Spin-orbit interaction and Dirac cones in d-orbital noble metal surface states

Band splittings, chiral spin polarization, and topological surface states generated by spin-orbit interactions at crystal surfaces are receiving a lot of attention for their potential device applications as well as fascinating physical properties. Most studies have focused on sp states near the Fermi energy, which are relevant for transport and have long lifetimes. Far less explored, though in principle stronger, are spin-orbit interaction effects within d states, including those deep below the Fermi energy. Here, we report a joint photoemission and ab initio study of spin-orbit effects in the deep d-orbital surface states of a 24-layer Au film grown on Ag(111) and a 24-layer Ag film grown on Au(111), singling out a conical intersection (Dirac cone) between two surface states in a large surface-projected gap at the time-reversal symmetric M¯ points. Unlike the often isotropic dispersion at Γ¯ point Dirac cones, the M¯ point cones are strongly anisotropic. An effective k·p Hamiltonian is derived to describe the anisotropic band splitting and spin polarization near the Dirac cone.