sea

The geometry of Fermi sea hosts a unique form of quantum topology that governs the conductance quantization of metal and is characterized by the Euler characteristic $\chi_F$, offering a new perspective in the study of topological quantum matter. Here, we discover that characterizing Fermi sea topology solely by $\chi_F$ is insufficient: Fermi seas with identical $\chi_F$ can exhibit fundamentally different fine-grained topological structures that cannot be connected without a Lifshitz transition. To encode this hidden structure, we introduce a structural resolution factor that captures the fine-grained Fermi sea topologies beyond $\chi_F$, revealing the deeper topological information within the Fermi sea. Considering the attractive Hubbard interaction of electrons on Fermi surfaces, we further demonstrate that the resulting topological superconducting phases can inherit the fine-grained Fermi sea topology of their parent metallic bands, with differences in these structures giving rise to anomalous gapless boundary states at the interface between two metal/superconductor heterojunctions. This work opens an avenue for understanding the topological richness of Fermi sea.