Snell’s Law for Surface Electrons: Refraction of an Electron Gas Imaged in Real Space

On [Formula presented] an interface state band is observed that descends from the surface-state band of the clean copper surface. This band exhibits a Moiré-pattern-induced one-dimensional band gap, which is accompanied by strong standing-wave patterns, as revealed in low-temperature scanning tunneling microscopy images. At NaCl island step edges, one can directly see the refraction of these standing waves, which obey Snell’s refraction law. © 2004 The American Physical Society.