AI 中文总结
该研究针对具有多元康托结构静电势垒的石墨烯，利用超周期势形式得到透射概率闭式表达式，揭示其量子输运随康托阶数演化的规律，建立了含四个控制参数的统一双对数标度律。
AI 中文摘要
我们研究了经受多元康托结构静电势的石墨烯中狄拉克电子的量子输运。利用超周期势形式，我们得到了透射概率的闭式表达式。随着康托阶数增加，透射谱从稀疏的超晶格共振集合演变为近透明区域，多元阶数决定了该演化速率。角响应取决于掺杂构型，在n-n-n、n-p-n和狄拉克点情形中表现出不同行为。在近透明区域，透射遵循关于四个独立控制参数的双对数标度律：康托阶数、势垒高度、初始长度和入射角。通过结合这些单独的标度关系，我们建立了支配量子输运的统一标度律。这些结果表明，势的层级自相似性决定了此类系统的输运性质。
英文摘要
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.
Comments18 pages, 11 figures
