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Design and characterization of electrons in a fractal geometry.

ABSTRACT: The dimensionality of an electronic quantum system is decisive for its properties. In one dimension electrons form a Luttinger liquid and in two dimensions they exhibit the quantum Hall effect. However, very little is known about the behavior of electrons in non-integer, or fractional dimensions1. Here, we show how arrays of artificial atoms can be defined by controlled positioning of CO molecules on a Cu (111) surface2-4, and how these sites couple to form electronic Sierpi?ski fractals. We characterize the electron wave functions at different energies with scanning tunneling microscopy and spectroscopy and show that they inherit the fractional dimension. Wave functions delocalized over the Sierpi?ski structure decompose into self-similar parts at higher energy, and this scale invariance can also be retrieved in reciprocal space. Our results show that electronic quantum fractals can be artificially created by atomic manipulation in a scanning tunneling microscope. The same methodology will allow future study to address fundamental questions about the effects of spin-orbit interaction and a magnetic field on electrons in non-integer dimensions. Moreover, the rational concept of artificial atoms can readily be transferred to planar semiconductor electronics, allowing for the exploration of electrons in a well-defined fractal geometry, including interactions and external fields.

SUBMITTER: Kempkes SN

PROVIDER: S-EPMC6420065 | biostudies-literature | 2019 Feb

REPOSITORIES: biostudies-literature

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Design and characterization of electrons in a fractal geometry.

Kempkes S N SN Slot M R MR Freeney S E SE Zevenhuizen S J M SJM Vanmaekelbergh D D Swart I I Smith C Morais CM

Nature physics 20181112 2

The dimensionality of an electronic quantum system is decisive for its properties. In one dimension electrons form a Luttinger liquid and in two dimensions they exhibit the quantum Hall effect. However, very little is known about the behavior of electrons in non-integer, or fractional dimensions1. Here, we show how arrays of artificial atoms can be defined by controlled positioning of CO molecules on a Cu (111) surface2-4, and how these sites couple to form electronic Sierpiński fractals. We cha ...[more]

PMID: 30886641

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Project description:Highly prevalent in nature, fractal patterns possess self-similar components that repeat at varying size scales. The perceptual experience of human-made environments can be impacted with inclusion of these natural patterns. Previous work has demonstrated consistent trends in preference for and complexity estimates of fractal patterns. However, limited information has been gathered on the impact of other visual judgments. Here we examine the aesthetic and perceptual experience of fractal 'global-forest' designs already installed in humanmade spaces and demonstrate how fractal pattern components are associated with positive psychological experiences that can be utilized to promote occupant wellbeing. These designs are composite fractal patterns consisting of individual fractal 'tree-seeds' which combine to create a 'global fractal forest.' The local 'tree-seed' patterns, global configuration of tree-seed locations, and overall resulting 'global-forest' patterns have fractal qualities. These designs span multiple mediums yet are all intended to lower occupant stress without detracting from the function and overall design of the space. In this series of studies, we first establish divergent relationships between various visual attributes, with pattern complexity, preference, and engagement ratings increasing with fractal complexity compared to ratings of refreshment and relaxation which stay the same or decrease with complexity. Subsequently, we determine that the local constituent fractal ('tree-seed') patterns contribute to the perception of the overall fractal design, and address how to balance aesthetic and psychological effects (such as individual experiences of perceived engagement and relaxation) in fractal design installations. This set of studies demonstrates that fractal preference is driven by a balance between increased arousal (desire for engagement and complexity) and decreased tension (desire for relaxation or refreshment). Installations of these composite mid-high complexity 'global-forest' patterns consisting of 'tree-seed' components balance these contrasting needs, and can serve as a practical implementation of biophilic patterns in human-made environments to promote occupant wellbeing.

Dataset Information

Design and characterization of electrons in a fractal geometry.

Publications

Design and characterization of electrons in a fractal geometry.

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