Electronic states in one-dimensional helical crystals: General properties and application to InSeI

In this paper, we systematically explore several key properties of electronic states in one-dimensional (1D) helical crystals, including the inheritance of orbital angular momentum from local atomic orbitals to the entire helical structure, the 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 the 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, respectively. 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.