Electron refraction at lateral atomic interfaces

Abstract

We present theoretical simulations of electron refraction at the lateral atomic interface between a 'homogeneous' Cu(111) surface and the >nanostructured> one-monolayer (ML) Ag/Cu(111) dislocation lattice. Calculations are performed for electron binding energies barely below the 1 ML Ag/Cu(111) M-point gap (binding energy E = 53 meV, below the Fermi level) and slightly above its Γ-point energy (E = 160 meV), both characterized by isotropic/circular constant energy surfaces. Using plane-wave-expansion and boundary-element methods, we show that electron refraction occurs at the interface, the Snell law is obeyed, and a total internal reflection occurs beyond the critical angle. Additionally, a weak negative refraction is observed for E = 53 meV electron energy at beam incidence higher than the critical angle. Such an interesting observation stems from the interface phase-matching and momentum conservation with the umklapp bands at the second Brillouin zone of the dislocation lattice. The present analysis is not restricted to our Cu-Ag/Cu model system but can be readily extended to technologically relevant interfaces with spin-polarized, highly featured, and anisotropic constant energy contours, such as those characteristic for Rashba systems and topological insulators. ; This work has been supported in part by the Spanish MINECO (Grant Nos. MAT2013–46593-C6–4-P, MAT2016–78293-C6–6-R, MAT2014-59096-P, and SEV2015-0522), the Basque Government (Grant No. IT621–13), the Catalan CERCA Program, Fundacio Privada Cellex, and AGAUR (Grant No. 2014 SGR 1400). ; Peer Reviewed