A mechanism for orbital angular momentum and giant spin-splitting in solids and nanostructures

Giant spin-splitting (GSS) of electronic bands, which is several orders of magnitude greater than Rashba model, has been observed in various systems including noble-metal surfaces, thin film of transition-metal dichalcogenides, often accompanied by the orbital angular momentum (OAM). Here, we study structural and orbital conditions for emergence of a GSS by using tight-binding and first-principles calculations. We find that broken mirror symmetry of local atomic structure around an atom can produce non-zero OAM at the atom. This OAM results in a GSS if the atom is a high-atomic number element. We demonstrate these structural and orbital conditions in the cases of simple atomic chains, WSe$_{\mathrm{2}}$ monolayer, Au(111) surface, and bulk HgTe. Based on this mechanism of the spin-splitting, we suggest methods to control the GSS, which can be used in applications such as spintronic devices. This work was supported by NRF of KOREA (Grant No. 2011-0018306) and KISTI supercomputing center (Project No. KSC-2015-C3-039).