Quantum transport in Sierpinski carpets

van Veen, Edo and Yuan, Shengjun and Katsnelson, Mikhail I. and Polini, Marco and Tomadin, Andrea (2016) Quantum transport in Sierpinski carpets. Physical review B, 93 (11). ISSN 2469-9950

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Recent progress in the design and fabrication of artificial two-dimensional (2D) materials paves the way for the experimental realization of electron systems moving on complex geometries, such as plane fractals. In this work, we calculate the quantum conductance of a 2D electron gas roaming on a Sierpinski carpet (SC), i.e., a plane fractal with Hausdorff dimension intermediate between 1 and 2. We find that the fluctuations of the quantum conductance are a function of energy with a fractal graph, whose dimension can be chosen by changing the geometry of the SC. This behavior is independent of the underlying lattice geometry.

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Journal Article
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Physical review B
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22 Nov 2018 16:28
Last Modified:
17 Sep 2023 02:25