Quantum confinement in free Cu(111), Ag(111), and Au(111) layers and apparent splitting of surface bands

Abstract

The apparent splitting of surface bands of Cu(111), Ag(111), and Au(111) films, obtained in calculations without account for spin-orbit coupling, is usually explained as a result of interaction of surface states located at opposite surfaces of the slabs. However, such twinning of the surface states is absent for other surfaces of noble metals despite the anticipated similar interaction. Here we suggest an alternative explanation and attribute the twinning of the bands to the quantum confinement effect.