Microscopic mechanism for asymmetric charge distribution in Rashba-type surface states and the origin of the the energy splitting scale

Microscopic mechanism for the Rashba-type band splitting is examined in detail. We show how asymmetric charge distribution is formed when local orbital angular momentum (OAM) and crystal momentum get interlocked due to surface effects. An electrostatic energy term in the Hamiltonian appears when such OAM and crystal momentum dependent asymmetric charge distribution is placed in an electric field produced from an inversion symmetry breaking (ISB). Analysis by using an effective Hamiltonian shows that, as the atomic spin-orbit coupling (SOC) strength increases from weak to strong, originally OAM-quenched states evolve into well-defined chiral OAM states and then to total angular momentum J-states. In addition, the energy scale of the band splitting changes from atomic SOC energy to electrostatic energy. To confirm the validity of the model, we study OAM and spin structures of Au(111) system by using an effective Hamiltonian for the d-orbitals case. As for strong SOC regime, we choose Bi2Te2Se as a prototype system. We performed circular dichroism angle resolved photoemission spectroscopy experiments as well as first-principles calculations. We find that the effective model can explain various aspects of spin and OAM structures of the system.