As fundamental one-dimensional defects, screw dislocations profoundly reshape the energy landscape and carrier dynamics of crystalline materials. By restoring the exact algebra of the screw dislocation group, we unveil the latent symmetry constraints that govern the electronic structure, providing a more rigorous physical picture than the conventional treatments. When applied to GaN, the method yields a band-connectivity constraint and rigorous dipole selection rules for polarization-resolved transitions. Combined with the computed Hamiltonian matrix, the approach gives symmetry-filtered radiative and dielectric calculations and reveals a piezoelectrical effect at the dislocation core that strongly suppresses radiative recombination. The pronounced dominance of nonradiative capture over radiative recombination highlights the detrimental impact of screw dislocations on the luminous efficiency of GaN, providing a theoretical foundation for optimizing dislocation-limited optoelectronic devices.

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• Disclinations & dislocations
• Electronic structure
• Nitrides
• Density functional theory
• Group theory