Quantum Kinetic Theory of Thermoelectric and Thermal Transport in a Magnetic Field

Abstract

We present a general quantum kinetic theory that accounts for the interplay between a temperature gradient, momentum-space Berry curvatures of Bloch electrons, and Bloch-state scattering. Using a theory that incorporates the presence of a temperature gradient by introducing a "thermal vector potential", we derive a quantum kinetic equation for Bloch electrons in the presence of disorder and a temperature gradient. Taking also into account the presence of electric and magnetic fields, the quantum kinetic equation we derive makes it possible to compute transport coefficients at arbitrary orders of electric-field $\vec{E}$, magnetic-field $\vec{B}$, and temperature-gradient $\nabla T$ strengths $|\vec{E}{|}^a|\vec{B}{|}^b|\nabla T{|}^c$. Our theory enables a systematic calculation of magnetothermoelectric and magnetothermal conductivities of systems with momentum-space Berry curvatures. As an illustration, we derive from a general microscopic electron model a general expression for the rate of pumping of electrons between valleys in parallel temperature gradient and magnetic field. From this expression we find a relation, which is analogous to the Mott relation, between the rate of pumping due to a temperature gradient and that due to an electric field. We also apply our theory to a two-band model for Weyl semimetals to study thermoelectric and thermal transport in a magnetic field. We show that the Mott relation is satisfied in the chiral-anomaly induced thermoelectric conductivity, and that the Wiedemann-Franz law is violated in the chiral-anomaly induced thermal conductivity, which are both consistent with the results obtained by invoking semiclassical wave-packet dynamics.

arXiv comment17 pages, 1 figure, 1 table

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• Axion Electrodynamics in Topological Materials
• Valley Hall effect caused by the phonon and photon drag
• Quantum kinetic theory of nonlinear thermal current
• Berry curvature induced nonlinear magnetoresistivity in two dimensional systems
• Quantum Theory of Nonlinear Thermal Response
• Intrinsic nonlinear thermal Hall transport of magnons: A Quantum kinetic theory approach
• Skew Scattering and Side Jump Drive Exciton Valley Hall Effect in Two-Dimensional Crystals
• Nonlinear magnetotransport in Weyl semimetal
• Intrinsic Contribution to Non-linear Thermoelectric Effect
• Valley and spin accumulation in ballistic and hydrodynamic channels
• Non-linear magnon transport in a bilayer van der Waals antiferromagnets
• Intrinsic nonlinear Nernst and Seebeck effect
• Nonlinear thermoelectric probes of anomalous electron lifetimes in topological Fermi liquids
• Interaction-induced nonlinear magnon transport in noncentrosymmetric magnets
• Microscopic theory of spin Nernst effect
• Quantum-geometric thermal conductivity of superconductors