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

The formation of a one-dimensional (1D) band gap in the two-dimensional (2D) electron gas of the NaCl/Cu(111) interface state band was demonstrated. It was shown that natural Moiré patterns, inherent in incommensurate growth, generate a band gap within a 2D interface state band. The band gap was observed in an scanning tunneling microscopy (STM) image displaying the electron-probability distribution in space and energy. The results show that at NaCl island step edges, one can directly see the refraction of the standing waves, which obey Snell's law of refraction.