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<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD with OASIS Tables with MathML3 v1.4 20241031//EN" "https://jats.nlm.nih.gov/archiving/1.4/JATS-archive-oasis-article1-4-mathml3.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" dtd-version="1.4" article-type="research-article" xml:lang="en"><front><journal-meta><journal-title-group><journal-title xml:lang="ru">Математическая физика и компьютерное моделирование</journal-title></journal-title-group><issn publication-format="print">2587-6325</issn><issn publication-format="electronic">2587-6902</issn></journal-meta><article-meta><article-id pub-id-type="doi">10.15688/mpcm.jvolsu.2023.2.5</article-id><article-categories><subj-group><subject>Other</subject></subj-group></article-categories><title-group><article-title xml:lang="ru">Вычисление тензора эффективной массы в ε- и ξ-фосфорене методом теории функционала плотности</article-title><trans-title-group xml:lang="en"><trans-title>Calculation of the Effective Mass Tensor in ε- and ξ-Phosphorene by the Density Functional Theory Method</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="ru"><surname>Бадикова</surname><given-names>Полина Вячеславовна</given-names></name><name xml:lang="en"><surname>Badikova</surname><given-names>Polina V.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff1"/><email>polin.badicova@gmail.com</email><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0542-1149</contrib-id></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="ru"><surname>Завьялов</surname><given-names>Дмитрий Викторович</given-names></name><name xml:lang="en"><surname>Zav’yalov</surname><given-names>Dmitry V.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff1"/><email>sinegordon@gmail.com</email><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9497-9613</contrib-id></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="ru"><surname>Конченков</surname><given-names>Владимир Игоревич</given-names></name><name xml:lang="en"><surname>Konchenkov</surname><given-names>Vladimir I.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff1"/><email>kontchenkov@yandex.ru</email><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-2525-0191</contrib-id></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="ru"><surname>Сивашова</surname><given-names>Екатерина Сергеевна</given-names></name><name xml:lang="en"><surname>Sivashova</surname><given-names>Ekaterina S.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff1"/><email>laei@mail.ru</email><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-0338-9133</contrib-id></contrib><aff-alternatives id="aff1"><aff xml:lang="en"><institution>Volgograd State Technical University (Volgograd, Russian Federation)</institution></aff><aff xml:lang="ru"><institution>Волгоградский государственный технический университет (Волгоград, Российская Федерация)</institution></aff></aff-alternatives></contrib-group><pub-date pub-type="epub" iso-8601-date="2023-05-20"><day>20</day><month>05</month><year>2023</year></pub-date><volume>26</volume><issue>2</issue><fpage>52</fpage><lpage>60</lpage><history><date date-type="received" iso-8601-date="2022-12-16"><day>16</day><month>12</month><year>2022</year></date><date date-type="accepted" iso-8601-date="2023-04-23"><day>23</day><month>04</month><year>2023</year></date></history><permissions><license xlink:href="https://creativecommons.org/licenses/by-nc/4.0/" xlink:title="CC BY-NC 4.0"><ali:license_ref>https://creativecommons.org/licenses/by-nc/4.0/</ali:license_ref><license-p xml:lang="ru">CC