On the separation of Hall and Ohmic nonlinear responses

Abstract

The symmetric and antisymmetric parts of the linear conductivity describe the dissipative (Ohmic) and nondissipative (Hall) parts of the current. The Hall current is always transverse to the applied electric field regardless of its orientation; the Ohmic current is purely longitudinal in cubic crystals, but in lower-symmetry crystals it has a transverse component whenever the field is not aligned with a principal axis. In this work, we extend that analysis beyond the linear regime. We consider all possible ways of partitioning the current at any order in the electric field without taking symmetry into account, and find that the Hall vs Ohmic decomposition is the only one that satisfies certain basic requirements. A general prescription is given for achieving that decomposition, and the case of the quadratic conductivity is analyzed in detail. By performing a symmetry analysis we find that in five of the 122 magnetic point groups the quadratic dc conductivity is purely Ohmic and even under time reversal, a type of response that is entirely disorder mediated.

arXiv comment16 pages

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Cited by in corpus (21)

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• Non-linear Hall Effects: Mechanisms and Materials
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• Microscopic mechanism for intrinsic nonlinear anomalous Hall conductivity in noncollinear antiferromagnetic metals
• Odd non-linear conductivity under spatial inversion in chiral Tellurium
• Scaling Law for Time-Reversal-Odd Nonlinear Transport
• An antiferromagnetic diode effect in even-layered MnBi2Te4
• Symmetry Origin and Microscopic Mechanism of Electrical Magnetochiral Anisotropy in Tellurium
• Giant Crystal Hall Effect in Collinear Antiferromagnetic $\gamma$-FeMn
• Intrinsic nonlinear Nernst and Seebeck effect
• Crystal tensor properties of magnetic materials with and without spin-orbit coupling. Application of spin point groups as approximate symmetries
• Nonlinear Hall effects with an exceptional ring
• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• Generalized Pitaevskii relation between rectifying and linear responses: its application to reciprocal magnetization induction
• Nonlinear longitudinal current of band-geometric origin in wires of finite thickness
• Intrinsic nonlinear Hall effect beyond Bloch geometry
• Orbital magnetization as the origin of the nonlinear Hall effect
• Light-induced nonlinear Edelstein effect under ferroaxial ordering
• Nonlinear Odd Viscoelastic Effect
• Theory of unidirectional magnetoresistance and nonlinear Hall effect