Quantization of the Thermal Hall Conductivity at Small Hall Angles

Area of Science:

• Condensed Matter Physics
• Topological States of Matter
• Quantum Magnetism

Background:

• Investigates chiral spin liquids with Ising anyons, such as Kitaev's non-Abelian spin liquid on a honeycomb lattice.
• Focuses on the regime where bulk phonon thermal conductivity dominates over quantized edge thermal Hall conductance.
• Addresses the small thermal Hall angle observed in experiments.

Purpose of the Study:

• To analyze the effect of coupling between phonons and chiral Majorana edges in gapped chiral spin liquids.
• To understand the emergence of an effective Hall conductivity from the interaction.
• To determine conditions for quantized thermal Hall conductance and the factors influencing measurement quality.

Main Methods:

• Modeling the interaction between Majorana edges and bulk phonons.
• Deriving general hydrodynamic equations for the coupled system.
• Calculating temperature and current profiles, and estimating coupling strength and its temperature dependence.

Main Results:

• The energy exchange between Majorana edges and phonons induces a transverse bulk current, leading to an effective Hall conductivity.
• This effective Hall conductivity equals the quantized value when the edge and bulk thermalize (L ≫ ℓ), with thermalization length ℓ ~ T^{-5}.
• Quantization quality depends on temperature measurement; lattice temperature measurement yields more robust quantization than spin temperature.

Conclusions:

• The coupling mechanism provides a plausible explanation for experimentally observed quantized thermal Hall conductivity in systems with small Hall angles, like α-RuCl₃.
• Highlights the importance of thermalization and measurement techniques in observing topological transport phenomena.
• Suggests that phonon-Majorana coupling is a key factor in the thermal transport properties of certain quantum spin liquids.