Orbital angular momentum analysis for giant spin splitting in solids and nanostructures

Giant spin splitting (GSS) of electronic bands, which is several orders of magnitude greater than the standard Rashba effect has been observed in various systems including noble-metal surfaces and thin films of transition-metal dichalcogenides. Previous studies reported that orbital angular momentum (OAM) is not quenched in some GSS materials and that the atomic spin-orbit interaction (SOI) generates spin splitting in some solid states via the interorbital hopping. Although the unquenched OAM may be closely related to the interorbital hopping, their relationship is hardly studied in the aspect of using the unquenched OAM as a control parameter of GSS. Here, we analyze OAM in GSS materials by using the interorbital-hopping mechanism and first-principles calculations. We report that the interatomic hopping between different-parity orbitals, which is generated by specific broken mirror symmetry, produces k-dependent OAM, resulting in valley-dependent GSS in WSe(2) monolayer, Rashba-type GSS in Au (111) surface, and Dresselhaus-type GSS in bulk HgTe. We also demonstrate systematic control of OAM by pressure, external fields, and substrates, thereby controlling the spin splitting, and discuss the temperature dependence of OAM. Our results provide a simplified picture for systematic design and control of GSS materials.