In this article, we employ the transfer matrix method to investigate relativistic particles in a superperiodic potential of arbitrary order $n$, with $n$ a positive integer. We calculate the reflection and transmission probabilities for the spinless Klein particle encountering rectangular potential barriers with superperiodic repetition. It is found that spinless relativistic particles exhibit Klein tunneling and a significantly higher degree of reflection compared to their nonrelativistic counterparts. Additionally, we analytically explore the behavior of the experimentally realizable massless Dirac electrons as they encounter rectangular potential barriers with a superperiodic pattern in a monolayer of graphene. In this system, the transmission probability, conductance, and Fano factor are evaluated as functions of the number of barriers, the order of superperiodicity, and the angle of incidence. Our findings reveal that the transmission probability shows a series of resonances that depend on the number of barriers and the order of superperiodicity. We extend our analysis to specific cases within the unified Cantor potential $\gamma$ system ($\gamma$ is a scaling parameter greater than 1), focusing on the general Cantor potential (GCP) and the general Smith-Volterra-Cantor (GSVC) system. For the GCP, we calculate the tunneling probability, which reveals sharp transmission peaks and progressively thinner single-cell potential as $G$ increases. In the GSVC system, we analyze the potential segment length and tunneling probability, observing nearly unity tunneling coefficients when $\gamma \approx 1$, as well as saturation behavior in transmission coefficients at higher stages $G$.

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• 2-dimensional systems
• Graphene
• Two-dimensional electron system