Spin and Orbital Angular Momentum Structures of Cu(111) and Au(111) Surface States

TL;DR

This study investigates the orbital and spin angular momentum structures of Cu(111) and Au(111) surface states using ARPES and first-principles calculations, revealing chiral OAM, band splitting behaviors, and the evolution of angular momentum with SOC strength.

Contribution

It provides the first experimental confirmation of local orbital angular momentum in Cu(111) surface states and develops an effective Hamiltonian to describe OAM and spin structures.

Findings

Cu(111) surface states exhibit chiral OAM despite weak SOC.

Au(111) shows split bands with parallel OAM for inner and outer bands.

OAM primarily originates from d-orbitals, with small p-orbital contributions.

Abstract

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.