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Main Authors: Shekhar, Sudhanshu, Mandal, Bhabani Prasad, Dutta, Anirban
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2412.13220
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author Shekhar, Sudhanshu
Mandal, Bhabani Prasad
Dutta, Anirban
author_facet Shekhar, Sudhanshu
Mandal, Bhabani Prasad
Dutta, Anirban
contents 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)-$γ$ system ($γ$ 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 $γ\approx 1$, as well as saturation behavior in transmission coefficients at higher stages $G$.
format Preprint
id arxiv_https___arxiv_org_abs_2412_13220
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Relativistic particles in super-periodic potentials: exploring graphene and fractal systems
Shekhar, Sudhanshu
Mandal, Bhabani Prasad
Dutta, Anirban
Mesoscale and Nanoscale Physics
Quantum Physics
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)-$γ$ system ($γ$ 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 $γ\approx 1$, as well as saturation behavior in transmission coefficients at higher stages $G$.
title Relativistic particles in super-periodic potentials: exploring graphene and fractal systems
topic Mesoscale and Nanoscale Physics
Quantum Physics
url https://arxiv.org/abs/2412.13220