BY-NC 4.0</license-p></license></permissions><abstract xml:lang="ru"><p>В работе из закона дисперсии электронов в зоне проводимости различных аллотропных модификаций фосфорена, рассчитанного с помощью теории функционала плотности, получен тензор эффективной массы. Для расчетов использовался пакет квантовохимического моделирования, OpenMX, который значительно сокращает время расчетов для систем, состоящих из сотен и тысяч атомов. Сравнение полученных результатов тензоров для черного и синего фосфорена с другими работами показало корректность используемых методов, которые в дальнейшем были применены для других, менее изученных аллотропных модификаций фосфорена. В частности, были изучены ε- и ξ-фосфорен, которые отличаются негексагональной кристаллической решеткой с непрямой запрещенной зоной. Это может быть интересно с точки зрения обнаружения в этих материалах интересных акусто-электронных свойств, например, резонансного поглощения акустических волн. Проведены параллели между аллотропами. С точки зрения тензоров эффективной массы ε-фосфорен изотропен как и синий, а ξ-фосфорен, напротив, имеет неизотропную структуру, как у черного фосфорена. Полученные в ходе исследования результаты могут быть использованы в дальнейшем изучении физических свойств материалов, например, таких, как проводимость, фотогальванические и акусто-электронные эффекты</p></abstract><abstract xml:lang="en" abstract-type="summary"><p>In this work, the effective mass tensor was obtained from the law of dispersion of electrons in the conduction band of various allotropic modifications of phosphorene, calculated using the density functional theory. For calculations, we used the quantum chemical modeling package, OpenMX, which significantly reduces the calculation time for systems consisting of hundreds and thousands of atoms. Comparison of the obtained results of tensors for black and blue phosphorene with other works showed the correctness of the methods used, which were subsequently applied to other less studied allotropic modifications of phosphorene. In particular, ε- and ξ-phosphorene were studied, which are characterized by a non-hexagonal crystal lattice with an indirect band gap. This may be of interest from the point of view of discovering interesting acoustic-electronic properties in these materials, for example, resonant absorption of acoustic waves. Parallels between allotropes are drawn. From the point of view of effective mass tensors, ε-phosphorene is isotropic, like blue phosphorene, while ξ-phosphorene, on the contrary, has a non-isotropic structure, like black phosphorene. The results obtained during the study can be used in further study of the physical properties of materials, such as conductivity and photovoltaic effects.</p></abstract><kwd-group xml:lang="ru"><kwd>фосфорен</kwd><kwd>теория функционала плотности</kwd><kwd>аллотроп</kwd><kwd>проводимость</kwd><kwd>эффективная масса.</kwd></kwd-group><kwd-group xml:lang="en"><kwd>phosphorene</kwd><kwd>density functional theory</kwd><kwd>allotrope</kwd><kwd>conductivity</kwd><kwd>effective mass</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена при поддержке гранта ВолгГТУ № 54/470-22.</funding-statement><funding-statement xml:lang="en">The work was supported by Volgograd State Technical University grant No. 54/470-22.</funding-statement></funding-group></article-meta></front><back><ref-list><ref id="ref1"><mixed-citation publication-type="other" xml:lang="ru">Вычислительный кластер ВолгГТУ. — Электрон. текстовые дан. — Режим доступа: https://cluster.vstu.ru/. — Загл. с экрана.