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Atomic staircases in noble-metal surfaces are model one-dimensional superlattices, where free-electron-like surface states transform into superlattice bands with sizable quantum size shifts and gaps. At critical step spacings d=n×(λF/2), such superlattice gaps lie at the Fermi energy, affecting the electronic energy and hence the structural stability of the step lattice, which is held by weak elastic interactions. We use Cu, Ag, and Au curved crystals to smoothly tune the superlattice constant d in angle-resolved photoemission (ARPES) and scanning tunneling microscopy (STM) experiments. With ARPES we accurately quantify terrace-size effects and determine the superlattice potential, which increases from Ag to Cu and to Au. With STM we analyze the d-dependent terrace width distribution for Cu and Ag, and observe nonlinear variations in Cu. On the grounds of simple electronic and elastic models, we conclude that terrace width distribution instabilities and electronic energy variations at d=n×(λF/2) have the same order of magnitude for Cu. In contrast, the weak superlattice potential in Ag, i.e., its smoother band-structure modulation, is not sufficient to alter the step lattice. ; This work was supported in part by the Spanish MICINN (MAT2007-63083), and the Basque Government (IT-257-07). The SRC is funded by the National Science Foundation (Grant No. DMR-0084402). ; Peer Reviewed

The deposition of submonolayer amounts of Au onto Cu(111) results in a Au-Cu surface alloy with temperature- and thickness-dependent stoichiometry. Upon alloying, the characteristic Shockley state of Cu(111) is modified, shifting to 0.53 eV binding energy for a particular surface Au2Cu concentration, which is a very high binding energy for a noble-metal surface. Based on a phase accumulation model analysis, we discuss how this unusually large shift is likely reflecting an effective increase in the topmost layer thickness of the order of, but smaller than, the value expected from the moiré undulation. © 2012 American Physical Society. ; This work was supported in part by the Spanish MINECO (Grants No. MAT2010-21156-C03-01 and No. MAT2010-21156-C03-03), and the Basque Government (Grant No. IT-257-07). The SRC is funded by the National Science Foundation (Award No. DMR-0084402). ; Peer Reviewed

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 reviewed

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).

5 páginas, 4 figuras.-- PACS numbers: 73.20.At, 73.22.-f, 79.60.Jv ; The two-dimensional, free-electron-like band structure of noble metal surfaces can be radically transformed by appropriate nanostructuration. A case example is the triangular dislocation network that characterizes the epitaxial Ag/Cu(111) system, which exhibits a highly featured band topology with a full band gap above EF and a hole-pocket-like Fermi surface. Here we show that controlled doping of the Ag/Cu(111) interface with Au allows one to observe a complete Lifshitz transition at 300 K; i.e., the hole pockets fill up, the band gap entirely shifts across EF, and the Fermi surface becomes electron-pocket-like. ; This work was supported by the Spanish MICINN (MAT2010-21156-C03-01 and -C03-03) and the Basque Government (IT-257-07). ; Peer reviewed

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

We investigate the scattering of electrons belonging to Shockley states of (111)-oriented noble metal surfaces using angle-resolved photoemission (ARPES) and scanning tunneling microscopy (STM). Both ARPES and STM indicate that monatomic steps on a noble metal surface may act either as strongly repulsive or highly transmissive barriers for surface electrons, depending on the coherence of the step lattice, and irrespectively of the average step spacing. By measuring curved crystal surfaces with terrace length ranging from 30 to 180 Å, we show that vicinal surfaces of Au and Ag with periodic step arrays exhibit a remarkable wave function coherence beyond 100 Å step spacings, well beyond the Fermi wavelength limit and independently of the projection of the bulk band gap on the vicinal plane. In contrast, the analysis of transmission resonances investigated by STM shows that a pair of isolated parallel steps defining a 58 Å wide terrace confines and decouples the surface state of the small terrace from that of the (111) surface. We conclude that the formation of laterally confined quantum well states in vicinal surfaces as opposed to propagating superlattice states depends on the loss of coherence driven by imperfection in the superlattice order. © 2013 American Physical Society. ; This work was supported in part by the Spanish MICINN (MAT2007-63083 and MAT2010-15659), the Basque Government (IT-257-07), and the Agència de Gestió d'Ajuts Universitaris i de Recerca (2009 SGR 695). The SRC is funded by the National Science Foundation (Award No. DMR-0084402). A.M. and J.L.-C. acknowledge funding from the Ramon y Cajal Fellowship program. ; Peer Reviewed

