Quantum Kinetic Theory of Nonlinear Optical Currents: Finite Fermi surface and Fermi sea contributions

Abstract

The quantum kinetic framework provides a versatile method for investigating the dynamical optical and transport currents of crystalline solids. In this paper, starting from the density-matrix equations of motion, we present a general theoretical path to obtain nonlinear optical responses elegantly and transparently. We devise a kinetic theory applicable to materials with arbitrary band structures and captures intraband and interband coherence effects, finite Fermi surfaces, and disorder effects. We present a classification of nonlinear optical currents arising from the interference of interband and intraband components of the density matrix with distinct symmetry and quantum geometrical origin for each contribution. In this context, we report four findings. (i) The Fermi Golden Rule approach is insufficient to derive the correct expression for the injection current, a shortcoming that we remedy in our theory while associating the injection current with the intraband-interband contribution to the second-order density matrix. (ii) The interband-intraband contribution yields a resonant current that survives irrespective of any symmetry constraint in addition to the well-known anomalous nonlinear current (non-resonant), which requires time-reversal symmetry. (iii) Quite generally, the nonlinear current is significantly enhanced by contributions from the finite Fermi surface. (iv) The finite Fermi surface and Fermi sea additionally lead to sizable novel nonlinear effects via contributions we term double resonant and higher-order pole. As an illustration, we compute the nonlinear response of topological antiferromagnet CuMnAs and thin film tilted Weyl semimetals dominated by interband coherence effects. We find that the nonlinear response of CuMnAs is responsive to the direction of finite magnetization field and choice of the polarization angle of the beam, while Weyl semimetal only to tilt.

16 pages, 4 figures, Comments/Suggestions are welcome

References in corpus (35)

• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Topological Semimetals
• Chiral Anomaly and Diffusive Magnetotransport in Weyl Metals
• Riemannian geometry of resonant optical responses
• Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs
• Intrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets
• Ordering of magnetic impurities and tunable electronic properties of topological insulators
• Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals
• Electric control of Dirac quasiparticles by spin-orbit torque in an antiferromagnet
• Berry curvature dipole senses topological transition in a moiré superlattice
• Quantum transport in Dirac materials: signatures of tilted and anisotropic Dirac and Weyl cones
• Abelian and Non-Abelian Quantum Geometric Tensor
• Quantum geometry induced second harmonic generation
• Doping Induced Second Harmonic Generation in Centrosymmetric Graphene from Quadrupole Response
• Anomalous Nernst and Thermal Hall Effects in Tilted Weyl Semimetals
• Shift charge and spin photocurrents in Dirac surface states of topological insulator
• Nonlinear transport in Weyl semimetals induced by Berry curvature dipole
• Giant nonlinear Hall effect in strained twisted bilayer graphene
• Generation of spin currents and spin densities in systems with reduced symmetry
• Generating a topological anomalous Hall effect in a non-magnetic conductor
• Resonant photovoltaic effect in doped magnetic semiconductors
• Nonlinear anomalous Hall effects probe topological phase-transitions in twisted double bilayer graphene
• Current-induced second harmonic generation in inversion-symmetric Dirac and Weyl semimetals
• Twisted photovoltaics at terahertz frequencies from momentum shift current
• Anomalous Hall response of topological insulators
• Intrinsic Fermi Surface Contribution to the Bulk Photovoltaic Effect
• The Berry dipole photovoltaic demon and the thermodynamics of photo-current generation within the optical gap of metals
• Berry curvature induced nonlinear magnetoresistivity in two dimensional systems
• Quantum Transport in Weyl Semimetal Thin Films in the Presence of Spin-Orbit Coupled Impurities
• Non-linear ballistic response of quantum spin-Hall edge states
• Intrinsic Contribution to Non-linear Thermoelectric Effect
• Nonlinear optical absorption and photocurrents in topological insulators
• Second Harmonic Helicity and Faraday Rotation in Gated Single-Layer 1T${}^{\prime }$-WTe${}_2$
• Raman Photogalvanic Effect: photocurrent at inelastic light scattering

Cited by in corpus (14)

• Anomalous skew-scattering nonlinear Hall effect and chiral photocurrents in {\it PT}-symmetric antiferromagnets
• Revealing Quantum Geometry in Nonlinear Quantum Materials
• Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect
• Intrinsic nonlinear thermal Hall transport of magnons: A Quantum kinetic theory approach
• Quantum kinetic theory of quadratic responses
• Room Temperature Ferroelectricity and Electrically Tunable Berry Curvature Dipole in III-V Monolayers
• Longitudinal DC Conductivity in Dirac Nodal Line Semimetals: Intrinsic and Extrinsic Contributions
• High-harmonic generation in graphene under the application of a DC electric current: From perturbative to nonperturbative regimes
• Disorder induced dynamical interband response in Dirac nodal line semimetals
• Light-induced Nonlinear Spin Hall Current in Single-layer WTe${}_2$
• Reshaping the anomalous Hall response in tilted 3D system with disorder correction
• Band Geometry Induced Third-Harmonic Generation
• Interband response in spin-orbit coupled nodal line semimetals
• Universal classes of disorder scatterings in in-plane anomalous Hall effect