Quantum transport and unified scaling law in graphene with polyadic Cantor electrostatic barriers

• URL: http://arxiv.org/abs/2608.28398v1
• Date: Fri, 28 Aug 2026 14:51:41 GMT
• Title: Quantum transport and unified scaling law in graphene with polyadic Cantor electrostatic barriers
• Abstract summary: We study the quantum transport of Dirac electrons in graphene subjected to a polyadic Cantor-structured electrostatic potential.<n>Results show that the hierarchical self-similarity of the potential governs the transport properties of such systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the quantum transport of Dirac electrons in graphene subjected to a polyadic Cantor-structured electrostatic potential. Using the superperiodic potential formalism, we obtain a closed-form expression for the transmission probability. As the Cantor stage increases, the transmission spectrum evolves from a sparse set of superlattice resonances to a near-transparent regime, with the polyadic order setting the rate of this evolution. The angular response depends on the doping configuration, showing distinct behavior in the $n$--$n$--$n$, $n$--$p$--$n$, and Dirac-point cases. In the near-transparent regime, the transmission follows double-logarithmic scaling laws with respect to four independent control parameters: the Cantor stage, the potential height, the initiator length, and the angle of incidence. By combining these individual scaling relations, we establish a unified scaling law governing quantum transport. These results show that the hierarchical self-similarity of the potential governs the transport properties of such systems.

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