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. ; Quantum well states of Ag films grown on stepped Au(111) surfaces are shown to undergo lateral scattering, in analogy with surface states of vicinal Ag(111). Applying angle resolved photoemission spectroscopy we observe quantum well bands with zone-folding and gap openings driven by surface/interface step lattice scattering. Experiments performed on a curved Au(111) substrate allow us to determine a subtle terrace-size effect, i.e., a fine step-density-dependent upward shift of quantum well bands. This energy shift is explained as mainly due to the periodically stepped crystal potential offset at the interface side of the film. Finally, the surface state of the stepped Ag film is analyzed with both photoemission and scanning tunneling microscopy. We observe that the stepped film interface also affects the surface state energy, which exhibits a larger terrace-size effect compared to surface states of bulk vicinal Ag(111)crystals. ; This work was supported in part by the Spanish Ministry of Economy (MINECO) through grants MAT2013–46593-C6–2-P, MAT2013–46593-C6–4-P, MAT2013–46593-C6–5-P, and FIS2010–19609-C02–02, by the German Sonderforschungsbereich SFB 1083, and by the Basque Government through Projects IT-621–13 and IT-756–13. ICN2 acknowledges support from the Severo Orchoa Program (MINECO, Grant SEV-2013-0295). ; Peer Reviewed

Trabajo presentado al 32nd Symposium on Surface Science (3S'19), celebrado en Baqueira Beret, Lleida (España) del 10 al 16 de marzo de 2019. ; Support by the Spanish Ministry of Economy, Industry and Competitiveness (MINECO, Grant No. MAT2016-78293-C6-6-R) from the regional Government of Aragón (RASMIA project) and from the European Regional Development Fund (ERDF) under the program Interreg V-A España-Francia-Andorra (Contract No. EFA 194/16 TNSI) is thankfully acknowledged.

Quantum dot arrays in the form of molecular nanoporous networks are renowned for modifying the electronic surface properties through quantum confinement. Here we show that, compared to the pristine surface state, the band bottom of the confined states can exhibit downward shifts accompanied by a lowering of the effective masses simultaneous to the appearance of tiny gaps at the Brillouin zone boundaries. We observed these effects by angle resolved photoemission for two self-Assembled homothetic (scalable) Co-coordinated metal-organic networks. Complementary scanning tunneling spectroscopy measurements confirmed these findings. Electron plane wave expansion simulations and density functional theory calculations provide insight into the nature of this phenomenon, which we assign to metal-organic overlayer-substrate interactions in the form of adatom-substrate hybridization. To date, the absence of the experimental band structure resulting from single metal adatom coordinated nanoporous networks has precluded the observation of the significant surface state renormalization reported here, which we infer to be general for low interacting and well-defined adatom arrays. ; We acknowledge Prof. J. García de Abajo for providing the EPWE code and the financial support from the Spanish Ministry of Economy, Industry and Competitiveness (MINECO, Grant No. MAT2016-78293-C6 and FIS2016-75862-P), from the Basque Government (Grant No. IT-1255-19 and IT-756-13), from the Regional Government of Aragon (RASMIA project), from the European Regional Development Fund (ERDF) under the program Interreg V-A España-Francia-Andorra (Contract No. EFA 194/16 TNSI) and from the European Research Council (ERC-2012-StG 307760-SURFPRO).

On-surface metal-organic nanoporous networks generally refer to adatom coordinated molecular arrays, which are characterized by the presence of well-defined and regular nanopores. These periodic structures constructed using two types of components confine the surface electrons of the substrate within their nanocavities. However, the confining (or scattering) strength that individual building units exhibit is a priori unknown. Here, we study the modification of the substrate's surface electrons by the interaction with a Cu-coordinated TPyB metal-organic network formed on Cu(111) and disentangle the scattering potentials and confinement properties. By means of STM and angle-resolved photoemission spectroscopy we find almost unperturbed free-electron-like states stemming from the rather weak electron confinement that yields significant coupling between adjacent pores. Electron plane wave expansion simulations match the superlattice induced experimental electronic structure, which features replicating bands and energy renormalization effects. Notably, the electrostatic potential landscape obtained from our ab initio calculations suggests that the molecules are the dominant scattering entities while the coordination metal atoms sandwiched between them act as leaky channels. These metal atom transmission conduits facilitate and enhance the coupling among quantum dots, which are prone to be exploited to engineer the electronic structure of surface electron gases. ; Financial support is acknowledged from the Spanish Ministry of Economy, Industry and Competitiveness (MINECO, Grants No. MAT2016-78293-C6 and No. FIS2016-75862-P), from the regional Government of Aragon (Grant No. E12-17R), from the Basque Government (Grant No. IT-1255-19), from the European Regional Development Fund (ERDF) under the program Interreg V-A España-Francia-Andorra (Contract No. EFA 194/16 TNSI) and from the Hong Kong RGC 16304016. ; Peer reviewed

