Interplay between structure and electronic states in step arrays explored with curved surfaces

Abstract

Atomic staircases in noble-metal surfaces are model one-dimensional superlattices, where free-electron-like surface states transform into superlattice bands with sizable quantum size shifts and gaps. At critical step spacings d=n×(λF/2), such superlattice gaps lie at the Fermi energy, affecting the electronic energy and hence the structural stability of the step lattice, which is held by weak elastic interactions. We use Cu, Ag, and Au curved crystals to smoothly tune the superlattice constant d in angle-resolved photoemission (ARPES) and scanning tunneling microscopy (STM) experiments. With ARPES we accurately quantify terrace-size effects and determine the superlattice potential, which increases from Ag to Cu and to Au. With STM we analyze the d-dependent terrace width distribution for Cu and Ag, and observe nonlinear variations in Cu. On the grounds of simple electronic and elastic models, we conclude that terrace width distribution instabilities and electronic energy variations at d=n×(λF/2) have the same order of magnitude for Cu. In contrast, the weak superlattice potential in Ag, i.e., its smoother band-structure modulation, is not sufficient to alter the step lattice.