Enhanced nonlinear optical responses in two-dimensional materials via laser-induced topological phase transitions

We develop a comprehensive theoretical framework to enhance nonlinear optical responses in two-dimensional (2D) materials, such as graphene and transition metal dichalcogenides (TMDs), by inducing topological phase transitions using intense laser fields. Employing Floquet engineering, we demonstrate that laser-driven topological edge states significantly boost second-harmonic generation (SHG) and third-harmonic generation (THG) efficiencies, enabling advanced photonic devices and nonlinear spectroscopy. We derive novel scaling laws for SHG ([Formula: see text]) and THG ([Formula: see text]) efficiencies, where [Formula: see text] is the laser intensity and ω is the frequency, using a quantum mechanical density matrix approach. These are off-resonant approximations; full resonant simulations show [Formula: see text] and [Formula: see text] Additionally, we introduce a defect-enhanced SHG model, accounting for lattice imperfections. Numerical simulations validate these models, showing a 60% increase in SHG and a 40% increase in THG for graphene at [Formula: see text] and [Formula: see text]. This framework offers a pathway for designing tunable, optically active 2D materials for next-generation photonic and quantum technologies.