Topology of Fermi Surfaces and Anomalies

作者: Alejandro Adem , Gordon W. Semenoff , Daniel Sheinbaum

DOI:

关键词: PhysicsInterpretation (model theory)Fermi Gamma-ray Space TelescopeHomogeneous spaceAdiabatic processSpectral flowTopologyTopology (chemistry)Chiral anomalyBrillouin zone

摘要: We derive a classification of topologically stable Fermi surfaces non-interacting, discrete translation-invariant systems from electronic band theory, adiabatic evolution and their topological interpretations. This derivation is rigorously compatible with $\mathit{K}$-theory. Given the Brillouin zone $\mathrm{X}$ our $d$-dimensional system, result implies that different classes belong in $\mathit{K^{-1}}\mathrm{(X)}$ for only translation-invariance. has chiral anomaly interpretation, as it reduces to spectral flow one dimensional systems. further show discuss some connections between symmetries other variants $\mathit{K}$-theory, together corresponding quantum interpretation.

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