Journal of High Energy Physics

, 2016:83 | Cite as

Topology of Fermi surfaces and anomaly inflows

  • Alejandro Adem
  • Omar Antolín Camarena
  • Gordon W. Semenoff
  • Daniel Sheinbaum
Open Access
Regular Article - Theoretical Physics


We derive a rigorous classification of topologically stable Fermi surfaces of non-interacting, discrete translation-invariant systems from electronic band theory, adiabatic evolution and their topological interpretations. For systems on an infinite crystal it is shown that there can only be topologically unstable Fermi surfaces. For systems on a half- space and with a gapped bulk, our derivation naturally yields a K -theory classification. Given the d − 1-dimensional surface Brillouin zone X s of a d-dimensional half-space, our result implies that different classes of globally stable Fermi surfaces belong in K −1 (Xs) for systems with only discrete translation-invariance. This result has a chiral anomaly inflow interpretation, as it reduces to the spectral flow for d = 2. Through equivariant homotopy methods we extend these results for symmetry classes AI, AII, C and D and discuss their corresponding anomaly inflow interpretation.


Anomalies in Field and String Theories Topological Field Theories Topological States of Matter 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Alejandro Adem
    • 1
  • Omar Antolín Camarena
    • 1
  • Gordon W. Semenoff
    • 2
  • Daniel Sheinbaum
    • 1
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Physics and AstronomyUniversity of British ColumbiaVancouverCanada

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