Revealing Quantum Geometry in Nonlinear Quantum Materials

Abstract

Berry curvature-related topological phenomena have been a central topic in condensed matter physics. Yet, until recently other quantum geometric quantities such as the metric and connection received only little attention due to the relatively few effects which have been documented for them. This review gives a modern perspective how quantum geometric quantities naturally enter the nonlinear responses of quantum materials and demonstrate their deep connection with excitation energy, lifetimes, symmetry, and corresponding physical processes. The multitude of nonlinear responses can be subdivided into nonlinear optical effects, subgap responses, and nonlinear transport phenomena. Such a distinction by energy scales facilitates an intuitive understanding of the underlying electronic transitions, giving rise to a unified picture of the electron motion beyond linear order. The well-known injection and shift currents constitute the main resonances in the optical regime. Exploiting their respective lifetime and symmetry dependencies, this review elucidates how these resonances can be distinguished by a corresponding quantum geometric quantity that shares the same symmetry. This is followed by a brief exposition of the role of quasiparticle lifetimes for nonlinear subgap responses, which presents a window into the microscopic short-term dynamics as well as the ground state correlation and localization. We conclude with an account of the anomalous motion due to the Berry curvature dipole and quantum metric dipole in nonlinear transport, clarifying the correspondence between physical observables and the underlying mechanisms. This review highlights the close relationship between quantum geometry and nonlinear response, showing the way towards promising probes of quantum geometry and enabling novel avenues to characterize complex materials.

Review, 21 + 21 pages, 7 figures, 5 tables, comments are welcome

References in corpus (118)

