Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule

Abstract

Electrons moving in a Bloch band are known to acquire an anomalous Hall velocity proportional to the Berry curvature of the band which is responsible for the intrinsic linear Hall effect in materials with broken time-reversal symmetry. Here, we demonstrate that there is also an anomalous correction to the electron acceleration which is proportional to the Berry curvature dipole and is responsible for the Nonlinear Hall effect recently discovered in materials with broken inversion symmetry. This allows us to uncover a deeper meaning of the Berry curvature dipole as a nonlinear version of the Drude weight that serves as a measurable order parameter for broken inversion symmetry in metals. We also derive a quantum rectification sum rule in time reversal invariant materials by showing that the integral over frequency of the rectification conductivity depends solely on the Berry connection and not on the band energies. The intraband spectral weight of this sum rule is exhausted by the Berry curvature dipole Drude-like peak, and the interband weight is also entirely controlled by the Berry connection. This sum rule opens a door to search for alternative photovoltaic technologies based on the Berry geometry of bands. We also describe the rectification properties of Weyl semimetals which are a promising platform to investigate these effects.

arXiv comment8 pages, 3 figures

References in corpus (37)

• Topological Insulators
• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• Anomalous Hall effect
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Maximally localized Wannier functions: Theory and applications
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Experimental realisation of the topological Haldane model
• Experimental discovery of Weyl semimetal TaAs
• Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Atomic quantum gases in periodically driven optical lattices
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Observation of the nonlinear Hall effect under time reversal symmetric conditions
• Quantized circular photogalvanic effect in Weyl semimetals
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Topological quantum properties of chiral crystals
• Direct optical detection of Weyl fermion chirality in a topological semimetal
• A new type of Weyl semimetal with quadratic double Weyl fermions in SrSi2
• Photocurrents in Weyl semimetals
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Disorder-induced nonlinear Hall effect with time-reversal symmetry
• Confinement-induced Berry phase and helicity-dependent photocurrents
• The Berry curvature dipole in Weyl semimetal materials: an ab initio study
• Diagrammatic approach to nonlinear optical response with application to Weyl semimetals
• Orbital magnetoelectric coupling in band insulators
• Strongly enhanced Berry dipole at topological phase transitions in BiTeI
• Measuring quantized circular dichroism in ultracold topological matter
• Symmetry and Quantum Kinetics of the Non-linear Hall Effect
• Theory of nonlinear Hall effects: renewed semiclassics from quantum kinetics
• Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs
• Gyrotropic Hall effect in Berry-curved materials
• Bulk photovoltaic effects in the presence of a static electric field
• Nonlinear anomalous photocurrents in Weyl semimetals
• Non-linear Hall effect in three-dimensional Weyl and Dirac semimetals
• Jerk current: A novel bulk photovoltaic effect

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