Simulation the response of graphene to an external electric field using the exact tight-binding model

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Abstract

Numerical simulation of the interaction of electromagnetic radiation with graphene allows us to reproduce fast nonlinear processes and their observed manifestations. The paper presents the results obtained in the process of developing a software solution for calculating the observed parameters of such processes.In graphene physics, the massless fermion approximation is classical. However, in the study of processes with high energy density, model based on this approximation are beyond the limits of their applicability and the results obtained on their basis can not be considered reliable. To solve this problem, a transition to a substantially more accurate model based on a strict account of the nearest-neighbor interaction in the crystal lattice (tight-binding model) has been made.Comparative testing of these two models shows that at low energy characteristics of the external perturbation the results coincide. However, as the energy characteristics of the affecting electromagnetic field increase, the divergence of the results becomes apparent and grows.The new exact model has a more complex mathematical formulation and requires more computational resources. When using the same hardware configuration it is expressed in the increase of counting time. Relative and absolute values for a number of examples are given.The obtained results allow us to expand the range of parameters for modeling of nonlinear processes in the considered material, for example, generation of high-frequency harmonics and ensure its reliability.

About the authors

Anatolii Dmitrievich Panferov

Saratov State University

Email: panferovad@sgu.ru
Ph.D., Deputy Head of DITD at N.G. Chernyshevsky Saratov State University. Scientific interests: high-performance computing, parallel programming, numerical solution of quantum kinetic equations, modeling of processes of vacuum particle birth in QED, generation of carriers in semiconductors including slotless ones, processes at early stages of relativistic nuclei collision.

Nikolay Andreevich Novikov

Saratov State University

Email: n_nik1997@mail.ru

Anastasiya Alekseevna Ulyanova

Saratov State University

Email: ulyanova.nastiya@yandex.ru

References

  1. Zhang H., Pincelli T., Jozwiak Ch., Kondo T., Ernstorfer R., Sato T., Zhou S.. “Angle-resolved photoemission spectroscopy”, Nature Reviews Methods Primers, 2 (2022), 54, 22 pp.
  2. Mikhailov S. A.. “Non-linear electromagnetic response of graphene”, Europhysics Letters, 79 (2007), 27002, 5 pp.
  3. Ishikawa K. L.. “Nonlinear optical response of graphene in time domain”, Phys. Rev. B, 82 (2010), 201402.
  4. Yoshikawa N.. “High-harmonic generation in graphene enhanced by elliptically polarized light excitation”, Science, 356:6339 (2017), pp. 736–738.
  5. Cha S., Kim M., Kim Y., Choi Sh., Kang S., Kim H., Yoon S., Moon G., Kim T., Lee Y. W., Cho G. Y., Park M. J., Kim Ch-J., Kim B. J., Lee JD., Jo M-H., Kim J.. “Gate-tunable quantum pathways of high harmonic generation in graphene”, Nature Communication, 13 (2022), 6630, 10 pp.
  6. Novoselo K. S., Geim A. K., Morozov S. V., Jiang D., Katsnelson M. I., Grigorieva I. V., Dubonos S. V., Firsov A. A.. “Two-dimensional gas of massless Dirac fermions in graphene”, Nature, 438 (2005), pp. 197–200.
  7. Castro Neto A. H., Guinea F., Peres N. M. R., Novoselov K. S., Geim A. K.. “The eletronic properties of graphene”, Rev. Mod. Phys, 81:1 (2009), 109.
  8. Panferov A., Smolyansky S., Blaschke D., Gevorgyan N.. “Comparing two different descriptions of the I-V characteristic of graphene: theory and experiment”, XXIV International Baldin Seminar on High Energy Physics Problems “Relativistic Nuclear Physics and Quantum Chromodynamics” (Baldin ISHEPP XXIV), EPJ Web Conf, 204 (2019), 06008, 6 pp.
  9. Smolyansky S., Panferov A., Blaschke D., Gevorgyan N.. “Nonperturbative kinetic description of electron-hole excitations in graphene in a time dependent electric field of arbitrary polarization”, Particles, 2:2 (2019), pp. 208–230.
  10. Smolyansky S. A., Blaschke D. B., Dmitriev V. V., Panferov A. D., Gevorgyan N. T.. “Kinetic equation approach to graphene in strong external fields”, Particles, 3:2 (2020), pp. 456–476.
  11. Boolakee T., Heide Ch., Wagner F., Ott Ch., Schlecht M., Ristein J., Weber H., Hommelhoff P.. “Length-dependence of light-induced currents in graphene”, J. Phys. B: At. Mol. Opt. Phys, 53:15 (2020), 154001, 5 pp.
  12. Ke M., Asmar M. M., Tse W. K.. “Nonequilibrium RKKY interaction in irradiated graphene”, Physical Review Research, 2:3 (2020), 033228.
  13. Li J., Han J. E.. “Nonequilibrium excitations and transport of Dirac electrons in electric-field-driven graphene”, Phys. Rev. B, 97:20 (2018), 205412.
  14. Chen Zi-Yu., Qin R.. “Circularly polarized extreme ultraviolet high harmonic generation in graphene”, Optics Express, 27:3 (2019), pp. 3761–3770.
  15. Li P., Shi R., Lin P., Ren X.. “First-principles calculations of plasmon excitations in graphene, silicene, and germanene”, Phys. Rev. B, 107:3 (2023), 035433.
  16. Панферов А. Д., Новиков Н. А., Трунов А. А.. «Моделирование поведения графена во внешних электрических полях», Программные системы: теория и приложения, 12:1(38) (2021), с. 3–19.
  17. Панферов А. Д., Поснова Н. В., Ульянова А. А.. «Моделирование поведения двухуровневой квантовой системы с использованием масштабируемых регулярных сеток», Программные сисемы: теория и приложения, 14:2(57) (2023), с. 27–47.
  18. Панферов А. Д., Новиков Н. А.. «Характеристики индуцированного излучения в условиях действия на графен коротких высокочастотных импульсов», Известия Саратовского университета. Новая серия. Серия: Физика, 23:3 (2023), с. 254–264.
  19. Reich S., Maultzsch J., Thomsen C., Ordejon P.. “Tight-binding description of graphene”, Phys. Rev. B, 66:3 (2002), 035412.
  20. Katsnelson M. I.. The Physics of Graphene, 2nd ed, Cambridge University Press, 2020, ISBN 9781108617567.
  21. Панферов А. Д., Щербаков И. А.. «Реализация квантового кинетического уравнения для графена на основе модели сильного взаимодействия ближайших соседей», Известия Саратовского университета. Новая серия. Серия: Физика, 24:3 (2024), с. 198–208.

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