Anisotropic scaling for 3D topological models

Abstract A proposal to study topological models beyond the standard topological classification and that exhibit breakdown of Lorentz invariance is presented. The focus of the investigation relies on their anisotropic quantum critical behavior. We study anisotropic effects on three-dimensional (3D) t...

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Autores principales:	S. Rufo, M. A. R. Griffith, Nei Lopes, Mucio A. Continentino
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/4410715c04244d5b8cd5d60aca527d35
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spelling	oai:doaj.org-article:4410715c04244d5b8cd5d60aca527d352021-11-21T12:16:29ZAnisotropic scaling for 3D topological models10.1038/s41598-021-01888-x2045-2322https://doaj.org/article/4410715c04244d5b8cd5d60aca527d352021-11-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-01888-xhttps://doaj.org/toc/2045-2322Abstract A proposal to study topological models beyond the standard topological classification and that exhibit breakdown of Lorentz invariance is presented. The focus of the investigation relies on their anisotropic quantum critical behavior. We study anisotropic effects on three-dimensional (3D) topological models, computing their anisotropic correlation length critical exponent $$\nu$$ ν obtained from numerical calculations of the penetration length of the zero-energy surface states as a function of the distance to the topological quantum critical point. A generalized Weyl semimetal model with broken time-reversal symmetry is introduced and studied using a modified Dirac equation. An approach to characterize topological surface states in topological insulators when applied to Fermi arcs allows to capture the anisotropic critical exponent $$\theta =\nu _{x}/\nu _{z}$$ θ = ν x / ν z . We also consider the Hopf insulator model, for which the study of the topological surface states yields unusual values for $$\nu$$ ν and for the dynamic critical exponent z. From an analysis of the energy dispersions, we propose a scaling relation $$\nu _{\bar{\alpha }}z_{\bar{\alpha }}=2q$$ ν α ¯ z α ¯ = 2 q and $$\theta =\nu _{x}/\nu _{z}=z_{z}/z_{x}$$ θ = ν x / ν z = z z / z x for $$\nu$$ ν and z that only depends on the Hopf insulator Hamiltonian parameters p and q and the axis direction $$\bar{\alpha }$$ α ¯ . An anisotropic quantum hyperscaling relation is also obtained.S. RufoM. A. R. GriffithNei LopesMucio A. ContinentinoNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-16 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q S. Rufo M. A. R. Griffith Nei Lopes Mucio A. Continentino Anisotropic scaling for 3D topological models
description	Abstract A proposal to study topological models beyond the standard topological classification and that exhibit breakdown of Lorentz invariance is presented. The focus of the investigation relies on their anisotropic quantum critical behavior. We study anisotropic effects on three-dimensional (3D) topological models, computing their anisotropic correlation length critical exponent $$\nu$$ ν obtained from numerical calculations of the penetration length of the zero-energy surface states as a function of the distance to the topological quantum critical point. A generalized Weyl semimetal model with broken time-reversal symmetry is introduced and studied using a modified Dirac equation. An approach to characterize topological surface states in topological insulators when applied to Fermi arcs allows to capture the anisotropic critical exponent $$\theta =\nu _{x}/\nu _{z}$$ θ = ν x / ν z . We also consider the Hopf insulator model, for which the study of the topological surface states yields unusual values for $$\nu$$ ν and for the dynamic critical exponent z. From an analysis of the energy dispersions, we propose a scaling relation $$\nu _{\bar{\alpha }}z_{\bar{\alpha }}=2q$$ ν α ¯ z α ¯ = 2 q and $$\theta =\nu _{x}/\nu _{z}=z_{z}/z_{x}$$ θ = ν x / ν z = z z / z x for $$\nu$$ ν and z that only depends on the Hopf insulator Hamiltonian parameters p and q and the axis direction $$\bar{\alpha }$$ α ¯ . An anisotropic quantum hyperscaling relation is also obtained.
format	article
author	S. Rufo M. A. R. Griffith Nei Lopes Mucio A. Continentino
author_facet	S. Rufo M. A. R. Griffith Nei Lopes Mucio A. Continentino
author_sort	S. Rufo
title	Anisotropic scaling for 3D topological models
title_short	Anisotropic scaling for 3D topological models
title_full	Anisotropic scaling for 3D topological models
title_fullStr	Anisotropic scaling for 3D topological models
title_full_unstemmed	Anisotropic scaling for 3D topological models
title_sort	anisotropic scaling for 3d topological models
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/4410715c04244d5b8cd5d60aca527d35
work_keys_str_mv	AT srufo anisotropicscalingfor3dtopologicalmodels AT margriffith anisotropicscalingfor3dtopologicalmodels AT neilopes anisotropicscalingfor3dtopologicalmodels AT mucioacontinentino anisotropicscalingfor3dtopologicalmodels
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Anisotropic scaling for 3D topological models

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