• Topological Insulators
• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• Anomalous Hall effect
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Topological Materials: Weyl Semimetals
• Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Observation of the nonlinear Hall effect under time reversal symmetric conditions
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Quantized circular photogalvanic effect in Weyl semimetals
• Three-Dimensional Topological Insulators
• Topological nature of nonlinear optical effects in solids
• Giant and nonreciprocal second harmonic generation from layered antiferromagnetism in bilayer CrI3
• Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals
• Direct optical detection of Weyl fermion chirality in a topological semimetal
• Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
• Colossal Bulk Photovoltaic Effect in a Weyl Semimetal
• Large Fermi Arcs in Unconventional Weyl Semimetal RhSi
• Design principles for shift current photovoltaics
• Nonlinear Hall Effects
• Photocurrents in Weyl semimetals
• Berry Curvature Enhanced Nonlinear Photogalvanic Response of Type-II Weyl Cone
• Geometry and non-adiabatic response in quantum and classical systems
• Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure
• Quantum metric-induced nonlinear transport in a topological antiferromagnet
• Large bulk photovoltaic effect and spontaneous polarization of single-layer monochalcogenides
• Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP
• Disorder-induced nonlinear Hall effect with time-reversal symmetry
• Optical characterization of topological insulator surface states: Berry curvature-dependent response
• Notes on Anomaly Induced Transport
• Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals
• Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs
• Room temperature nonlinear Hall effect and wireless RF rectification in Weyl semimetal TaIrTe4
• The Berry curvature dipole in Weyl semimetal materials: an ab initio study
• Diagrammatic approach to nonlinear optical response with application to Weyl semimetals
• Observation of Topological Photocurrents in the Chiral Weyl Semimetal RhSi
• Band signatures for strong nonlinear Hall effect in bilayer WTe${}_2$
• High-frequency rectification via chiral Bloch electrons
• Intrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets
• Quantum theory of the third-order nonlinear electrodynamic effects in graphene
• Third order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature
• Magnetically Switchable Light-Matter Interaction in the Two-Dimensional Magnet CrI3
• Ab initio calculation of the shift photocurrent by Wannier interpolation
• Topology and geometry under the nonlinear electromagnetic spotlight
• When chiral photons meet chiral fermions - Photoinduced anomalous Hall effects in Weyl semimetals
• Essay: Where Can Quantum Geometry Lead Us?
• Giant topological longitudinal circular photo-galvanic effect in the chiral multifold semimetal CoSi
• Chiral photocurrent in parity-violating magnet and enhanced response in topological antiferromagnet
• Quantum theory of the nonlinear Hall effect
• Consequences of Time-reversal-symmetry Breaking in the Light-Matter Interaction: Berry Curvature, Quantum Metric and Diabatic Motion
• Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry
• Symmetry and Quantum Kinetics of the Non-linear Hall Effect
• Quantum frequency doubling in the topological insulator Bi2Se3
• Quantum geometry induced nonlinear transport in altermagnets
• Gauge covariances and nonlinear optical responses
• Coherent wave-packet evolution in coupled bands
• Theory of nonlinear Hall effects: renewed semiclassics from quantum kinetics
• Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect
• Photogalvanic Effect in Weyl Semimetals from First Principles
• Pseudo-electromagnetic fields in topological semimetals
• Enhancement of bulk photovoltaic effect in topological insulators
• Giant $c$-axis nonlinear anomalous Hall effect in T${}_d$-MoTe${}_2$ and WTe${}_2$
• Quantitative relationship between polarization differences and the zone-averaged shift photocurrent
• Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule
• Giant nonlinear Hall effect in twisted WSe${}_2$
• Photogalvanic effect in Weyl semimetals
• Ballistic and shift currents in the bulk photovoltaic effect theory
• Nonlinear optical responses of crystalline systems: Results from a velocity gauge analysis
• Berry connection polarizability tensor and third-order Hall effect
• Gyrotropic Hall effect in Berry-curved materials
• Difference frequency generation in topological semimetals
• Interactions remove the quantization of the chiral photocurrent at Weyl points
• Nonlinear electric transport in odd-parity magnetic multipole systems: Application to Mn-based compounds
• Thermal transport, geometry, and anomalies
• Shift charge and spin photocurrents in Dirac surface states of topological insulator
• Giant linearly-polarized photogalvanic effect and second harmonic generation in two-dimensional axion insulators
• Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects
• Shift current bulk photovoltaic effect influenced by quasiparticles and excitons
• Quantum geometry in condensed matter
• Quantum Theory of the Third-Harmonic Generation in Graphene
• Strong Room-Temperature Bulk Nonlinear Hall Effect in a Spin-Valley Locked Dirac Material
• Magnus Hall Effect
• Systematic analysis method for nonlinear response tensors
• Phonon-Assisted Ballistic Current From First Principles Calculations
• Effects of renormalization and non-Hermiticity on nonlinear responses in strongly-correlated electron systems
• Resonant photovoltaic effect in doped magnetic semiconductors
• Circular and magnetoinduced photocurrents in Weyl semimetals
• Twisted photovoltaics at terahertz frequencies from momentum shift current
• Semiclassical equations of motion for disordered conductors: extrinsic interband velocity, corrected collision integral and spin-orbit torques
• Nontrivial quantum geometry of degenerate flat bands
• Unifying semiclassics and quantum perturbation theory at nonlinear order
• Semiclassical theory of the circular photogalvanic effect in gyrotropic systems
• Geometric aspects of nonlinear and nonequilibrium phenomena
• Nonreciprocal optical response in parity-breaking superconductors
• Quantized Integrated Shift Effect in Multigap Topological Phases
• Third-order intrinsic anomalous Hall effect with generalized semiclassical theory
• Optical manifestations and bounds of topological Euler class
• Nonvanishing sub-gap photocurrent as a probe of lifetime effects
• The Berry dipole photovoltaic demon and the thermodynamics of photo-current generation within the optical gap of metals
• General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect
• Quantum Kinetic Theory of Nonlinear Optical Currents: Finite Fermi surface and Fermi sea contributions
• The Fermi-Dirac staircase occupation of Floquet bands and current rectification inside the optical gap of metals: a rigorous perspective
• Beyond the Berry Phase: Extrinsic Geometry of Quantum States
• Anomalous shift and optical vorticity in the steady photovoltaic current
• Equivalence of semiclassical and response theories for second-order nonlinear ac Hall effects
• Photocurrent response in parity-time symmetric current-ordered states
• Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals
• Quantum kinetic theory of quadratic responses
• Surface photogalvanic effect in Weyl semimetals
• Photogalvanic response in multi-Weyl semimetals
• Effects of relaxation on photovoltaic effect and possibility of photocurrent within transparent region
• Raman Photogalvanic Effect: photocurrent at inelastic light scattering
• Hybrid-order topology in unconventional magnets of Eu-based Zintl compounds with surface-dependent quantum geometry
• Magnetic Bulk Photovoltaic Effect: Strong and Weak Field
• Nonlinear Nonreciprocal Photocurrents under Phonon Dressing
• Electrical magnetochiral anisotropy and quantum metric in chiral conductors

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• Modulation of quantum geometry and its coupling to pseudo-electric field by dynamic strain
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• Quantum geometric map of magnetotransport
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• Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
• Quantum geometry and low-frequency optical conductivity of nodal planes