Nonlinear and time-dependent edge state dynamics in 2D topological insulators

Abstract Topological insulators (TIs) host robust edge states that are promising for quantum technologies. However, their response to nonlinear and time-dependent perturbations has not been fully explored. We present a theoretical framework to examine edge state propagation in two-dimensional TIs under linear and nonlinear time-varying potentials, with examples from systems like HgTe/CdTe quantum wells. By combining Floquet theory with the Hubbard-Stratonovich transformation to address nonlinear interactions within a mean-field approximation, we obtain expressions for a generalized dispersion relation and scattering amplitudes that suggest potential nonlinear phase modulation and resonant scattering effects. The model predicts a dispersion shift of approximately 0.3 units and resonant scattering peaks at ± ω / A , which enable tunable quantum transport and are accessible via time-resolved ARPES or differential conductance measurements. Numerical simulations provide support for these findings, suggesting possible applications in topological quantum computing, spintronics, and quantum device engineering. These results establish a pathway toward tunable topological devices and may advance the development of next-generation quantum technologies.