Topological Random Fractals

• URL: http://arxiv.org/abs/2112.08824v1
• Date: Thu, 16 Dec 2021 12:11:19 GMT
• Title: Topological Random Fractals
• Authors: Moein N. Ivaki, Isac Sahlberg, Kim P\"oyh\"onen, Teemu Ojanen
• Abstract summary: topological random fractals exhibit a robust mobility gap, support quantized conductance and represent a well-defined thermodynamic phase of matter. Our results establish topological random fractals as the most complex systems known to support nontrivial band topology with their distinct unique properties.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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