Non-local correlation dynamics in two-dimensional graphene

Abdel-Baset A Mohamed; Abdel-Haleem Abdel-Aty; Montasir Qasymeh; Hichem Eleuch

doi:10.1038/s41598-022-07204-5

Non-local correlation dynamics in two-dimensional graphene

Sci Rep. 2022 Mar 4;12(1):3581. doi: 10.1038/s41598-022-07204-5.

Authors

Abdel-Baset A Mohamed^{1

2}, Abdel-Haleem Abdel-Aty^{3

4}, Montasir Qasymeh⁵, Hichem Eleuch^{6

7

8}

Affiliations

¹ Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam bin Abdulaziz University, Al-Kharj, Saudi Arabia. abdelbastm@aun.edu.eg.
² Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt. abdelbastm@aun.edu.eg.
³ Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha, 61922, Saudi Arabia.
⁴ Physics Department, Faculty of Science, Al-Azhar University, Assiut, 71524, Egypt.
⁵ Department of Electrical and Computer Engineering, Abu Dhabi University, Abu Dhabi, 59911, United Arab Emirates.
⁶ Department of Applied Physics and Astronomy, University of Sharjah, Sharjah, United Arab Emirates.
⁷ College of Arts and Sciences, Abu Dhabi University, Abu Dhabi, 59911, United Arab Emirates.
⁸ Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX, 77843, USA.

Abstract

We explore the non-local correlation dynamics in a Graphene sheet of disordered electrons in a two-dimensional honeycomb lattice, containing two sublattices, induced by the interaction range of impurity potentials of two Dirac points. The Bell function, uncertainty-induced non-locality, and concurrence are used to investigate the formation and robustness of the non-local correlation between the honeycomb lattice and the Dirac point. The generated lattice-point non-local correlations are explored when the lattice-point system is initially in the uncorrelated state. Due to the lattice-point interaction, the resulting Bell-function non-locality and entanglement concurrence satisfy the hierarchy principle. The generated uncertainty-induced non-locality correlation has a higher degree of stability and robustness than the Bell non-locality and concurrence. We analyze the robustness of the initial maximal non-local correlations under the effects of the band parameter, the intravalley scattering processes, the wave numbers, and the intrinsic decoherence. The formation and stability of lattice-point correlations are highly dependent on the honeycomb lattice and Dirac point characteristics.