Difference frequency generation in topological semimetals

Abstract

When two lasers are applied to a non-centrosymmetric material, light can be generated at the difference of the incoming frequencies $\Delta \omega$, a phenomenon known as difference frequency generation (DFG), well characterized in semiconductors. In this work, we derive a general expression for DFG in metals, which we use to show that the DFG in chiral topological semimetals under circular polarized light is quantized in units of $e^3/h^2$ and independent of material parameters, including the scattering time $\tau$, when $\Delta \omega \gg {\tau }^{-1}$. In this regime, DFG provides a simpler alternative to measure a quantized response in metals compared to previous proposals based on single frequency experiments. Our general derivation unmasks, in addition, a free-carrier contribution to the circular DFG beyond the semiclassical one. This contribution can be written as a Fermi surface integral, features strong frequency dependence, and oscillates with a $\pi /2$ shift with respect to the quantized contribution. We make predictions for the circular DFG of chiral and non-chiral materials using generic effective models, and ab-initio calculations for TaAs and RhSi. Our work provides a complete picture of the DFG in the length gauge approach, in the clean, non-interacting limit, and highlights a plausible experiment to measure topologically quantizated photocurrents in metals.

arXiv comment4+epsilon+10 pages, 3 figures

References in corpus (44)

• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Observation of Weyl nodes in TaAs
• Quantized circular photogalvanic effect in Weyl semimetals
• Topological nature of nonlinear optical effects in solids
• Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals
• Topological quantum properties of chiral crystals
• Multiple types of topological fermions in transition metal silicides
• Direct optical detection of Weyl fermion chirality in a topological semimetal
• Colossal Bulk Photovoltaic Effect in a Weyl Semimetal
• Large Fermi Arcs in Unconventional Weyl Semimetal RhSi
• A new type of Weyl semimetal with quadratic double Weyl fermions in SrSi2
• Discovery of topological chiral crystals with helicoid arc states
• New classes of chiral topological nodes with non-contractible surface Fermi arcs in CoSi
• Photocurrents in Weyl semimetals
• Observation of Chiral Fermions with a Large Topological Charge and and Associated Fermi-Arc Surface States in CoSi
• Chiral Topological Semimetal with Multifold Band Crossings and Long Fermi arcs
• Weyl Node and Spin Texture in Trigonal Tellurium and Selenium
• Disorder-induced nonlinear Hall effect with time-reversal symmetry
• Optical characterization of topological insulator surface states: Berry curvature-dependent response
• 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
• Chiral Optical Response of Multifold Fermions
• Existence of bulk chiral fermions and crystal symmetry
• Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals
• Symmetry and Quantum Kinetics of the Non-linear Hall Effect
• Spatially dispersive circular photogalvanic effect in a Weyl semimetal
• Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs
• Photogalvanic Effect in Weyl Semimetals from First Principles
• Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule
• Photogalvanic effect in Weyl semimetals
• Gyrotropic Hall effect in Berry-curved materials
• Anomalous Hall Effect in type-I Weyl metals
• Nonlinear anomalous photocurrents in Weyl semimetals
• Global band topology of simple and double Dirac-point (semi-)metals
• Circular and magnetoinduced photocurrents in Weyl semimetals
• Photocurrents in gyrotropic Weyl semimetals
• Photocurrents in Bi2Se3: bulk versus surface, and injection versus shift currents
• Momentum-Space Electromagnetic Induction in Weyl Semimetals
• Circular photocurrent in Weyl semimetals with mirror symmetry

Cited by in corpus (59)

