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 κxx due to phonons is much larger than the expected quantized thermal Hall conductance κ q xy = πT 12 k 2 B 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 ∼ 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. 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. arXiv:1805.10532v2 [cond-mat.str-el]

Large Contribution of Fermi Arcs to the Conductivity of Topological Metals

“…In the limit W l sb we recover the infinite-system conductivity (1) by inverting the resistivity tensor ρ xx = ρ yy = E/(j s + j b ) and ρ yx = −ρ xy = E ⊥ /(j s + j b ). For finite l sb /W , the transverse resistivity is not well defined due to the chemical-potential difference between surface and bulk states -it depends on to which subsystem the apparatus measuring the Hall voltage couples [17,18]. The longitudinal resistivity remains well defined, however, see Fig.…”

Phase diagram and thermal Hall conductivity of the spin-liquid Kekulé-Kitaev model

“…Thermal transport through the chiral Majorana edge states and the role of bulk phonons discussed in Refs. [34,35] could account for the quantization observed experimentally.…”

Bulk thermal transport coefficients in a quantum Hall system and the fundamental difference between thermal and charge response

“…It is important to point out that the inclusion of gapless chiral edge states that connect both edges, will allow thermal conductance at low temperatures, with the correct universal value, and restore Wiedemann-Franz law [7]. The universal value might also be restored when other gapless modes of transferring heat between the edges exist, such as bulk phonons that couple to the edge modes, as was pointed in two recent studies [12,13].…”