Proximity spin-orbit coupling in a small-diameter armchair carbon nanotube on monolayer bismuthene

We study the spin-orbit proximity effects in a hybrid heterostructure built from a one-dimensional (1D) armchair carbon nanotube and two-dimensional (2D) buckled monolayer bismuthene. We show, by performing first-principles calculations, that Dirac electrons in the nanotube exhibit large spin-orbit coupling due to the close vicinity of bismuthene. The calculated low-energy band structure and the spin texture of the proximitized nanotube display a strong dependence on the position of the nanotube on the substrate, similar to the twist-angle dependence found in 2D heterostructures. Based on the first-principles results, we formulate an effective low-energy Hamiltonian of the nanotube, and we identify key interactions governing the proximity spin-orbit coupling. The proximity-induced spin splitting of Dirac cone bands is in the meV range, confirming an efficient transfer of spin-orbit coupling from bismuthene to the nanotube. © 2023 American Physical Society.