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

Abstract

On NaCl(100)/Cu(111) 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.

Boron Nitride on Cu(111): An Electronically Corrugated Monolayer

“…On Cu they represent the well-known Shockley-type surface state electrons scattered by defects 49 , whereas on BN they are assigned to an interface state band 50 . A close inspection of Fig.…”

Measuring Electric Field Induced Subpicometer Displacement of Step Edge Ions

“…The measurement of potential variations near step edges is fundamental in surface physics, and unique quantum physical phenomena, such as a two-dimensional electron gas behavior, have been revealed on conductive surfaces by detailed studies on electrostatic potential variations with scanning tunneling spectroscopy, especially at low temperature [1][2][3]. Because of their high band gap, ionic crystal surfaces have recently attracted a lot of attention as a template for molecular electronic devices [4,5].…”

Modification of electronic surface states by graphene islands on Cu(111)

“…Several recent experiments have taken advantage of these exposed surface states of crystalline metal substrates for such studies. [4][5][6][7] On Cu(111), an occupied Shockley surface state forms in the projected band gap leading to a quasi-2D electron gas, 8 which can act as a sensitive probe of changes in the surface electronic potential. Additional unoccupied surface states form due to the potential well created by an electron and its image charge.…”

“…Studies of Shockley states and IPS can help determine the interaction between adlayers and substrates as well as the resulting charge transfer to the adlayer. 1 Most of these studies have involved either thin dielectric films 7 , noble gases 9 , few-layer metals, 10,11 or self-assembled molecular monolayers. 12 As graphene is a metallic 2D crystal with weak van der Waals substrate coupling, surface state changes due to a graphene sheet may lead to new understanding of graphene/metal interactions as well as surface state physics.…”