skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantization of the Thermal Hall Conductivity at Small Hall Angles

Abstract

We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev’s non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity κ x x due to phonons is much larger than the expected quantized thermal Hall conductance $$κ$$ $$^{q}_{xy}$$ = (πT/12)($$k$$ $$^{2}_{B}$$/ℏ) of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the interaction between a Majorana edge and bulk phonons, we show that the exchange of energy between the two subsystems leads to a transverse component of the bulk current and thereby an effective Hall conductivity. Remarkably, the latter is equal to the quantized value when the edge and bulk can thermalize, which occurs for a Hall bar of length L >> ℓ, where ℓ is a thermalization length. We obtain ℓ ~ T –5 for a model of the Majorana-phonon coupling. We also find that the quality of the quantization depends on the means of measuring the temperature and, surprisingly, a more robust quantization is obtained whenmore » the lattice, not the spin, temperature is measured. We present general hydrodynamic equations for the system, detailed results for the temperature and current profiles, and an estimate for the coupling strength and its temperature dependence based on a microscopic model Hamiltonian. Furthermore, our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, κ xyxx ~ 10 –3, in α–RuCl 3.« less

Authors:
 [1];  [2];  [3];  [2]
  1. Univ. of Minnesota, Minneapolis, MN (United States); Univ. of California, Santa Barbara, CA (United States)
  2. Univ. of California, Santa Barbara, CA (United States)
  3. Univ. de Lyon (France)
Publication Date:
Research Org.:
Univ. of California, Santa Barbara, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1610005
Alternate Identifier(s):
OSTI ID: 1475084
Grant/Contract Number:  
FG02-08ER46524
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 121; Journal Issue: 14; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; physics; anyons; frustrated magnetism; quantum spin liquid; thermal Hall effect

Citation Formats

Ye, Mengxing, Halász, Gábor B., Savary, Lucile, and Balents, Leon. Quantization of the Thermal Hall Conductivity at Small Hall Angles. United States: N. p., 2018. Web. doi:10.1103/physrevlett.121.147201.
Ye, Mengxing, Halász, Gábor B., Savary, Lucile, & Balents, Leon. Quantization of the Thermal Hall Conductivity at Small Hall Angles. United States. https://doi.org/10.1103/physrevlett.121.147201
Ye, Mengxing, Halász, Gábor B., Savary, Lucile, and Balents, Leon. Mon . "Quantization of the Thermal Hall Conductivity at Small Hall Angles". United States. https://doi.org/10.1103/physrevlett.121.147201. https://www.osti.gov/servlets/purl/1610005.
@article{osti_1610005,
title = {Quantization of the Thermal Hall Conductivity at Small Hall Angles},
author = {Ye, Mengxing and Halász, Gábor B. and Savary, Lucile and Balents, Leon},
abstractNote = {We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev’s non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity κ x x due to phonons is much larger than the expected quantized thermal Hall conductance $κ$ $^{q}_{xy}$ = (πT/12)($k$ $^{2}_{B}$/ℏ) of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the interaction between a Majorana edge and bulk phonons, we show that the exchange of energy between the two subsystems leads to a transverse component of the bulk current and thereby an effective Hall conductivity. Remarkably, the latter is equal to the quantized value when the edge and bulk can thermalize, which occurs for a Hall bar of length L >> ℓ, where ℓ is a thermalization length. We obtain ℓ ~ T–5 for a model of the Majorana-phonon coupling. We also find that the quality of the quantization depends on the means of measuring the temperature and, surprisingly, a more robust quantization is obtained when the lattice, not the spin, temperature is measured. We present general hydrodynamic equations for the system, detailed results for the temperature and current profiles, and an estimate for the coupling strength and its temperature dependence based on a microscopic model Hamiltonian. Furthermore, our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, κxy/κxx ~ 10–3, in α–RuCl3.},
doi = {10.1103/physrevlett.121.147201},
url = {https://www.osti.gov/biblio/1610005}, journal = {Physical Review Letters},
issn = {0031-9007},
number = 14,
volume = 121,
place = {United States},
year = {2018},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 16 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Anyons in an exactly solved model and beyond
journal, January 2006


Non-Abelian anyons and topological quantum computation
journal, September 2008


α RuCl 3 : A spin-orbit assisted Mott insulator on a honeycomb lattice
journal, July 2014


Fault-tolerant quantum computation by anyons
journal, January 2003


Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales
journal, June 2016


Quantum spin liquids: a review
journal, November 2016


Majorana zero modes in superconductor–semiconductor heterostructures
journal, May 2018


Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
journal, July 2018


Observation of half-integer thermal Hall conductance
journal, June 2018


Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3
journal, May 2015


Nonabelions in the fractional quantum hall effect
journal, August 1991


    Works referencing / citing this record:

    Hydrodynamics of three-dimensional skyrmions in frustrated magnets
    journal, August 2019


    Theory of the field-revealed Kitaev spin liquid
    journal, June 2019


    Unfolding the complexity of phonon quasi-particle physics in disordered materials
    journal, January 2020


    Heisenberg–Kitaev physics in magnetic fields
    journal, July 2019


    Thermal-transport studies of kagomé antiferromagnets
    journal, November 2019


    Finite field regime for a quantum spin liquid in α RuCl 3
    journal, August 2019


    Terahertz excitations in α RuC l 3 : Majorana fermions and rigid-plane shear and compression modes
    journal, September 2019


    Quantized thermal Hall conductance from edge current calculations in lattice models
    journal, October 2019


    Chiral spin order in some purported Kitaev spin-liquid compounds
    journal, November 2018


    Phenomenological theory of heat transport in the fractional quantum Hall effect
    journal, January 2019


    Non-Kitaev spin liquids in Kitaev materials
    journal, May 2019


    Impact of off-diagonal exchange interactions on the Kitaev spin-liquid state of α RuCl 3
    journal, June 2019


    Large Contribution of Fermi Arcs to the Conductivity of Topological Metals
    journal, August 2019


    Thermal Hall signatures of non-Kitaev spin liquids in honeycomb Kitaev materials
    journal, August 2019


    Field-induced QCD 3 -Chern-Simons quantum criticalities in Kitaev materials
    journal, January 2020


    Quantum spin liquids
    journal, January 2020