</mixed-citation></ref><ref id="ref2"><mixed-citation publication-type="other" xml:lang="ru">Cai, Y. Layer-Dependent Band Alignment and Work Function of Few-Layer Phosphorene / Y. Cai, G. Zhang, Y. W. Zhang // Scientific Reports. — 2014. — Vol. 4. — Article ID: 6677. — DOI: https://doi.org/10.1038/srep06677</mixed-citation></ref><ref id="ref3"><mixed-citation publication-type="other" xml:lang="ru">Electronic Structure and Simulated STM Images of Non-Honeycomb Phosphorene Allotropes / S. Kaur, A. Kumar, S. Srivastava, K. Tankeshwar // AIP Conference Proceedings. — 2018. — Vol. 1942. — Article ID: 080020. — DOI: https://doi.org/10.1063/1.5028854</mixed-citation></ref><ref id="ref4"><mixed-citation publication-type="other" xml:lang="ru">Jain, A. Strongly Anisotropic In-Plane Thermal Transport in Single-Layer Black Phosphorene / A. Jain, A. McGaughey // Scientific Reports. — 2015. — Vol. 5. — Article ID: 8501. — DOI: https://doi.org/10.1038/srep08501</mixed-citation></ref><ref id="ref5"><mixed-citation publication-type="other" xml:lang="ru">Kryuchkov, S. V. Nonlinear Electromagnetic Waves in Semi-Dirac Nanostructures with Superlattice / S. V. Kryuchkov, E. I. Kukhar // European Physical Journal B. — 2020. — Vol. 93. — Article ID: 62. — DOI: https://doi.org/10.1140/epjb/e2020-100575-4</mixed-citation></ref><ref id="ref6"><mixed-citation publication-type="other" xml:lang="ru">Kumar, U. Anisotropic Nonlinear Optical Response of Phosphorene / U. Kumar, V. Kumar, Enamullah // Physica E: Low-Dimensional Systems and Nanostructures. — 2019. — Vol. 108. — P. 288–295. — DOI: https://doi.org/10.1016/j.physe.2018.11.003</mixed-citation></ref><ref id="ref7"><mixed-citation publication-type="other" xml:lang="ru">Nine New Phosphorene Polymorphs with Non-Honeycomb Structures: A Much Extended Family / M. Wu, H. Fu, L. Zhou, K. Yao, X. Ch. Zeng // Nano Letters. — 2017. — Vol. 15, iss. 1. — P. 3557–3562. — DOI: https://doi.org/10.1021/acs.nanolett.5b01041</mixed-citation></ref><ref id="ref8"><mixed-citation publication-type="other" xml:lang="ru">Ozaki, T. Variationally Optimized Atomic Orbitals for Large-Scale Electronic Structures / T. Ozaki // Physical Review B. — 2003. — Vol. 67. — Article ID: 155108. — DOI: https://doi.org/10.1103/PhysRevB.67.155108</mixed-citation></ref><ref id="ref9"><mixed-citation publication-type="other" xml:lang="ru">Ψ-Phosphorene: A New Allotrope of Phosphorene / H. Wang, X. Li, Zh. Liu, J. Yang // Physical Chemistry Chemical Physics. — 2017. — Vol. 19. — P. 2402–2408. — DOI: https://pubs.rsc.org/en/content/articlelanding/2017/CP/C6CP07944J</mixed-citation></ref><ref id="ref10"><mixed-citation publication-type="other" xml:lang="ru">Phosphorene − an Emerging Two-Dimensional Material: Recent Advances in Synthesis, Functionalization, and Applications / V. Chaudhary, P. Neugebauer, O. Mounkachi, S. Lahbabi, A. El. Fatimy // 2D Materials. — 2022. — Vol. 9. — Article ID: 032001. — DOI: https://doi.org/10.1088/2053-1583/ac6dc2</mixed-citation></ref><ref id="ref11"><mixed-citation publication-type="other" xml:lang="ru">Phosphorene: From Theory to Applications / A. Carvalho, M. Wang, X. Zhu, A. S. Rodin, H. Su, A. H. Castro Neto // Nature Review Materials. — 2016. — Vol. 1. — Article ID: 16061. — DOI: https://doi.org/10.1038/natrevmats.2016.61</mixed-citation></ref><ref id="ref12"><mixed-citation publication-type="other" xml:lang="ru">Zhang, J. Tuning of the Optical Properties of Monolayer Blue Phosphorene / J. Zhang, H. Zhang // Plasmonics. — 2021. — Vol. 16. — P. 1213–1221. — DOI: https://doi.org/10.1007/s11468-020-01350-0</mixed-citation></ref><ref id="ref13"><mixed-citation publication-type="other" xml:lang="en">Vychislitelnyy klaster VolgGTU [Computing Cluster of VolgSTU]. URL: https://cluster.vstu.ru/.