Approximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons

The recent observation of a half-integer quantized thermal Hall effect in α-RuCl_{3} is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless...

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Autores principales:	Yuval Vinkler-Aviv, Achim Rosch
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2018
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/34f06f3418d540939c41b53f31fb4b5b
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spelling	oai:doaj.org-article:34f06f3418d540939c41b53f31fb4b5b2021-12-02T11:19:14ZApproximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons10.1103/PhysRevX.8.0310322160-3308https://doaj.org/article/34f06f3418d540939c41b53f31fb4b5b2018-08-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.8.031032http://doi.org/10.1103/PhysRevX.8.031032https://doaj.org/toc/2160-3308The recent observation of a half-integer quantized thermal Hall effect in α-RuCl_{3} is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity κ_{xy} is never exactly quantized in real materials. Here, we investigate how phonons affect the quantization of the thermal conductivity, focusing on the edge theory. As an example, we consider a Kitaev spin liquid gapped by an external magnetic field coupled to acoustic phonons. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized, and we argue that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The strength of this edge coupling does, however, not affect the conductivity. We argue that for sufficiently clean systems the leading correction to the quantized thermal Hall effect, Δκ_{xy}/T∼sign(B)T^{2}, arises from an intrinsic anomalous Hall effect of the acoustic phonons due to Berry phases imprinted by the chiral (spin) liquid in the bulk. This correction depends on the sign but not the amplitude of the external magnetic field.Yuval Vinkler-AvivAchim RoschAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 8, Iss 3, p 031032 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Yuval Vinkler-Aviv Achim Rosch Approximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons
description	The recent observation of a half-integer quantized thermal Hall effect in α-RuCl_{3} is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity κ_{xy} is never exactly quantized in real materials. Here, we investigate how phonons affect the quantization of the thermal conductivity, focusing on the edge theory. As an example, we consider a Kitaev spin liquid gapped by an external magnetic field coupled to acoustic phonons. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized, and we argue that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The strength of this edge coupling does, however, not affect the conductivity. We argue that for sufficiently clean systems the leading correction to the quantized thermal Hall effect, Δκ_{xy}/T∼sign(B)T^{2}, arises from an intrinsic anomalous Hall effect of the acoustic phonons due to Berry phases imprinted by the chiral (spin) liquid in the bulk. This correction depends on the sign but not the amplitude of the external magnetic field.
format	article
author	Yuval Vinkler-Aviv Achim Rosch
author_facet	Yuval Vinkler-Aviv Achim Rosch
author_sort	Yuval Vinkler-Aviv
title	Approximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons
title_short	Approximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons
title_full	Approximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons
title_fullStr	Approximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons
title_full_unstemmed	Approximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons
title_sort	approximately quantized thermal hall effect of chiral liquids coupled to phonons
publisher	American Physical Society
publishDate	2018
url	https://doaj.org/article/34f06f3418d540939c41b53f31fb4b5b
work_keys_str_mv	AT yuvalvinkleraviv approximatelyquantizedthermalhalleffectofchiralliquidscoupledtophonons AT achimrosch approximatelyquantizedthermalhalleffectofchiralliquidscoupledtophonons
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Approximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons

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