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

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Tetrads in Solids : from Elasticity Theory to Topological Quantum Hall Systems and Weyl Fermions. / Nissinen, J.; Volovik, G. E.

In: Journal of Experimental and Theoretical Physics, Vol. 127, No. 5, 01.11.2018, p. 948-957.

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@article{9cf1be1075a441aeb7f816d53a4ed6b2,
title = "Tetrads in Solids: from Elasticity Theory to Topological Quantum Hall Systems and Weyl Fermions",
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.",
author = "J. Nissinen and Volovik, {G. E.}",
note = "| openaire: EC/H2020/694248/EU//TOPVAC",
year = "2018",
month = "11",
day = "1",
doi = "10.1134/S1063776118110080",
language = "English",
volume = "127",
pages = "948--957",
journal = "Journal of Experimental and Theoretical Physics",
issn = "1063-7761",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "5",

}

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TY - JOUR

T1 - Tetrads in Solids

T2 - from Elasticity Theory to Topological Quantum Hall Systems and Weyl Fermions

AU - Nissinen, J.

AU - Volovik, G. E.

N1 - | openaire: EC/H2020/694248/EU//TOPVAC

PY - 2018/11/1

Y1 - 2018/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85060638981&partnerID=8YFLogxK

U2 - 10.1134/S1063776118110080

DO - 10.1134/S1063776118110080

M3 - Article

VL - 127

SP - 948

EP - 957

JO - Journal of Experimental and Theoretical Physics

JF - Journal of Experimental and Theoretical Physics

SN - 1063-7761

IS - 5

ER -

ID: 32108747