Quantum Theory of Nonlinear Thermal Response

Abstract

The Linear behavior of thermal transport has been widely explored, both theoretically and ex?perimentally. On the other hand, the nonlinear thermal response has not been fully discussed. In light of the thermal vector potential theory [Phys. Rev. Lett. 114, 196601 (2015)], we develop a general formulation to calculate the linear and nonlinear dynamic thermal responses. In the DC limit, we recover the well-known Mott relation and the Wiedemann-Franz (WF) law at the linear order response, which link the thermoelectric conductivity η, thermal conductivity \k{appa} and electric conductivity σ together. To be specific, the linear Mott relation describes the linear η is proportional to the first derivative of σ with respect to Fermi energy (for brevity we call the first derivative, the others are similar); and the linear WF law shows the linear \k{appa} is proportional to the zero derivative (i.e. the σ itself). We found there are higher-order Mott relation and WF law which follow an order-dependent relation. At the second order, the Mott relation indicates that the second order σ is proportional to the zero derivative of the second order η; but the second WF law shows that the second σ is proportional to the first derivative of \k{appa}. At the third order, the derivative order in?creases once. Although we only did explicit calculate up to the third order response, we can deduce that the n-th order electric conductivity is proportional to the n-2-th derivative of the n-th order thermoelectric conductivity for the nonlinear Mott relation; and the n-th order electric conductivity is proportional to the n-1-th derivative of the n-th order thermal conductivity for the nonlinear WF law.

References in corpus (10)

• Berry phase effect in anomalous thermoelectric transport
• Theoretical prediction of rotating magnon wavepacket in ferromagnets
• Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
• High harmonic generation in undoped graphene: Interplay of inter- and intraband dynamics
• Linear and nonlinear optical response of crystals using length and velocity gauges: Effect of basis truncation
• Thermal vector potential theory of transport induced by temperature gradient
• Topological Nonlinear Anomalous Nersnt Effect in Strained Transition Metal Dichalcogenides
• Berry phase mediated topological thermoelectric transport in gapped single and bilayer graphene
• Anomalous Nernst effect from a chiral d-density wave state in underdoped cuprate superconductors
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• Disorder in the non-linear anomalous Hall effect of $\mathcal{P}\mathcal{T}$-symmetric Dirac fermions
• Thermal Hall effect incorporating magnon damping in localized spin systems
• Intrinsic nonlinear Nernst and Seebeck effect
• Anomalous Luttinger equivalence between temperature and curved spacetime: From black hole's atmosphere to thermal quenches
• Scattering theory of thermal and bipolar thermoelectric diodes
• Intrinsic Second-Order magnon Thermal Hall Effect
• Nonlinear Edelstein Effect in Strongly Correlated Electron Systems
• Nonlinear Spectroscopy via Generalized Quantum Phase Estimation
• Fermions in $(1+2)$-dimensions modified by nonminimal coupling and its applications to condensed matter physics
• Quantum theory of nonlinear electromagnetic response