Atomic Chains at Surfaces

Lateral confinement effects of M¯-point Tamm state in vicinal Cu(100) surfaces

“…Steps act as a potential barrier for the surface electrons and depending on the superperiodicity, the wave function of the surface state switches at a critical miscut angle from being localized at the terraces to being delocalized along the optical surface. This means that the 2D surface states displaying superlattice band folding split into 1D quantum well levels with increasing terrace size (d) [12,[14][15][16][17][18][19][20]. The switching has been attributed to a decrease in the effective step barrier, due to the closing of the band gap after a critical miscut angle [12,14,21,22], or to localization induced by disorder [17].…”

Oxide−Metal Nanowires by Oxidation of a One-Dimensional Mn−Pd Alloy: Stability and Reactivity

“…[1][2][3][4] Vicinal metal surfaces, which exhibit periodic arrays of steps, offer a convenient and accessible way to pattern regular superlattices of nanowires assembled with atomic precision, with the considerable advantage that the resulting physical and chemical properties can be investigated by spatially averaging techniques, such as high-resolution electron spectroscopies and diffraction methods. As such, arrays of 1D nanostructures created on stepped metal surfaces serve as well-defined model systems for tuning the chemical reactivity of metal surfaces, 5,6 for fundamental studies of 1D electronic structure [7][8][9][10] and quantum effects, 11 and for pioneering research of magnetism in reduced dimensions. [12][13][14][15] While the self-assembly of metal wires on stepped metal and semiconductor surfaces 3,16 has been the subject of intense research in the past decade, there are only sparse examples of metal oxide nanochains created by exploiting the step decoration mechanism.…”

“…The decoration of monatomic steps of metal surfaces with transition metal adatoms is a well-established route to prepare one-dimensional (1D) systems in the form of highly ordered atomic chains, nanowires, and nanostripes. − Vicinal metal surfaces, which exhibit periodic arrays of steps, offer a convenient and accessible way to pattern regular superlattices of nanowires assembled with atomic precision, with the considerable advantage that the resulting physical and chemical properties can be investigated by spatially averaging techniques, such as high-resolution electron spectroscopies and diffraction methods. As such, arrays of 1D nanostructures created on stepped metal surfaces serve as well-defined model systems for tuning the chemical reactivity of metal surfaces, , for fundamental studies of 1D electronic structure − and quantum effects, and for pioneering research of magnetism in reduced dimensions. − …”

Generalized Kronig-Penney model for ultracold atomic quantum systems

“…The atom-ion interaction clearly has a threedimensional character, but an effective 1D theory can be developed for systems that are tightly trapped in the transverse direction [26]. Hence, we make such assumption for the atom and we write the transverse potential, in E * and R * units, as V ⊥ (ρ) = α ⊥ ρ 2 with α ⊥ = (R * /ℓ ⊥ ) 4 and ℓ ⊥ = /mω ⊥ . On the other hand, in the axial direction, x, we assume that the atom experiences no external confinement.…”

“…Although mostly considered to be of academic and educational -rather than quantitative -interest, a number of laboratory systems have become available for which the KP-model provides a useful starting point. These experiments range from solid state and surface science where one-dimensional structures of atoms can be surface-deposited in scanning tunnelling microscopy [3][4][5] to cold atomic systems in periodic potentials [6]. In such model systems, a setup in which one species forms a lattice of atoms -or ions -through which a second, untrapped, species can move, would create a situation reminiscent of the KP-model.…”