Electron refraction at lateral atomic interfaces

El-Fattah, Zakaria M. Abd; Kher-Elden, M. A.; Yassin, O.; El-Okr, Mohamed; Ortega, J. E.; Abajo, F. Javier García de

doi:10.1063/1.5005062

Cited by 4 publications

(6 citation statements)

References 26 publications

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“…Within this vast playground we can relate established optical effects to low-dimensional quantum systems using the ability to directly image the QPI patterns generated by these nanostructures, with the benefit of a 1000-fold reduction in wavelength and structural parameters (García de Abajo et al, 2010). Indeed, exotic refraction anomalies leading to few nanometer electron focusing (collimation) or negative refraction and beam splitting have been predicted for triangular superlattices (García de Abajo et al, 2010;Abd El-Fattah et al, 2017); see Figs. 27(a) and 27(b).…”

Section: Discussionmentioning

confidence: 99%

“…Although EPWE is applicable to nonperiodic and finite confining structures following the supercell scheme at the expense of computational cost, alternative methods were implemented. The electron BEM (EBEM), adapted from routines used in optics, was successfully used to model the confinement and/or propagation of surface electrons within finite nanostructures and at lateral interfaces (Knipp and Reinecke, 1996;García de Abajo et al, 2010;Abd El-Fattah et al, 2017;Kher-Elden et al, 2017). Within the EBEM approach, the boundaries defining the muffin-tin potential are finely discretized, and electron sources placed at these boundaries are propagated through each potential region using the 2D Green's function of the Helmholtz equation (Klappenberger et al, 2011;Kher-Elden et al, 2017).…”

Section: B Principles Of Surface-state Confinement and Their Modelingmentioning

confidence: 99%

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Engineering quantum states and electronic landscapes through surface molecular nanoarchitectures

et al. 2022

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Surfaces are at the frontier of every known solid. They provide versatile supports for functional nanostructures and mediate essential physicochemical processes. Intimately related to two-dimensional materials, interfaces and atomically thin films often feature distinct electronic states with respect to the bulk, which is key to many relevant properties, such as catalytic activity, interfacial charge-transfer, and crystal growth mechanisms. To induce novel quantum properties via lateral scattering and confinement, reducing the surface electrons' dimensionality and spread with atomic precision is of particular interest. Both atomic manipulation and supramolecular principles provide access to custom-designed molecular assemblies and superlattices, which tailor the surface electronic landscape and influence fundamental chemical and physical properties at the nanoscale. Here the confinement of surface-state electrons is reviewed, with a focus on their interaction with molecular scaffolds created by molecular manipulation and self-assembly protocols under ultrahigh vacuum conditions. Starting with the quasifree twodimensional electron gas present at the ð111Þ-oriented surface planes of noble metals, the intriguing molecule-based structural complexity and versatility is illustrated. Surveyed are low-dimensional confining structures in the form of artificial lattices, molecular nanogratings, or quantum dot arrays, which are constructed upon an appropriate choice of their building constituents. Whenever the realized (metal-)organic networks exhibit long-range order, modified surface band structures with characteristic features emerge, inducing noteworthy physical phenomena such as discretization, quantum coupling or energy, and effective mass renormalization. Such collective electronic states can be additionally modified by positioning guest species at the voids of open nanoarchitectures. The designed scattering potential landscapes can be described with semiempirical models, bringing thus the prospect of total control over surface electron confinement and novel quantum states within reach.

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Section: Discussionmentioning

confidence: 99%

Section: B Principles Of Surface-state Confinement and Their Modelingmentioning

confidence: 99%

Engineering quantum states and electronic landscapes through surface molecular nanoarchitectures

et al. 2022

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“…What makes these variations experimentally accessible and potentially relevant for technology in the graphene case, and in other 2D atomic lattices, is the combination of a large M -point gap (several eV), which for superlattices reduces to just a few meV, and the steep dispersion near the K points. Finally, this simple NFE description of graphene and its nanostructures should have large impact on the efficient simulation of graphene-based devices and phenomena, such as negative refraction and super lenses in p-n junctions, using, for example, the complementary electronic boundary-element method (EBEM) solver, which was previously used to describe similar effects in 2D metallic superlattices 68,69 .…”

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confidence: 99%

Graphene: Free electron scattering within an inverted honeycomb lattice

et al. 2019

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Theoretical progress in graphene physics has largely relied on the application of a simple nearestneighbor 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 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 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 planewave approach holds great potential for gaining insight into the electronic states and the electrooptical properties of graphene nanostructures and other two-dimensional materials with intact or gapped Dirac-like dispersions.The two-dimensional (2D) honeycomb carbon-atom lattice known as graphene 1 is a promising material for applications in optical and electronic devices 2-4 . In particular, its peculiar conical electronic dispersion 5,6 and 2D character enable a uniquely large optical tunability 7,8 and a suitable playground for quantum electrodynamics phenomena, such as the relativistic Klein tunneling 9 , as well as a customizable zoo of exotic band structures when decorated with defects 10 , arranged in twisted bilayers 11 , or laterally patterned into ribbons 12,13 . Energy-gap engineering in graphene, an essential prerequisite for nanoelectronics applications, demands controlled and selective sub-lattice perturbations at the atomic scale, such as chemical doping 14,15 or gating 16 , lateral strain 17,18 , and substrate-induced sublattice asymmetry [19][20][21][22] .Graphene nanoribbons (GNRs) have been extensively studied as simple, appealing nanostructures that lead to electronic band features, such as gap opening, due to quantum confinement, and peculiar edge states that can readily be tuned through their width, shape, and edgeterminations 12,13 . The rapidly progressing on-surface chemistry, which allows controlled-synthesis of novel graphene-based nanostructures, such as GNRs with complex architectures 23-28 , combined with the precise mapping of their electronic structures using angle-resolved photomission spectroscopy (ARPES) and scanning tunneling spectroscopy (STS) 29-32 , make GNRs promising candidates for the realization of exotic graphene-based nanodevices [33][34][35] .Theoretical understanding and prediction of extended graphene and GNRs properties has been instrumental in the development of the field. Density-functional theo...

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“…, the Dirac point of 2D graphene), m eff is the effective mass (here, m eff = m e ), V ( R ) is the 2D potential as a function of spatial coordinates R = ( x , y ), and ψ ( R ) is the electron wave function. We then solve eqn (1) using either an electron-plane-wave expansion (EPWE) or boundary element method (EBEM) implementations, respectively, for extended and finite systems, as detailed in ref. 30, 33 and 34.…”

Section: Methodsmentioning

confidence: 99%