Fundamental relations for anomalous thermoelectric transport coefficients in the non-linear regime

Abstract

In a series of recent papers anomalous Hall and Nernst effects have been theoretically discussed in the non-linear regime and have seen some early success in experiments. In this paper, by utilizing the role of Berry curvature dipole, we derive the fundamental mathematical relations between the anomalous electric and thermoelectric transport coefficients in the non-linear regime. The formulae we derive replace the celebrated Wiedemann-Franz law and Mott relation of anomalous thermoelectric transport coefficients defined in the linear response regime. In addition to fundamental and testable new formulae, an important byproduct of this work is the prediction of nonlinear anomalous thermal Hall effect which can be observed in experiments.

arXiv comment6 pages, 4 figures. Accepted version

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• Nonlinear Hall Effects
• Higher-Order Nonlinear Anomalous Hall Effects Induced by Berry Curvature Multipoles
• Nonlinear transport in Weyl semimetals induced by Berry curvature dipole
• Giant nonlinear Hall effect in strained twisted bilayer graphene
• Nonlinear magnon spin Nernst effect in antiferromagnets and strain-tunable pure spin current
• Systematic analysis method for nonlinear response tensors
• Nonlinear anomalous Hall effects probe topological phase-transitions in twisted double bilayer graphene
• Chiral anomaly induced nonlinear Nernst and thermal Hall effects in Weyl semimetals
• Non-linear transport without spin-orbit coupling or warping in two-dimensional Dirac semimetals
• Infinite Berry Curvature of Weyl Fermi Arcs
• Quantum kinetic theory of nonlinear thermal current
• Quantum Theory of Nonlinear Thermal Response
• Intrinsic nonlinear thermal Hall transport of magnons: A Quantum kinetic theory approach
• Electrically switchable giant Berry curvature dipole in silicene, germanene and stanene
• Nonlinear Hall effect induced by internal Coulomb interaction and phase relaxation process in a four-terminal system with time-reversal symmetry
• Fundamental Distinction between Intrinsic and Extrinsic Nonlinear Thermal Hall Effects
• Non-Linear Hall Effect in Multi-Weyl Semimetals
• Distinct signatures of particle-hole symmetry breaking in transport coefficients for generic multi-Weyl semimetals
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• Quantum nonlinear ac transport theory at low frequency
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• Chiral Anomaly Induced Transverse Planar Transport Phenomena in Three Dimensional Spin-Orbit Coupled Metals
• Intrinsic nonlinear valley Nernst effect
• Intrinsic nonlinear valley Nernst effect in the strained bilayer graphene