  In this article, we systematically explore several key properties of
electronic states in helical materials systems, including the inheritance of
orbital angular momentum (OAM) from local atomic orbitals to the entire helical
structure, the conservation of helical momentum, and the emergence of
helical-induced spin-orbit coupling (hSOC). We then apply this comprehensive
theoretical framework to elucidate the electronic structure of one-dimensional
(1D) helical crystal InSeI. Our analysis reveals the influence of hSOC, evident
in spin-mixing energy gaps within the electronic band structure, as calculated
through density functional theory. Utilizing a combination of tight-binding
modeling and first-principles calculations, we ascertain the spin-polarized
electric response and the chiral-switchable second-order photocurrent response
of InSeI, characterized as the Landauer-Buttiker ballistic transport and shift
current response. The results highlight the potential of 1D InSeI for
applications in spintronics and optoelectronics. The overarching theoretical
framework established in this work will prove invaluable for the investigation
of other helical electronic systems.
