Engineering nanostructured optical materials via the purposeful distortion of their constituent nanocrystals requires the knowledge of how various distortions affect the nanocrystals' electronic subsystem and its interaction with light. We use the geometric theory of defects in solids to calculate the linear permittivity tensor of semiconductor nanocrystals whose crystal lattice is arbitrarily distorted by imperfections or strains. The result is then employed to systematically analyze the optical properties of nanocrystals with spatial dispersion caused by screw dislocations and Eshelby twists. We demonstrate that Eshelby twists create gyrotropy in nanocrystals made of isotropic semiconductors whereas screw dislocations can produce it only if the nanocrystal material itself is inherently anisotropic. We also show that the dependence of circular dichroism spectrum on the aspect ratio of dislocation-distorted semiconductor nanorods allows resonant enhancing their optical activity (at least by a factor of 2) and creating highly optically active nanomaterials.

The search for the optimal geometry of optically active semiconductor nanostructures is making steady progress and has far-reaching benefits. Yet the helical springlike shape, which is very likely to provide a highly dissymmetric optical response, remains somewhat understudied theoretically. Here we comprehensively analyze the optical activity of semiconductor nanosprings using a fully quantum-mechanical model of their electronic subsystem and taking into account the anisotropy of their interaction with light. We show that the circular dichroism of semiconductor nanosprings can exceed that of ordinary semiconductor nanocrystals by a factor of 100 and be comparable to the circular dichroism of metallic nanosprings. It is also demonstrated that nanosprings can feature a total dissymmetry of optical response for certain ratios between their length and coil height. The magnitude and sign of the circular dichroism signal can be controlled by stretching or compressing the nanosprings, which makes them a promising material base for optomechanical sensors, polarization controllers, and other types of optically active nanophotonic devices.

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