Topological Random Fractals

Moein N. Ivaki; Isac Sahlberg; Kim Pöyhönen; Teemu Ojanen

doi:10.1038/s42005-022-01101-z

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arXiv · 2112.08824

Topological Random Fractals

Moein N. Ivaki·Isac Sahlberg·Kim Pöyhönen·Teemu Ojanen

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Abstract

We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological random fractals exhibit a robust mobility gap, support quantized conductance and represent a well-defined thermodynamic phase of matter. The finite-size scaling analysis further suggests that the critical properties are not consistent with the class $D$ systems in two dimensions. Our results establish topological random fractals as the most complex systems known to support nontrivial band topology with their distinct unique properties.

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Moein N. Ivaki, Isac Sahlberg, Kim Pöyhönen, Teemu Ojanen. 2021-12-16. Topological Random Fractals. https://doi.org/10.1038/s42005-022-01101-z

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