Relativistic particles in super-periodic potentials: exploring graphene and fractal systems

• URL: http://arxiv.org/abs/2412.13220v1
• Date: Mon, 16 Dec 2024 06:42:43 GMT
• Title: Relativistic particles in super-periodic potentials: exploring graphene and fractal systems
• Authors: Sudhanshu Shekhar, Bhabani Prasad Mandal, Anirban Dutta,
• Abstract summary: We calculate the reflection and transmission probabilities for spinless Klein particles encountering rectangular potential barriers with super-periodic repetition. We analytically explore the behavior of experimentally realizable massless Dirac electrons in a monolayer of graphene. Our findings reveal that the transmission probability shows a series of resonances that depend on the number of barriers and the order of super-periodicity.
• Score: 1.1812062577871032
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• Abstract: In this article, we employ the transfer matrix method to investigate relativistic particles in super-periodic potentials (SPPs) of arbitrary order $n \in I^{+}$. We calculate the reflection and transmission probabilities for spinless Klein particles encountering rectangular potential barriers with super-periodic repetition. It is found that spinless relativistic particles exhibit Klein tunneling and a significantly higher degree of reflection compared to their non-relativistic counterparts. Additionally, we analytically explore the behavior of experimentally realizable massless Dirac electrons as they encounter rectangular potential barriers with a super-periodic 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 super-periodicity, 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 super-periodicity. We extend our analysis to specific cases within the Unified Cantor Potentials (UCPs)-$\gamma$ system ($\gamma$ is a scaling parameter greater than $1$), focusing on the General Cantor fractal system and the General Smith-Volterra-Cantor (GSVC) system. For the General Cantor fractal system, we calculate the tunneling probability, which reveals sharp transmission peaks and progressively thinner unit cell potentials 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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