Nonlinear Hall effect in two-dimensional class AI metals

Abstract

In a time-reversal invariant system, while the anomalous Hall effect identically vanishes in the linear response regime due to the constraint of time-reversal symmetry on the distribution of Berry curvature, a nonlinear Hall effect can emerge in the second-order response regime if the inversion symmetry is broken to allow a nonzero Berry curvature dipole (BCD) on the Fermi surface. In this work, we study the nonlinear Hall effect of the BCD origin in two-dimensional doped insulators and semimetals belonging to the symmetry class AI which has spinless time-reversal symmetry. Despite that the class AI does not host any strong topological insulator phase in two dimensions, we find that they can still be classified as topologically obstructed insulators and trivial insulators if putting certain constraint on the Hamiltonians. When the insulator gets closer to the phase boundary of the two distinct phases, we find that the BCDs will become more prominent if the doping level is located near the band edge. Moreover, when the insulator undergoes a phase transition between the two distinct phases, we find that the BCDs will dramatically change their signs. For the semimetals without inversion symmetry, we find that the BCDs will sharply reverse their signs when the doping level crosses the Dirac points. With the shift of the locations of Dirac points in energy, the critical doping level at which the BCDs sharply reverse their signs will accordingly change. Our study reveals that class AI materials can also have interesting geometrical and topological properties, and remarkable nonlinear Hall effect can also appear in this class of materials even though the spin-orbit coupling is negligible. Our findings broaden the scope of materials to study the nonlinear Hall effect and provide new perspectives for the application of this effect.

13 pages, 8 figures

References in corpus (11)

• The electronic properties of graphene
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• The Berry curvature dipole in Weyl semimetal materials: an ab initio study
• Band signatures for strong nonlinear Hall effect in bilayer WTe${}_2$
• Topology and geometry under the nonlinear electromagnetic spotlight
• Berry Curvature Dipole in Strained Graphene: a Fermi Surface Warping Effect
• Gyrotropic Hall effect in Berry-curved materials
• Probing quantum criticality using nonlinear Hall effect in a metallic Dirac system
• Divergent bulk photovoltaic effect in Weyl semimetals

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• Extrinsic and Intrinsic Nonlinear Hall Effects across Berry-Dipole Transitions
• Intrinsic nonlinear Hall effect in two-dimensional honeycomb topological antiferromagnets