Electron refraction at lateral atomic interfaces

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 ¯...

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Bibliographic Details
Published in:Journal of applied physics 2017-11, Vol.122 (19)
Main Authors: Abd El-Fattah, Z. M., Kher-Elden, M. A., Yassin, O., El-Okr, M. M., Ortega, J. E., García de Abajo, F. J.
Format: Article
Language:English
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Summary: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 EB = 53 meV, below the Fermi level) and slightly above its Γ ¯ -point energy (EB = 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 EB = 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.
ISSN:0021-8979
1089-7550
DOI:10.1063/1.5005062