Gapless Fermionic Systems as Phase-space Topological Insulators: Non-perturbative Results from Anomalies

Abstract

We present a theory unifying the topological responses and anomalies of various gapless fermion systems exhibiting Fermi surfaces, including those with Berry phases, and nodal structures, which applies beyond non-interacting limit. As our key finding, we obtain a general approach to directly relate gapless fermions and topological insulators in phase space, including first- and higher-order insulators. Using this relation we show that the low-energy properties and response theories for gapless fermionic systems can be directly obtained without resorting to microscopic details. Our results provide a unified framework for describing such systems using well-developed theories from the study of topological phases of matter.

12 pages, 2 figures; fixed an issue that accidentally removed the Supplemental Material

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Cited by in corpus (3)

• Fermion liquids as quantum Hall liquids in phase space: A unified approach for anomalies and responses
• Interaction robustness of the chiral anomaly in Weyl semimetals and Luttinger liquids from a mixed anomaly approach
• Chiral charge conservation and ballistic magnetotransport in a disordered Weyl semimetal