• Riemannian geometry of resonant optical responses
• Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals
• Observation of Topological Photocurrents in the Chiral Weyl Semimetal RhSi
• Topology and geometry under the nonlinear electromagnetic spotlight
• 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
• Observation and control of maximal Chern numbers in a chiral topological semimetal
• Consequences of Time-reversal-symmetry Breaking in the Light-Matter Interaction: Berry Curvature, Quantum Metric and Diabatic Motion
• Photocurrent as a multi-physics diagnostic of quantum materials
• First Principles Calculations for Topological Quantum Materials
• Quantum geometry induced second harmonic generation
• Giant nonlinear photocurrent in $\mathcal{P}\mathcal{T}$-symmetric magnetic topological quantum materials
• Interactions remove the quantization of the chiral photocurrent at Weyl points
• Linear and nonlinear optical responses in the chiral multifold semimetal RhSi
• Optical signatures of multifold fermions in the chiral topological semimetal CoSi
• Semiconductor-Bloch Formalism: Derivation and Application to High-Harmonic Generation from Dirac Fermions
• Revealing Quantum Geometry in Nonlinear Quantum Materials
• An ab-initio study of circular photogalvanic effect in chiral multifold semimetals
• Intrinsic Fermi Surface Contribution to the Bulk Photovoltaic Effect
• Geometric aspects of nonlinear and nonequilibrium phenomena
• Nonreciprocal optical response in parity-breaking superconductors
• Nonlinear magnetoconductivity in Weyl and multi-Weyl semimetal in quantizing magnetic field
• Role of time reversal symmetry and tilting in circular photogalvanic responses
• Acoustogalvanic effect in Dirac and Weyl semimetals
• Nonvanishing sub-gap photocurrent as a probe of lifetime effects
• Rabi Regime of Current Rectification in Solids
• Quantum Kinetic Theory of Nonlinear Optical Currents: Finite Fermi surface and Fermi sea contributions
• Electronic structure and unconventional non-linear response in double Weyl semimetal SrSi${}_2$
• The Fermi-Dirac staircase occupation of Floquet bands and current rectification inside the optical gap of metals: a rigorous perspective
• A comprehensive theory of second-order spin photocurrents
• Nonlinear optical responses in noncentrosymmetric superconductors
• Strain-induced large injection current in twisted bilayer graphene
• Equivalence of semiclassical and response theories for second-order nonlinear ac Hall effects
• Computing observables without eigenstates: applications to Bloch Hamiltonians
• Bulk photovoltaic effects in altermagnets
• Polariton-drag enabled quantum geometric photocurrents in high symmetry materials
• Photon-drag photovoltaic effects and quantum geometric nature
• Photogalvanic response in multi-Weyl semimetals
• Effects of relaxation on photovoltaic effect and possibility of photocurrent within transparent region
• Second Harmonic Helicity and Faraday Rotation in Gated Single-Layer 1T${}^{\prime }$-WTe${}_2$
• Magnetic parity violation and parity-time-reversal-symmetric magnets
• Including many-body effects into the Wannier-interpolated quadratic photoresponse tensor
• Skin Effect of Nonlinear Optical Responses in Antiferromagnets
• Multiplicative topological semimetals
• The Berry Phase Rectification Tensor and The Solar Rectification Vector
• Intrinsic and extrinsic photogalvanic effects in twisted bilayer graphene
• Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$
• Generalized Pitaevskii relation between rectifying and linear responses: its application to reciprocal magnetization induction
• Higher-order bulk photovoltaic effects, quantum geometry and application to $p$-wave magnets
• Tunable optical bistability of two-dimensional tilted Dirac system
• Nonlinear bulk photocurrent probe Z2 topological phase transition
• Nonlinear Hall effect driven by spin-charge-coupled motive force
• Photon absorption in twisted bilayer graphene
• Large circular photogalvanic effect in the noncentrosymmetric magnetic Weyl semimetal CeAlSi
• Intrinsic efficiency of injection photocurrents in magnetic materials
• Quantum geometry in low-energy linear and nonlinear optical responses of magnetic Rashba semiconductor (Ge,Mn)Te
• Axion dark matter detection via shift current
• Wavefunction-Free Approach for Predicting Nonlinear Responses in Weyl Semimetals
• Optical Response from Charge-Density Waves in Weyl Semimetals