najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2023-14-5-539-543najo-290Research ArticlePHYSICSФИЗИКАVerification of continuum-based model of carbon materialsВерификация сплошносредной модели углеродных материаловhttps://orcid.org/0000-0002-8725-7743ЦиберкинК.TsiberkinK. B.

Кирилл Циберкин

ул. Букирева, 15, г. Пермь, 614068

Kirill B. Tsiberkin

Bukireva, 15, Perm, 614068

kbtsiberkin@psu.ruПермский государственный национальный исследовательский университетPerm State University202308062025145539543Copyright © Tsiberkin K.B., 20252025Циберкин К.Tsiberkin K.B.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/290

The continuous medium approximation to the description of a carbon material previously used to model the properties of spherical carbon shells of nanometer diameter. This approach is based on the transition from lattice operators to field operators. The present study verifies the given model evaluating the energy spectrum of electrons in a perfect flat carbon monolayer. An implementation of the Dirac cones within the continuous medium framework is demonstrated. Its are close to the positions of the vertices of the Brillouin zone for graphene. Increase of the Taylor series expansion order of field operators makes the result precise, and the approximate positions of the Dirac cones match the exact data for graphene.

Сплошносредное приближение к описанию углеродного материала, основанное на переходе от решёточных операторов к полевым, ранее использовано для моделирования свойств сферических углеродных оболочек нанометрового диаметра. В настоящей работе подход верифицирован посредством расчёта энергетического спектра электронов в идеальном плоском монослое углерода. Продемонстрирована возможность реализации конусов Дирака в модели сплошной среды, положения которых близки к истинным положениям вершин зоны Бриллюэна для графена. По мере повышения порядка разложения полевых операторов в ряд Тейлора и роста точности улучшается соответствие модели с точными данными для графена.

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The authors declare that there are no conflicts of interest present.