Optical conductivity of a quantum electron gas in a Sierpinski carpet

van Veen, Edo and Tomadin, Andrea and Polini, Marco and Katsnelson, M. I. and Yuan, Shengjun (2017) Optical conductivity of a quantum electron gas in a Sierpinski carpet. Physical review B, 96 (23). ISSN 2469-9950

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Recent advances in nanofabrication methods have made it possible to create complex two-dimensional artificial structures, such as fractals, where electrons can be confined. The optoelectronic and plasmonic properties of these exotic quantum electron systems are largely unexplored. In this paper, we calculate the optical conductivity of a two-dimensional electron gas in a Sierpinski carpet (SC). The SC is a paradigmatic fractal that can be fabricated in a planar solid-state matrix by means of an iterative procedure. We show that the optical conductivity as a function of frequency (i.e., the optical spectrum) converges, at finite temperature, as a function of the fractal iteration. The calculated optical spectrum features sharp peaks at frequencies determined by the smallest geometric details at a given fractal iteration. Each peak is due to excitations within sets of electronic state-pairs, whose wave functions are characterized by quantum confinement in the SC at specific length scales, related to the frequency of the peak.

Item Type:
Journal Article
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Physical review B
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Deposited On:
22 Nov 2018 13:40
Last Modified:
16 Sep 2023 01:49