Berlin 2024 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 3: Topology: Quantum Hall Systems
TT 3.11: Talk
Monday, March 18, 2024, 12:30–12:45, H 2053
Quantum kinetic equation and thermal conductivity tensor for bosons — •Léo Mangeolle1,2,3, Lucile Savary1,2, and Leon Balents2 — 1ENS de Lyon, CNRS, Laboratoire de Physique, 46 allée d'Italie, 69007 Lyon, France — 2Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 — 3Technical University of Munich, School of Natural Sciences, Physics Department, 85748 Garching, Germany
We obtain a systematic derivation of the semi-classical kinetic equation for neutral bosons from their full quantum kinetic equation. It incorporates the semi-classical topological dynamics of wavepackets in the form of geometric properties of the energy eigenstates, such as the Berry phases and curvatures, generalized to phase space. This makes it possible to treat inhomogeneous systems, including boundaries, textures, etc., in a compact and natural manner. We compute the associated observable quantities, such as energy and current densities, away from equilibrium. In particular, the thermal conductivity tensor, which describes the energy current induced by a temperature gradient, is exactly obtained. This provides a self-contained and exact derivation of the intrinsic thermal Hall effect of neutral bosons such as phonons and magnons, in agreement with Kubo formula results while being considerably more intuitive, and naturally avoiding subtleties associated with magnetization currents. I will eventually present a few calculations using the derived quantum kinetic equation: - the local thermal Hall current of topological magnons in a collinear antiferromagnet, - the energy density and local currents in a skyrmion lattice.
Keywords: thermal transport; kinetic equations; topology; magnons; skyrmions