Damped photonic modes in helical graphene

We analyze the behavior of spin-1 vector bosons in helical spacetime, focusing on photonic modes in helical graphene structures. We model the helical graphene surface as a smooth, continuous, and distortion-free manifold, effectively adopting the continuum approximation. By solving the fully covariant vector boson equation, we derive exact solutions that describe the quantum states of photons in a curved helical background, revealing their energy spectra, mode profiles, and decay dynamics. We find that the decay times of damped photonic modes range from $10^{-16}$ to $10^{-13}$ seconds as the helical pitch ($a$) varies from $10^3$ nanometers to $1$ nanometer, indicating that the structure efficiently absorbs all photonic modes. Additionally, the probability density functions exhibit time dependence, complementing their spatial variation. These findings provide a foundation for the design of ultrafast graphene photodetectors, graphene photodevices for high-speed optical communications, advanced photonic devices, and quantum materials based on helical graphene for various nanophotonic applications.