Quantum transport and unified scaling law in graphene with polyadic Cantor electrostatic barriers
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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BibTeX
@misc{shekhar2026quantum,
title = {{Quantum transport and unified scaling law in graphene with polyadic Cantor electrostatic barriers}},
author = {Sudhanshu Shekhar and Mohammad Umar and Bhabani Prasad Mandal},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28398},
eprint = {2608.28398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28398},
}
RIS
TY - UNPB
TI - Quantum transport and unified scaling law in graphene with polyadic Cantor electrostatic barriers
AU - Sudhanshu Shekhar
AU - Mohammad Umar
AU - Bhabani Prasad Mandal
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28398
UR - https://arxiv.org/abs/2608.28398
AB - 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.
ER -