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We propose that the existence of local orbital angular momentum (OAM) on the surfaces of high-Z materials plays a crucial role in the formation of Rashba-type surface band splitting. Local OAM state in a Bloch wave function produces an asymmetric charge distribution (electric dipole). The surface-normal electric field then aligns the electric dipole and results in chiral OAM states and the relevant Rashba-type splitting. Therefore, the band splitting originates from electric dipole interaction, not from the relativistic Zeeman splitting as proposed in the original Rashba picture. The characteristic spin chiral structure of Rashba states is formed through the spin-orbit coupling and thus is a secondary effect to the chiral OAM. Results from first-principles calculations on a single Bi layer under an external electric field verify the key predictions of the new model.

We performed angle resolved photoemission (ARPES) studies on Cu(111) and Au(111) surface states with circularly polarized light. Existence of local orbital angular momentum (OAM) is confirmed as has been predicted to be broadly present in a system with an inversion symmetry breaking (ISB). The single band of Cu(111) surface states is found to have chiral OAM in spite of very small spin-orbit coupling (SOC) in Cu, which is consistent with theoretical prediction. As for Au(111), we observe split bands for which OAM for the inner and outer bands are parallel, unlike the Bi2Se3 case. We also performed first principles calculation and the results are found to be consistent with the experimental results. Moreover, majority of OAM is found to be from d-orbitals and a small contribution has p-orbital origin which is anti-aligned to the spins. We derive an effective Hamiltonian that incorporates the role of OAM and used it to extract the OAM and spin structures of surface states with various SOC strength. We discuss the evolution of angular momentum structures from pure OAM case to a strongly spin-orbit entangled state. We predict that the transition occurs through reversal of OAM direction at a k-point in the inner band if the system has a proper SOC strength.PACS numbers: 71.15.Mb

We show, by way of tight-binding and first-principles calculations, that a one-to-one correspondence between electron's crystal momentum k and non-zero orbital angular momentum (OAM) is a generic feature of surface bands. The OAM forms a chiral structure in momentum space much as its spin counterpart in Rashba model does, as a consequence of the inherent inversion symmetry breaking at the surface but not of spin-orbit interaction. Circular dichroism (CD) angle-resolved photoemission (ARPES) experiment is an efficient way to detect this new order, and we derive formulas explicitly relating the CD-ARPES signal to the existence of OAM in the band structure. The cases of degenerate p-and d-orbital bands are considered. PACS numbers:Electron spins are quenched in ordinary crystalline solids in the sense that each crystal momentum k comes in degenerate pairs of spin-up and spin-down electrons. Such degeneracy is lifted in an interesting manner for the so-called Rashba system [1], in which the given momentum state in the band has only one spin state associated with it. Examples of Rashba-split bands are many by now [2]. On symmetry grounds, as Rashba originally argued, the inherent inversion symmetry breaking (ISB) at the surface termination allows an interaction term, the Rashba term, of the form H R = λ Rẑ · (k × σ) involving the coupling of the electron's spin operator σ/2 and its momentum k (We set ≡ 1). The chiral spin angular momentum (SAM) structure in momentum space follows as a direct consequence of the Rashba Hamiltonian H R [3, 4].One must note, however, that other physical quantities having the character of angular momentum can take the place of σ in the Rashba Hamiltonian. For instance, in bands where the orbital angular momentum (OAM) remains unquenched, one can equally well consider a coupling of k to OAM operator, L. In this paper, we expand this observation to show that chiral OAM in one-to-one correspondence with the electron's linear momentum is indeed a general consequence of ISB for the surface bands. Unlike the chiral SAM structure which typically occurs in materials with strong spin-orbit interaction (SOI)[2], we show that chiral OAM occurs even for materials with no SOI.We begin by providing a simple, tight-binding (TB) model Hamiltonian in two dimensions where the abovementioned chiral OAM structure emerges. A three-fold degenerate p-orbital system is considered, while the spin degrees of freedom is suppressed in order to emphasize the notion of chiral OAM emerging from ISB alone without the requirement of SOI. The TB model is the triangular lattice version of the square one originally considered by Petersen and Hedegård [5] in their study of Rashba phenomena in p-orbital bands. By suppressing spin degrees of freedom, we do away with the notion of conventional Rashba spin splitting. The idea of ISB-induced chiral OAM was not considered in Ref. 5 or in any other literature we are aware of [6].We introduce two Slater-Koster parameters V 1 and V 2 for σ-and π-bonding amplitudes, respectively, and ...