Topology and geometry under the nonlinear electromagnetic spotlight

Abstract

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their wavefunctions. A key challenge is to identify and implement experiments that probe or control these quantum properties. In this review, we describe recent progress in this direction, focusing on nonlinear electromagnetic responses that arise directly from quantum geometry and topology. We give an overview of the field by discussing new theoretical ideas, groundbreaking experiments, and the novel materials that drive them. We conclude by discussing how these techniques can be combined with new device architectures to uncover, probe, and ultimately control novel quantum phases with emergent topological and correlated properties.

arXiv commentNature Materials (In Press)

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Cited by in corpus (84)

• Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure
• Light-induced emergent phenomena in 2D materials and topological materials
• Berry curvature dipole senses topological transition in a moiré superlattice
• Photocurrent as a multi-physics diagnostic of quantum materials
• Quantum geometry in condensed matter
• Orbital Magneto-Nonlinear Anomalous Hall Effect in Kagome Magnet Fe${}_3$Sn${}_2$
• Tunable moiré materials for probing Berry physics and topology
• Analysis of model parameter dependences on the second-order nonlinear conductivity in $\mathcal{P}\mathcal{T}$-symmetric collinear antiferromagnetic metals with magnetic toroidal moment on zigzag chains
• Time-Reversal-Even Nonlinear Current Induced Spin Polarization
• Revealing Quantum Geometry in Nonlinear Quantum Materials
• Non-linear Hall Effects: Mechanisms and Materials
• Nontrivial quantum geometry of degenerate flat bands
• Non-linear Transport in Non-centrosymmetric Systems: From Fundamentals to Applications
• Symmetry analysis with spin crystallographic groups: Disentangling effects free of spin-orbit coupling in emergent electromagnetism
• Visualizing bulk and edge photocurrent flow in anisotropic Weyl semimetals
• Photovoltaic effect by soft phonon excitation
• Cavity engineering of solid-state materials without external driving
• Multipole theory of optical spatial dispersion in crystals
• Terahertz photocurrent probe of quantum geometry and interactions in magic-angle twisted bilayer graphene
• Theory of topological exciton insulators and condensates in flat Chern bands
• Exciton enhanced nonlinear optical responses in monolayer h-BN and MoS2: Insight from first-principles exciton-state coupling formalism and calculations
• Tracing out the Berry curvature dipole and multipoles in second harmonic Hall responses of time-reversal symmetric insulators
• Equivalence of semiclassical and response theories for second-order nonlinear ac Hall effects
• Electric quadrupole second harmonic generation revealing dual magnetic orders in a magnetic Weyl semimetal
• Probing topology in nonlinear topological materials using numerical $K$-theory
• Multidimensional Terahertz Probes of Quantum Materials
• Supercurrent induced resonant optical response
• Nonlinear optical diode effect in a magnetic Weyl semimetal
• Abnormal Surface Nonlinear Optical Responses in Topological Materials
• Extrinsic and Intrinsic Nonlinear Hall Effects across Berry-Dipole Transitions
• Ab initio study of the nonlinear optical properties and d.c. photocurrent of the Weyl semimetal TaIrTe${}_4$
• Quantum optics measurement scheme for quantum geometry and topological invariants
• Tailoring Photocurrent in Weyl Semimetals via Intense Laser Irradiation
• Observation of terahertz second harmonic generation from Dirac surface states in the topological insulator Bi${}_2$Se${}_3$
• Polariton-drag enabled quantum geometric photocurrents in high symmetry materials
• Giant Third-Order Nonlinearity Induced by the Quantum Metric Quadrupole in Few-Layer WTe2
• Topological Circular Dichroism in Chiral Multifold Semimetals
• Photon-drag photovoltaic effects and quantum geometric nature
• Photogalvanic response in multi-Weyl semimetals
• Nonlinear Hall effect in two-dimensional class AI metals
• Intrinsic gyrotropic magnetic current from Zeeman quantum geometry
• Nonlinear optical responses and quantum geometry in rhombohedral trilayer graphene
• Terahertz control of surface topology probed with subatomic resolution
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• Second Harmonic Helicity and Faraday Rotation in Gated Single-Layer 1T${}^{\prime }$-WTe${}_2$
• Ultrafast Carrier Relaxation Dynamics in a Nodal-Line Semimetal PtSn${}_4$
• Magnetic parity violation and parity-time-reversal-symmetric magnets
• Intrinsic nonlinear Hall effect in two-dimensional honeycomb topological antiferromagnets
• Plasmonic quantum nonlinear Hall effect in noncentrosymmetric 2D materials
• Standing and Traveling Waves in a Model of Periodically Modulated One-dimensional Waveguide Arrays
• Nonlinear optical responses in multi-orbital topological superconductors
• Review: Advanced characterization of the spatial variation of moiré heterostructures and moiré excitons
• Electrical control of intrinsic nonlinear Hall effect in antiferromagnetic topological insulator sandwiches
• Diverging shift current responses in the gapless limit of two-dimensional systems
• Extracting Nonlinear Dynamical Response Functions from Time Evolution
• Nonlinear Nonreciprocal Photocurrents under Phonon Dressing
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• Quantum geometric moment encodes stacking order of moiré matter
• Soliton metacrystals: topology and chirality
• Broken symmetries associated with a Kagome chiral charge order
• Nonlinear photomagnetization in insulators
• Nonlinear optical response in kagome lattice with inversion symmetry breaking
• Band Structure and Polarization Effects in Photothermoelectric Spectroscopy of a Bi2Se3 Device
• Quantization of spin circular photogalvanic effect in altermagnetic Weyl semimetals
• Topological phase transitions via attosecond x-ray absorption spectroscopy
• Optically-induced Umklapp shift currents in striped cuprates
• Hall Coulomb drag induced by electron-electron skew scattering
• Nonlinear longitudinal current of band-geometric origin in wires of finite thickness
• Floquet engineering of effective pairing interactions in a doped band insulator
• Role of Ward-Takahashi identity in an electron-phonon coupled system -- Revisiting phonon shift current
• Second-order magnetic responses in quantum magnets: Magnetization under ac magnetic fields
• Quantum geometry in low-energy linear and nonlinear optical responses of magnetic Rashba semiconductor (Ge,Mn)Te
• Intrinsic ultrafast edge photocurrent dynamics in WTe${}_2$ driven by broken crystal symmetry
• Nonlinear edge transport in a quantum Hall system
• Demonstration of geometric diabatic control of quantum states
• Direct Measurement of Helicoid Surface States in RhSi using Nonlinear Optics
• Quantum geometric map of magnetotransport
• Van Roosbroeck's equations with topological terms: the case of Weyl semimetals
• Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
• Wavefunction-Free Approach for Predicting Nonlinear Responses in Weyl Semimetals
• Local phase-space Berry curvature and Hall transport in textured twisted bilayer graphene
• Transverse Photoresistivity from Photothermal Current Deflection in Metal Films
• Quantum theory of nonlinear electromagnetic response
• Floquet solitons in square lattices: Existence, Stability and Dynamics