Nonlinear optical response induced by non-Abelian Berry curvature in time-reversal-invariant insulators

Abstract

We propose a general framework of nonlinear optics induced by non-Abelian Berry curvature in time-reversal-invariant (TRI) insulators. We find that the third-order response of a TRI insulator under optical and terahertz light fields is directly related to the integration of the non-Abelian Berry curvature over the Brillouin zone. We apply the result to insulators with rotational symmetry near the band edge. Under resonant excitations, the optical susceptibility is proportional to the flux of the Berry curvature through the iso-energy surface, which is equal to the Chern number of the surface times $2\pi$. For the III-V compound semiconductors, microscopic calculations based on the six-band model give a third-order susceptibility with the Chern number of the iso-energy surface equal to three.

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Cited by in corpus (14)

• Strong-field physics in three-dimensional topological insulators
• Dynamical birefringence: Electron-hole recollisions as probes of Berry curvature
• Femtosecond valley polarization and topological resonances in transition metal dichalcogenides
• Topological resonance and single-optical-cycle valley polarization in gapped graphene
• Fundamentally fastest optical processes at the surface of a topological insulator
• Detection of the anomalous velocity with sub-picosecond time resolution in semiconductor nanostructures
• Probing dephasing time of crystals via spectral properties of high-harmonic generation
• Non-Abelian Berry phase for open quantum systems: Topological protection vs geometric dephasing
• Non-Abelian Geometric Dephasing
• Femtosecond currents in transition metal dichalcogenides monolayers
• Laser pulse waveform control of Dirac fermions in graphene
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Universal intrinsic orbital dynamics from Berry curvature in electronic two-band systems
• Light-induced inverse spin Hall effect and field-induced circular photogalvanic effect in GaAs revealed by two-dimensional terahertz Fourier analysis