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


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Article Info

DATE

2018-11

AUTHORS

J. Nissinen, G. E. Volovik

ABSTRACT

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. More... »

PAGES

948-957

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s1063776118110080

DOI

http://dx.doi.org/10.1134/s1063776118110080

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1111619154


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42 schema:description 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.
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