Nonlinear optics from an ab-initio approach by means of the dynamical Berry phase: Application to second- and third-harmonic generation in semiconductors

Abstract

We present an ab-initio real-time-based computational approach to study nonlinear optical properties in condensed matter systems that is especially suitable for crystalline solids and periodic nanostructures. The equations of motion and the coupling of the electrons with the external electric field are derived from the Berry-phase formulation of the dynamical polarization [Souza et al., Phys. Rev. B 69, 085106 (2004)]. Many-body effects are introduced by adding single-particle operators to the independent-particle Hamiltonian. We add a Hartree operator to account for crystal local effects and a scissor operator to correct the independent particle band structure for quasiparticle effects. We also discuss the possibility of accurately treating excitonic effects by adding a screened Hartree-Fock self-energy operator. The approach is validated by calculating the second-harmonic generation of SiC and AlAs bulk semiconductors: an excellent agreement is obtained with existing ab initio calculations from response theory in frequency domain [Luppi et al., Phys. Rev. B 82, 235201 (2010)]. We finally show applications to the second-harmonic generation of CdTe and the third-harmonic generation of Si.

10 pages, 9 figures

References in corpus (1)

• Speeding up the solution of the Bethe-Salpeter equation by a double-grid method and Wannier interpolation

Cited by in corpus (31)

• Many-body perturbation theory calculations using the yambo code
• Second Harmonic Generation in h-BN and MoS${}_2$ monolayers: the role of electron-hole interaction
• Ab initio calculations of ultra-short carrier dynamics in 2D materials: valley depolarization in single-layer WSe${}_2$
• First-Principles Studies of Second-Order Nonlinear Optical Properties of Organic-Inorganic Hybrid Halide Perovskites
• Bulk Photovoltaic Effect Driven by Collective Excitations in a Correlated Insulator
• Two-photon absorption in two-dimensional materials: The case of hexagonal boron nitride
• Optical properties of periodic systems within the current-current response framework: pitfalls and remedies
• How strong is the Second Harmonic Generation in single-layer monochalcogenides? A response from first-principles real-time simulations
• Excitonic effects in third harmonic generation: the case of carbon nanotubes and nanoribbons
• Exciton-Enhanced Spontaneous Parametric Down-Conversion in Two-Dimensional Crystals
• Nonlinear polarization evolution using time-dependent density functional theory
• Dielectrics in a time-dependent electric field: a real-time approach based on density-polarization functional theory
• Exciton enhanced nonlinear optical responses in monolayer h-BN and MoS2: Insight from first-principles exciton-state coupling formalism and calculations
• Exciton-driven giant non-linear overtone signals from buckled hexagonal monolayer GaAs
• Nonlinear Light Absorption in Many-Electron Systems Excited by an Instantaneous Electric Field: A Non-Perturbative Approach
• Full ab initio band structure analysis of interband and intraband contributions for third harmonic generation coefficient of bulk silicon: implementation and application of the sum-over-states
• Adiabatic corrections for velocity-gauge simulations of electron dynamics in periodic potentials
• Im$\{{\chi }^{(3)}\}$ spectra of 110-cut GaAs, GaP, and Si near the two-photon absorption band edge
• Expeditious computation of nonlinear optical properties of arbitrary order with native electronic interactions in the time domain
• Including many-body effects into the Wannier-interpolated quadratic photoresponse tensor
• Polaronic Enhancement of Second-Harmonic Generation in Lithium Niobate
• Accelerating the discovery of high-performance nonlinear optical materials using active learning and high-throughput screening
• Exciton Shift Currents: DC Conduction with Sub-bandgap Photo Excitations
• Extracting Nonlinear Dynamical Response Functions from Time Evolution
• A real-time approach to frequency-mixing spectroscopies: application to sum and difference frequency generation in two-dimensional crystals
• Shift current in 2D Janus Transition-Metal Dichalcogenides: the role of excitons
• Floquet formulation of the dynamical Berry-phase approach to non-linear optics in extended systems
• Photon pumping, photodissociation and dissipation at interplay for the fluorescence of a molecule in a cavity
• Non-linear response in extended systems: a real-time approach
• Electron charge dynamics and charge separation: A response theory approach
• Tangent equations of motion for nonlinear response functions