</mixed-citation></ref><ref id="ref14"><mixed-citation publication-type="other" xml:lang="en">Cai Y., Zhang G., Zhang Y.W. Layer-Dependent Band Alignment and Work Function of Few-Layer Phosphorene. Scientific Reports, 2014, vol. 4, article ID: 6677. DOI: https://doi.org/10.1038/srep06677</mixed-citation></ref><ref id="ref15"><mixed-citation publication-type="other" xml:lang="en">Kaur S., Kumar A., Srivastava S., Tankeshwar K. Electronic Structure and Simulated STM Images of Non-Honeycomb Phosphorene Allotropes. AIP Conference Proceedings, 2018, vol. 1942, article ID: 080020. DOI: https://doi.org/10.1063/1.5028854</mixed-citation></ref><ref id="ref16"><mixed-citation publication-type="other" xml:lang="en">Jain A., McGaughey A. Strongly Anisotropic In-Plane Thermal Transport in Single-Layer Black Phosphorene. Scientific Reports, 2015, vol. 5, article ID: 8501. DOI: https://doi.org/10.1038/srep08501</mixed-citation></ref><ref id="ref17"><mixed-citation publication-type="other" xml:lang="en">Kryuchkov S.V., Kukhar E.I. Nonlinear Electromagnetic Waves in Semi-Dirac Nanostructures with Superlattice. European Physical Journal B, 2020, vol. 93, article ID: 62. DOI: https://doi.org/10.1140/epjb/e2020-100575-4</mixed-citation></ref><ref id="ref18"><mixed-citation publication-type="other" xml:lang="en">Kumar U., Kumar V., Enamullah Anisotropic Nonlinear Optical Response of Phosphorene. Physica E: Low-Dimensional Systems and Nanostructures, 2019, vol. 108, pp. 288-295. DOI: https://doi.org/10.1016/j.physe.2018.11.003</mixed-citation></ref><ref id="ref19"><mixed-citation publication-type="other" xml:lang="en">Wu M., Fu H., Zhou L., Yao K., Zeng X.Ch. Nine New Phosphorene Polymorphs with Non-Honeycomb Structures: A Much Extended Family. Nano Letters, 2017, vol. 15, iss. 1, pp. 3557-3562. DOI: https://doi.org/10.1021/acs.nanolett.5b01041</mixed-citation></ref><ref id="ref20"><mixed-citation publication-type="other" xml:lang="en">Ozaki T. Variationally Optimized Atomic Orbitals for Large-Scale Electronic Structures. Physical Review B, 2003, vol. 67, article ID: 155108. DOI: https://doi.org/10.1103/PhysRevB.67.155108</mixed-citation></ref><ref id="ref21"><mixed-citation publication-type="other" xml:lang="en">Wang H., Li X., Liu Zh., Yang J. Ψ-Phosphorene: A New Allotrope of Phosphorene. Physical Chemistry Chemical Physics, 2017, vol. 19, pp. 2402-2408. DOI: https://pubs.rsc.org/en/content/articlelanding/2017/CP/C6CP07944J</mixed-citation></ref><ref id="ref22"><mixed-citation publication-type="other" xml:lang="en">Chaudhary V., Neugebauer P., Mounkachi O., Lahbabi S., Fatimy A.El. Phosphorene − an Emerging Two-Dimensional Material: Recent Advances in Synthesis, Functionalization, and Applications. 2D Materials, 2022, vol. 9, article ID: 032001. DOI: https://doi.org/10.1088/20531583/ac6dc2</mixed-citation></ref><ref id="ref23"><mixed-citation publication-type="other" xml:lang="en">Carvalho A., Wang M., Zhu X., Rodin A.S., Su H., Castro Neto A.H. Phosphorene: From Theory to Applications. Nature Review Materials, 2016, vol. 1, article ID: 16061. DOI: https://doi.org/10.1038/natrevmats.2016.61</mixed-citation></ref><ref id="ref24"><mixed-citation publication-type="other" xml:lang="en">Zhang J., Zhang H. Tuning of the Optical Properties of Monolayer Blue Phosphorene. Plasmonics, 2021, vol. 16, pp. 1213-1221. DOI: https://doi.org/10.1007/s11468-020-01350-0</mixed-citation></ref></ref-list></back></article>
