Quantization of the Thermal Hall Conductivity at Small Hall Angles

Mengxing Ye, Gábor B. Halász, Lucile Savary, and Leon Balents
Phys. Rev. Lett. 121, 147201 – Published 1 October 2018
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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 κxx due to phonons is much larger than the expected quantized thermal Hall conductance κxyq=(πT/12)(kB2/) 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, where is a thermalization length. We obtain T5 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. Our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, κxy/κxx103, in αRuCl3.

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  • Received 7 June 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.147201

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Mengxing Ye1,2, Gábor B. Halász2, Lucile Savary3, and Leon Balents2

  • 1School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 2Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
  • 3Université de Lyon, École Normale Supérieure de Lyon, Université Claude Bernard Lyon I, CNRS, Laboratoire de physique, 46, allée d’Italie, 69007 Lyon, France

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Issue

Vol. 121, Iss. 14 — 5 October 2018

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