We investigate the scattering of electrons belonging to Shockley states of (111)-oriented noble metal surfaces using angle-resolved photoemission (ARPES) and scanning tunneling microscopy (STM). Both ARPES and STM indicate that monatomic steps on a noble metal surface may act either as strongly repulsive or highly transmissive barriers for surface electrons, depending on the coherence of the step lattice, and irrespectively of the average step spacing. By measuring curved crystal surfaces with terrace length ranging from 30 to 180 Å, we show that vicinal surfaces of Au and Ag with periodic step arrays exhibit a remarkable wave function coherence beyond 100 Å step spacings, well beyond the Fermi wavelength limit and independently of the projection of the bulk band gap on the vicinal plane. In contrast, the analysis of transmission resonances investigated by STM shows that a pair of isolated parallel steps defining a 58 Å wide terrace confines and decouples the surface state of the small terrace from that of the (111) surface. We conclude that the formation of laterally confined quantum well states in vicinal surfaces as opposed to propagating superlattice states depends on the loss of coherence driven by imperfection in the superlattice order. © 2013 American Physical Society.

This work was supported in part by the Spanish MICINN (MAT2007-63083 and MAT2010-15659), the Basque Government (IT-257-07), and the Agència de Gestió d’Ajuts Universitaris i de Recerca (2009 SGR 695). The SRC is funded by the National Science Foundation (Award No. DMR-0084402). A.M. and J.L.-C. acknowledge funding from the Ramon y Cajal Fellowship program.

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