Tetrads in Solids: from Elasticity Theory to Topological Quantum Hall Systems and Weyl Fermions

J. Nissinen*, G. E. Volovik

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)


Theory of elasticity in topological insulators has many common features with relativistic quantum fields interacting with gravitational fields in the tetrad form. Here we discuss several issues in the effective topological (pseudo)electromagnetic response in three-dimensional weak crystalline topological insulators with no time-reversal symmetry that feature elasticity tetrads, including a mixed “axial-gravitational” anomaly. This response has some resemblance to “quasitopological” terms proposed for massless Weyl quasiparticles with separate, emergent fermion tetrads. As an example, we discuss the chiral/axial anomaly in superfluid 3He-A. We demonstrate the principal difference between the elasticity tetrads and the Weyl fermion tetrads in the construction of the topological terms in the action. In particular, the topological action expressed in terms of the elasticity tetrads cannot be expressed in terms of the Weyl fermion tetrads since in this case the gauge invariance is lost.

Original languageEnglish
Pages (from-to)948-957
Number of pages10
JournalJournal of Experimental and Theoretical Physics
Issue number5
Publication statusPublished - 1 Nov 2018
MoE publication typeA1 Journal article-refereed

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