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Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions
Multi-point probability measures along with the dielectric function of Dirac Fermions in mono-layer graphene containing particle-particle and white-noise (out-plane) disorder interactions on an equal footing in the Thomas-Fermi-Dirac approximation is investigated. By calculating the one-body carrier...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Nature Publishing Group UK
2019
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6403372/ https://www.ncbi.nlm.nih.gov/pubmed/30842596 http://dx.doi.org/10.1038/s41598-019-39254-7 |
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author | Najafi, M. N. |
author_facet | Najafi, M. N. |
author_sort | Najafi, M. N. |
collection | PubMed |
description | Multi-point probability measures along with the dielectric function of Dirac Fermions in mono-layer graphene containing particle-particle and white-noise (out-plane) disorder interactions on an equal footing in the Thomas-Fermi-Dirac approximation is investigated. By calculating the one-body carrier density probability measure of the graphene sheet, we show that the density fluctuation (ζ(−1)) is related to the disorder strength (n(i)), the interaction parameter (r(s)) and the average density ([Formula: see text] ) via the relation [Formula: see text] for which [Formula: see text] leads to strong density inhomogeneities, i.e. electron-hole puddles (EHPs), in agreement with the previous works. The general equation governing the two-body distribution probability is obtained and analyzed. We present the analytical solution for some limits which is used for calculating density-density response function. We show that the resulting function shows power-law behaviors in terms of ζ with fractional exponents which are reported. The disorder-averaged polarization operator is shown to be a decreasing function of momentum like ordinary 2D parabolic band systems. It is seen that a disorder-driven momentum q(ch) emerges in the system which controls the behaviors of the screened potential. We show that in small densities an instability occurs in which imaginary part of the dielectric function becomes negative and the screened potential changes sign. Corresponding to this instability, some oscillations in charge density along with a screening-anti-screening transition are observed. These effects become dominant in very low densities, strong disorders and strong interactions, the state in which EHPs appear. The total charge probability measure is another quantity which has been investigated in this paper. The resulting equation is analytically solved for large carrier densities, which admits the calculation of arbitrary-point correlation function. |
format | Online Article Text |
id | pubmed-6403372 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-64033722019-03-11 Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions Najafi, M. N. Sci Rep Article Multi-point probability measures along with the dielectric function of Dirac Fermions in mono-layer graphene containing particle-particle and white-noise (out-plane) disorder interactions on an equal footing in the Thomas-Fermi-Dirac approximation is investigated. By calculating the one-body carrier density probability measure of the graphene sheet, we show that the density fluctuation (ζ(−1)) is related to the disorder strength (n(i)), the interaction parameter (r(s)) and the average density ([Formula: see text] ) via the relation [Formula: see text] for which [Formula: see text] leads to strong density inhomogeneities, i.e. electron-hole puddles (EHPs), in agreement with the previous works. The general equation governing the two-body distribution probability is obtained and analyzed. We present the analytical solution for some limits which is used for calculating density-density response function. We show that the resulting function shows power-law behaviors in terms of ζ with fractional exponents which are reported. The disorder-averaged polarization operator is shown to be a decreasing function of momentum like ordinary 2D parabolic band systems. It is seen that a disorder-driven momentum q(ch) emerges in the system which controls the behaviors of the screened potential. We show that in small densities an instability occurs in which imaginary part of the dielectric function becomes negative and the screened potential changes sign. Corresponding to this instability, some oscillations in charge density along with a screening-anti-screening transition are observed. These effects become dominant in very low densities, strong disorders and strong interactions, the state in which EHPs appear. The total charge probability measure is another quantity which has been investigated in this paper. The resulting equation is analytically solved for large carrier densities, which admits the calculation of arbitrary-point correlation function. Nature Publishing Group UK 2019-03-06 /pmc/articles/PMC6403372/ /pubmed/30842596 http://dx.doi.org/10.1038/s41598-019-39254-7 Text en © The Author(s) 2019 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. |
spellingShingle | Article Najafi, M. N. Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions |
title | Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions |
title_full | Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions |
title_fullStr | Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions |
title_full_unstemmed | Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions |
title_short | Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions |
title_sort | interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6403372/ https://www.ncbi.nlm.nih.gov/pubmed/30842596 http://dx.doi.org/10.1038/s41598-019-39254-7 |
work_keys_str_mv | AT najafimn interactiondisorderdrivencharacteristicmomentumingrapheneapproachofmultibodydistributionfunctions |