Au-induced atomic wires on stepped Ge(<i>hhk</i>) surfaces

Wagner, Timo; Aulbach, J.; Schäfer, J.; Claessen, R.

doi:10.1103/physrevmaterials.2.123402

Cited by 5 publications

(14 citation statements)

References 44 publications

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“…In view of this overall inconclusive situation, the authors of this review have very recently performed additional elaborate ARPES experiments in direct combination with in situ STM/ STS measurements on the same Ge(0 0 1)-Au samples [44].…”

Section: Band Mapping By Arpes: Anisotropymentioning

confidence: 99%

One-dimensional quantum matter: gold-induced nanowires on semiconductor surfaces

Dudy

Aulbach

Wagner

et al. 2017

J. Phys.: Condens. Matter

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Interacting electrons confined to only one spatial dimension display a wide range of unusual many-body quantum phenomena, ranging from Peierls instabilities to the breakdown of the canonical Fermi liquid paradigm to even unusual spin phenomena. The underlying physics is not only of tremendous fundamental interest, but may also have bearing on device functionality in future micro- and nanoelectronics with lateral extensions reaching the atomic limit. Metallic adatoms deposited on semiconductor surfaces may form self-assembled atomic nanowires, thus representing highly interesting and well-controlled solid-state realizations of such 1D quantum systems. Here we review experimental and theoretical investigations on a few selected prototypical nanowire surface systems, specifically Ge(0 0 1)-Au and Si(hhk)-Au, and the search for 1D quantum states in them. We summarize the current state of research and identify open questions and issues.

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Section: Band Mapping By Arpes: Anisotropymentioning

confidence: 99%

One-dimensional quantum matter: gold-induced nanowires on semiconductor surfaces

Dudy

Aulbach

Wagner

et al. 2017

J. Phys.: Condens. Matter

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“…Later on, we continue with the first term of ( 22) in (25). Before, we do so, we first consider the second and third term of ( 22) and show that they vanish in the limit (lim inf →0 lim n→∞ ).…”

Section: Introduction Of the First Artificial Scalementioning

confidence: 99%

“…or to more advanced compositions of the nanochains. One-dimensional chains of atoms find applications in carbon atom wires [12,19,26] or as Au-chains on substrates [25]. Further, they serve as toy-models for higher dimensional systems.…”

mentioning

confidence: 99%

Mechanical behaviour of heterogeneous nanochains in the $Γ$-limit of stochastic particle systems

Lauerbach¹,

Neukamm²,

Schäffner³

et al. 2019

Preprint

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Nanochains of atoms, molecules and polymers have gained recent interest in the experimental sciences. This article contributes to an advanced mathematical modeling of the mechanical properties of nanochains that allow for heterogenities, which may be impurities or a deliberately chosen composition of different kind of atoms. We consider one-dimensional systems of particles which interact through a large class of convex-concave potentials, which includes the classical Lennard-Jones potentials.We allow for a stochastic distribution of the material parameters and investigate the effective behaviour of the system as the distance between the particles tends to zero. The mathematical methods are based on Γ-convergence, which is a suitable notion of convergence for variational problems, and on ergodic theorems as is usual in the framework of stochastic homogenization. The allowed singular structure of the interaction potentials causes mathematical difficulties that we overcome by an approximation. We consider the case of K interacting neighbours with K ∈ N arbitrary, i.e., interactions of finite range.

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“…(ii) If the external force f also depends on the Eulerian coordinate, which models what is sometimes called live loads and is, e.g., of interest in the case of a chain of atoms that is placed on a substrate [30], the potential reads…”

Section: Settingmentioning

confidence: 99%

“…In nanomaterials research, one-dimensional particle systems have recently gained interest, for instance as carbon atom wires [12,26,33] or one-dimensional systems of silicon [25]. One-dimensional surface nanostructures on semiconductor surfaces such as chains of gold atoms on certain substrates, see, e.g., [30], raise the interest of mechanical properties of such chains depending on the forces exerted by the substrate since the electronic properties strongly depend on the lattice constants. Similarly, chains of fullerenes in carbon nanotubes experience external forces which influence the chain's mechanical properties, see, e.g., [31].…”

Section: Introductionmentioning

confidence: 99%

External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a $Γ$-development

Carioni¹,

Fischer²,

Schlömerkemper³

2018

Preprint

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This paper is concerned with equilibrium configurations of one-dimensional particle systems with non-convex nearest-neighbour and next-to-nearest-neighbour interactions and its passage to the continuum. The goal is to derive compactness results for a Γ-development of the energy with the novelty that external forces are allowed. In particular, the forces may depend on Lagrangian or Eulerian coordinates and thus may model dead as well as live loads. Our result is based on a new technique for deriving compactness results which are required for calculating the first-order Γ-limit in the presence of external forces: instead of comparing a configuration of n atoms to a global minimizer of the Γ-limit, we compare the configuration to a minimizer in some subclass of functions which in some sense are "close to" the configuration. The paper is complemented with the study of the minimizers of the Γ-limit.

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Au-induced atomic wires on stepped Ge(hhk) surfaces

Cited by 5 publications

References 44 publications

One-dimensional quantum matter: gold-induced nanowires on semiconductor surfaces

One-dimensional quantum matter: gold-induced nanowires on semiconductor surfaces

Mechanical behaviour of heterogeneous nanochains in the $Γ$-limit of stochastic particle systems

External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a $Γ$-development

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