Quantum kinetic theory of thermoelectric and thermal transport in a magnetic field
| Autor: | Naoto Nagaosa, Akihiko Sekine |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Free electron model
Physics Condensed Matter - Materials Science Condensed Matter - Mesoscale and Nanoscale Physics Condensed matter physics Scattering Materials Science (cond-mat.mtrl-sci) FOS: Physical sciences Semiclassical physics 02 engineering and technology Electron 021001 nanoscience & nanotechnology 01 natural sciences Boltzmann equation Magnetic field symbols.namesake Mesoscale and Nanoscale Physics (cond-mat.mes-hall) 0103 physical sciences Boltzmann constant symbols Nabla symbol 010306 general physics 0210 nano-technology |
| Zdroj: | Physical Review B. 101 |
| ISSN: | 2469-9969 2469-9950 |
| DOI: | 10.1103/physrevb.101.155204 |
| Popis: | 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. Comment: 17 pages, 1 figure, 1 table |
| Databáze: | OpenAIRE |
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