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.

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Surface States Protected From Backscattering by Chiral Spin Texture
• Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
• Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets
• Semiclassical theories of the anomalous Hall effect
• Optical Hall conductivity in ordinary and graphene QHE systems
• Second-order nonlinear optical effects of spin currents
• Direct measurement of a pure spin current by a polarized light beam

Cited by in corpus (6)

• Dynamical birefringence: Electron-hole recollisions as probes of Berry curvature
• Probing dephasing time of crystals via spectral properties of high-harmonic generation
• Femtosecond currents in transition metal dichalcogenides monolayers
• Universal intrinsic orbital dynamics from Berry curvature in electronic two-band systems
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Light-induced inverse spin Hall effect and field-induced circular photogalvanic effect in GaAs revealed by two-dimensional terahertz Fourier analysis