Generic reduction theory for Fermi sea topology in metallic systems
arXiv:2403.19125 · doi:10.1103/PhysRevB.111.155115
Abstract
The Fermi sea of a metal can host exotic quantum topology, which governs its conductance quantization and is characterized by the Euler characteristic (). In contrast to the well-known band topology, which is determined by the global features of wave functions, the topology of such metallic systems is intrinsically linked to the geometry of the Fermi sea. As a result, probing and identifying in high-dimensional systems presents a challenge. Here, we propose a generic dimensional reduction theory for the Fermi sea topology in -dimensional metallic systems, showing that can be determined by the features of so-called reduced critical points on Fermi surfaces. Moreover, we reveal that can be interpreted as a topological invariant of band topology by mapping a metallic system to a gapped system. Building on this nontrivial result, we identify a broad class of topological superconductors (SCs) whose topological numbers are precisely determined by the of their normally filled bands. This provides an indirect method to capture by measuring the (pseudo)spin polarizations of these topological SCs. Our findings are expected to significantly advance research into Fermi sea topology.
arXiv comment11 pages, 7 figures, 1 table, References are updated
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