Journal of Experimental and Theoretical Physics

, Volume 127, Issue 5, pp 948–957 | Cite as

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

  • J. NissinenEmail author
  • G. E. Volovik


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.



This work has been supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement no. 694248).


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Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Low Temperature Laboratory, Aalto University, P.O. Box 15100AaltoFinland
  2. 2.Landau Institute for Theoretical PhysicsChernogolovkaRussia

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