Heat transport as torsional responses and Keldysh formalism in a curved spacetime

Abstract

We revisit a theory of heat transport in the light of a gauge theory of gravity and find the proper heat current with a corresponding gauge field, which yields the natural definitions of the heat magnetization and the Kubo-formula contribution to the thermal conductivity as torsional responses. We also develop a general framework for calculating gravitational responses by combining the Keldysh and Cartan formalisms. By using this framework, we explicitly calculate these two quantities and reproduce the Wiedemann-Franz law for the thermal Hall conductivity in the clean and non-interacting case. Finally, we discuss an effective action for the quantized thermal Hall effect in $(2+1)$-D topological superconductors.

14 pages, no figures

References in corpus (10)

• Observation of the Magnon Hall Effect
• Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
• Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets
• Effects of mechanical rotation on spin currents
• Topological field theory and thermal responses of interacting topological superconductors
• Quantum Thermal Hall Effect in a Time-Reversal-Symmetry-Broken Topological Superconductor in Two Dimensions : Approach From Bulk Calculations
• Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance
• Theory of Non-Equilibirum States Driven by Constant Electromagnetic Fields: Non-Commutative Quantum Mechanics in the Keldysh Formalism
• Hybrid skew scattering regime of the anomalous Hall effect in Rashba systems: unifying Keldysh, Boltzmann, and Kubo formalisms
• Theory of Charge and Heat Polarizations with the Keldysh Formalism

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