Topological control of third-harmonic generation in a mesoscopic quantum ring with spiral dislocation

Abstract

We investigate the nonlinear optical response of a two-dimensional mesoscopic quantum ring subjected to a spiral dislocation, with emphasis on third-harmonic generation (THG). The topological defect is modeled through a torsion-induced deformation of space, which modifies the effective metric without introducing curvature. By combining the minimal-coupling prescription in curved space with a radial ring confinement and a perpendicular magnetic field, we derive the effective radial Schr\"odinger problem, obtain the bound states, and evaluate the nonlinear susceptibilities within the electric-dipole approximation. We show that the axial symmetry of the topologically deformed ring preserves the dipole selection rule $\Delta m=\pm 1$ and therefore suppresses second-harmonic generation, while THG remains allowed through multistep transition chains. The study is further expanded through three complementary analyses that can be implemented without changing the Hamiltonian: a dephasing-controlled study of spectral resolution, three-dimensional waterfall spectra showing the dependence on $\beta$ and $B$, and a channel-resolved decomposition of the THG amplitude. Together, these results establish the spiral dislocation as a robust geometric knob for tuning nonlinear optical activity in mesoscopic ring-shaped nanostructures.