Designing molecular organic semiconductors with distinct frontier orbitals is key for the development of devices with desirable properties. Generating defined organic nanostructures with atomic precision can be accomplished by on-surface synthesis. We use this "dry" chemistry to introduce topological variations in a conjugated poly(para-phenylene) chain in the form of meta-junctions. As evidenced by STM and LEED, we produce a macroscopically ordered, monolayer thin zigzag chain film on a vicinal silver crystal. These cross-conjugated nanostructures are expected to display altered electronic properties, which are now unraveled by highly complementary experimental techniques (ARPES and STS) and theoretical calculations (DFT and EPWE). We find that meta-junctions dominate the weakly dispersive band structure, while the band gap is tunable by altering the linear segment's length. These periodic topology effects induce significant loss of the electronic coupling between neighboring linear segments leading to partial electron confinement in the form of weakly coupled quantum dots. Such periodic quantum interference effects determine the overall semiconducting character and functionality of the chains. ; We acknowledge the financial support from the Spanish Ministry of Economy, Industry and Competitiveness (MINECO, Grant No. MAT2016-78293-C6), from the Basque Government (Grant No. IT-621-13), from the regional Government of Aragon (RASMIA project), from the European Regional Development Fund (ERDF) under the program Interreg V-A España-Francia-Andorra (Contract No. EFA 194/16 TNSI), from the German Science Foundation (DFG) through the CRC 1083 and Grant No. GO 1812/2 and funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 635919). ; Peer reviewed

Quantum dots are known to confine electrons within their structure. Whenever they periodically aggregate into arrays and cooperative interactions arise, novel quantum properties suitable for technological applications show up. Control over the potential barriers existing between neighboring quantum dots is therefore essential to alter their mutual crosstalk. Here we show that precise engineering of the barrier width can be experimentally achieved on surfaces by a single atom substitution in a haloaromatic compound, which in turn tunes the confinement properties through the degree of quantum dot intercoupling. We achieved this by generating self-assembled molecular nanoporous networks that confine the two-dimensional electron gas present at the surface. Indeed, these extended arrays form up on bulk surface and thin silver films alike, maintaining their overall interdot coupling. These findings pave the way to reach full control over two-dimensional electron gases by means of self-assembled molecular networks. ; This work was supported in part by the Spanish Ministry of Economy (grants MAT2013-46593-C6-4-P, MAT2016-78293-C6-6-R and FIS2013-48286-C2-1-P), by the Spanish Research Council (CSIC- 201560I022), by the Basque Government (grants IT621-13 and IT-756-13), by the Japan Science and Technology Agency (JST), 'Precursory Research for Embryonic Science and Technology' (PRESTO) for a project of 'Molecular technology and creation of new function', by JSPS KAKENHI Grant Number 15K21765, by the Swiss National Science Foundation, by the Swiss Nanoscience Institute, and by COST Action (European Cooperation in Science and Technology) MP1303. Swiss National Supercomputing Center in Lugano (Project s499 and s621) is acknowledged. ; Peer Reviewed

Monolayer hexagonal boron nitride (hBN) is attracting considerable attention because of its potential applications in areas such as nano- and opto-electronics, quantum optics and nanomagnetism. However, the implementation of such functional hBN demands precise lateral nanostructuration and integration with other two-dimensional materials, and hence, novel routes of synthesis beyond exfoliation. Here, a disruptive approach is demonstrated, namely, imprinting the lateral pattern of an atomically stepped one-dimensional template into a hBN monolayer. Specifically, hBN is epitaxially grown on vicinal Rhodium (Rh) surfaces using a Rh curved crystal for a systematic exploration, which produces a periodically textured, nanostriped hBN carpet that coats Rh(111)-oriented terraces and lattice-matched Rh(337) facets with tunable width. The electronic structure reveals a nanoscale periodic modulation of the hBN atomic potential that leads to an effective lateral semiconductor multi-stripe. The potential of such atomically thin hBN heterostructure for future applications is discussed. ; The authors acknowledge financial support from the Spanish Ministry of Science and Innovation (Grants MAT-2017-88374-P, PID2019-107338RB-C63, MAT2017-88492-R, and Severo Ochoa CEX2019-000910-S), the CSIC (Grant 2020AEP178), the Basque Government (Grant IT-1255-19), the Marie Sklodowska-Curie European Union's Horizon 2020 program (grant MagicFACE 797109), the European Research Council (Advanced Grant 789104-eNANO), and Elettra Sincrotrone Trieste for providing access to its synchrotron radiation facilities. I.P. and F.B. acknowledge funding from EUROFEL, and D.U. from the Ministry of Science and Higher Education of the Russian Federation [Grant No. 075-15-2020-797 (13.1902.21.0024)]. A.A.M. acknowledges the German Ministry for Education and Research (Grant 05K19KER). ; Peer reviewed