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-point gap (binding energy EB ¼53 meV, below the Fermi level) and slightly above its C -point energy (EB ¼160 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 ¼53 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 spinpolarized, highly featured, and anisotropic constant energy contours, such as those characteristic for Rashba systems and topological insulators. Published by AIP Publishing.Peer ReviewedPostprint (published version

Tuning the Indirect Band Gap of Square Metallic Superlattices

Shockley surface states at noble metal surface are textbook examples o

Analogous electronic states in graphene and planer metallic quantum dots

Abstract Graphene nanostructures offer wide range of applications due to their distinguished and tunable electronic properties. Recently, atomic and molecular graphene were modeled following simple free-electron scattering by periodic muffin tin potential leading to remarkable agreement with density functional theory. Here we extend the analogy of the $$\pi$$ π -electronic structures and quantum effects between atomic graphene quantum dots (QDs) and homogeneous planer metallic counterparts of similar size and shape. Specifically, we show that at high binding energies, below the $$\overline{M}$$ M ¯ -point gap, graphene QDs enclose confined states and standing wave quasiparticle interference patterns analogous to those reported on coinage metal surfaces for nanoscale confining structures such as vacancy islands and quantum corrals. These confined and quantum corral-like states in graphene QDs can be resolved in tomography experiments using angle-resolved photoemission spectroscopy. Likewise, the shape of near-Fermi frontier orbitals in graphene quantum dots can be reproduced from electron confinement within homogeneous metal QDs of identical size and shape. Furthermore, confined states analogous to those found in metallic quantum stadiums can be realized in coupled QDs of graphene for reduced separation. The present study offer a simple fundamental understanding of graphene electronic structures and also open the way towards efficient modeling of novel graphene-based nanostructures

Metallic bands in chevron-type polyacenes

We present electronic structure calculations based on a single-parameter plane wave expansion method for basic graphene building blocks, namely n-oligophenylenes and n-oligoacenes, revealing excellent agreement with density-functional theory. When oligophenylene molecules are joined through meta (zigzag) or ortho (chevron) junctions, the resulting molecular dimers and polymers exhibit a semiconducting character. While zigzag dimers of oligoacenes also exhibit gapped electronic structures, their chevron-phase features a sharp metallic band at the Fermi energy. This zero-point-energy state, which transforms into Dirac-like band in chevron polymers, survives at the outer elbows of the dimer irrespective of the molecular length, and has the same origin as reported for the polyacetylene and topologically induced edge states at edge-decorated graphene nanoribbons. These findings assist the engineering of topological electronic states at the molecular level and complement the toolbox of quantum phases in carbon-based nanostructures.JEO acknowledges financial support from the Spanish Ministry of Science and Innovation (Grants PID2019-107338RB-C63) and the Basque Government (Grant IT-1255-19).Peer reviewe

Graphene: Free electron scattering within an inverted honeycomb lattice

Theoretical progress in graphene physics has largely relied on the application of a simple nearest-neighbor tight-binding model capable of predicting many of the electronic properties of this material. However, important features that include electron-hole asymmetry and the detailed electronic bands of basic graphene nanostructures (e.g., nanoribbons with different edge terminations) are beyond the capability of such a simple model. Here we show that a similarly simple plane-wave solution for the one-electron states of an atom-based two-dimensional potential landscape, defined by a single fitting parameter (the scattering potential), performs better than the standard tight-binding model, and levels to density-functional theory in correctly reproducing the detailed π-band structure of a variety of graphene nanostructures. In particular, our approach identifies the three hierarchies of nonmetallic armchair nanoribbons, as well as the doubly-degenerate flat bands of free-standing zigzag nanoribbons with their energy splitting produced by symmetry breaking. The present simple plane-wave approach holds great potential for gaining insight into the electronic states and electro-optical properties of graphene nanostructures and other two-dimensional materials with intact or gapped Dirac-like dispersions.This work has been supported in part by the Spanish MINECO (Grants No. MAT2014-59096-P, No. MAT2016-78293-C6, No. MAT-2017-88374-P, No. MAT2017-88492-R, and No. SEV2015-0522), the Basque Government (Grant No. IT-1255-19), the European Research Council (Advanced Grant No. 789104-eNANO), the European Commission (Graphene Flagship 696656), the Catalan CERCA Program, Fundació Privada Cellex, and AGAUR (Grant No. 2017 SGR 1651)

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-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 Reviewe

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-point gap (binding energy EB ¼53 meV, below the Fermi level) and slightly above its C -point energy (EB ¼160 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 ¼53 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 spinpolarized, highly featured, and anisotropic constant energy contours, such as those characteristic for Rashba systems and topological insulators. Published by AIP Publishing.Peer Reviewe

Near Fermi superatom state stabilized by surface state resonances in a multiporous molecular network

Resumen del trabajo presentado a la 15th European Conference on Surface Crystallography and Dynamics (ECSCD) y a la 13th International Conference on the Structure of Surfaces (ICSOS), celebradas del 22 al 26 de mayo de 2023 en Grainau (Germany).Two-dimensional (2D) honeycomb molecular networks confine the substrate’s surface electrons within their pores, providing an ideal playground to investigate the quantum electron scattering phenomena. Besides surface state confinement, laterally protruding organic states can collectively hybridize at the smallest pores into superatom molecular orbitals (SAMOs). Although both types of pore states could be simultaneously hosted within nanocavities, their coexistence and possible interaction are unexplored. Here, we show that these two types of pore states do coexist within the smallest nanocavities of a 2D halogen-bonding multiporous network grown on Ag(111) studied. We find that SAMOs undergo an important stabilization when hybridizing with the confined surface states. These findings provide further control over the surface electronic structure exerted by 2D nanoporous systems.Peer reviewe

Near fermi superatom state stabilized by surface state resonances in a multiporous molecular network

Two-dimensional honeycomb molecular networks confine a substrate’s surface electrons within their pores, providing an ideal playground to investigate the quantum electron scattering phenomena. Besides surface state confinement, laterally protruding organic states can collectively hybridize at the smallest pores into superatom molecular orbitals. Although both types of pore states could be simultaneously hosted within nanocavities, their coexistence and possible interaction are unexplored. Here, we show that these two types of pore states do coexist within the smallest nanocavities of a two-dimensional halogen-bonding multiporous network grown on Ag(111) studied using a combination of scanning tunneling microscopy and spectroscopy, density functional theory calculations, and electron plane wave expansion simulations. We find that superatom molecular orbitals undergo an important stabilization when hybridizing with the confined surface state, following the significant lowering of its free-standing energy. These findings provide further control over the surface electronic structure exerted by two-dimensional nanoporous systems.We acknowledge the financial support from the Japan Society for the Promotion of Science (JSPS) KAKENHI (19H00856, JP17H05155, and 21F21058), from the Iran Science Elites Federation (M/99118), from the Spanish Ministry of Economy, Industry, and Competitiveness (MINECO, MAT2016-78293-C6-R6 and PID2019-107338RB-C64), from the regional Government of Aragon (E12-20R), and from the European Regional Development Fund (ERDF) under the program Interreg V-A España-Francia-Andorra (EFA 194/16 TNSI).Peer reviewe