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Thomas–Fermi theory of out-of-plane charge screening in graphene

Vitaly Moroz Orcid Logo, Cyrill B. Muratov

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume: 480, Issue: 2294

Swansea University Author: Vitaly Moroz Orcid Logo

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DOI (Published version): 10.1098/rspa.2023.0570

Abstract

This paper provides a variational treatment of the effect of external charges on the free charges in an infinite free-standing graphene sheet within the Thomas–Fermi theory. We establish existence, uniqueness and regularity of the energy minimizers corresponding to the free charge densities that scr...

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Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
ISSN: 1471-2946
Published: The Royal Society 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa66548
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first_indexed 2024-05-31T12:51:17Z
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spelling v2 66548 2024-05-31 Thomas–Fermi theory of out-of-plane charge screening in graphene 160965ff7131686ab9263d39886c8c1a 0000-0003-3302-8782 Vitaly Moroz Vitaly Moroz true false 2024-05-31 MACS This paper provides a variational treatment of the effect of external charges on the free charges in an infinite free-standing graphene sheet within the Thomas–Fermi theory. We establish existence, uniqueness and regularity of the energy minimizers corresponding to the free charge densities that screen the effect of an external electrostatic potential at the neutrality point. For the potential due to one or several off-layer point charges, we also prove positivity and a precise universal asymptotic decay rate for the screening charge density, as well as an exact charge cancellation by the graphene sheet. We also treat a simpler case of the non-zero background charge density and establish similar results in that case. Journal Article Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 480 2294 The Royal Society 1471-2946 Thomas–Fermi model, fractional Laplacian,Riesz potential, universal decay estimate 31 7 2024 2024-07-31 10.1098/rspa.2023.0570 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University SU Library paid the OA fee (TA Institutional Deal) Swansea Unversity 2024-08-01T11:29:01.7764120 2024-05-31T13:49:48.3693190 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Vitaly Moroz 0000-0003-3302-8782 1 Cyrill B. Muratov 2 66548__31021__d4810aa5dc9a4c868a98b2c2118e3e1a.pdf 66548.VoR.pdf 2024-08-01T11:27:31.1277694 Output 625025 application/pdf Version of Record true Copyright: 2024 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License. true eng http://creativecommons.org/licenses/by/4.0/
title Thomas–Fermi theory of out-of-plane charge screening in graphene
spellingShingle Thomas–Fermi theory of out-of-plane charge screening in graphene
Vitaly Moroz
title_short Thomas–Fermi theory of out-of-plane charge screening in graphene
title_full Thomas–Fermi theory of out-of-plane charge screening in graphene
title_fullStr Thomas–Fermi theory of out-of-plane charge screening in graphene
title_full_unstemmed Thomas–Fermi theory of out-of-plane charge screening in graphene
title_sort Thomas–Fermi theory of out-of-plane charge screening in graphene
author_id_str_mv 160965ff7131686ab9263d39886c8c1a
author_id_fullname_str_mv 160965ff7131686ab9263d39886c8c1a_***_Vitaly Moroz
author Vitaly Moroz
author2 Vitaly Moroz
Cyrill B. Muratov
format Journal article
container_title Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
container_volume 480
container_issue 2294
publishDate 2024
institution Swansea University
issn 1471-2946
doi_str_mv 10.1098/rspa.2023.0570
publisher The Royal Society
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
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description This paper provides a variational treatment of the effect of external charges on the free charges in an infinite free-standing graphene sheet within the Thomas–Fermi theory. We establish existence, uniqueness and regularity of the energy minimizers corresponding to the free charge densities that screen the effect of an external electrostatic potential at the neutrality point. For the potential due to one or several off-layer point charges, we also prove positivity and a precise universal asymptotic decay rate for the screening charge density, as well as an exact charge cancellation by the graphene sheet. We also treat a simpler case of the non-zero background charge density and establish similar results in that case.
published_date 2024-07-31T11:29:02Z
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score 11.035634

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