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Crossing Points in Spectra and Light Absorption in Spheroidal and Cone-Shaped Quantum Dots

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Optics and Its Applications

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 281))

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Abstract

We briefly review the analysis of the energy spectrum, the envelope eigenfunctions of electron, hole and exciton states, and the direct interband light absorption in cone-shaped and spheroidal impenetrable quantum dots. We apply high-order finite element method and calculation schemes of Kantorovich method in comparison with the adiabatic approximation (in the strong size quantization limit) for solving boundary-value problems that describe axially symmetric quantum dots. We demonstrate the efficiency of the algorithms and software by benchmark calculations of spectral and optical characteristics of the cone-shaped and spheroidal quantum dots and crossing points in their spectra.

Partially supported by the RFBR (grant No. 17-51-44003 Mong_a) and the RUDN University Strategic Academic Leadership Program.

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Notes

  1. 1.

    For electron(e) and hole(h) states \(2 V_C(\rho ,z)=0\), and for exciton states \(2V_C(\rho ,z)=-2/\sqrt{\rho ^2+z^2}\), \(2V_C(\rho ,z)= \tilde{V}_C(\tilde{\rho },\tilde{z})/E_{R}\), \(\tilde{V}_C(\tilde{\rho },\tilde{z})= -2e/(\kappa \sqrt{\tilde{\rho }^2+\tilde{z}^2})\), where e and \(m_e\) are the electron charge and mass, \(\kappa \) is the static permittivity. For GaAs model we use the reduced atomic units, \(m_e^*=0.067 m_e\), \(m_h^*=m_e^*/0.12\), \(\kappa =13.18\), \(a_B=104\)Å, \(E_R=5.275\) meV, i.e., \(\mathcal{E}=2E=\tilde{E}/E_{R}\), \(\Psi (\rho ,z)=a_{B}^{3/2}\tilde{\Psi }^{e}(\tilde{\rho },\tilde{z})\), \(\rho =\tilde{\rho }/a_B\), \(z=\tilde{z}/a_B\), where \(\tilde{E}\), \(\tilde{V}_C(\tilde{\rho },\tilde{z})\), \(\tilde{\rho }\) and \(\tilde{z}\) are dimensioned quantities.

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Author information

Authors and Affiliations

  1. N.G. Chernyshevsky Saratov National Research State University, Saratov, Russia

    V. L. Derbov

  2. Joint Institute for Nuclear Research, Dubna, MR, 141980, Russia

    A. A. Gusev, O. Chuluunbaatar & S. I. Vinitsky

  3. Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences, Ulaanbaatar, 13330, Mongolia

    O. Chuluunbaatar

  4. Ho Chi Minh city University of Education, Ho Chi Minh city, Vietnam

    L. L. Hai

  5. Peoples’ Friendship University of Russia (RUDN University), 117198, Moscow, Russia

    S. I. Vinitsky

  6. Russian-Armenian (Slavonic) University, H. Emin 123, 0051, Yerevan, Armenia

    E. M. Kazaryan & H. A. Sarkisyan

  7. Peter the Great Saint-Petersburg Polytechnic University, Polytechnicheskaya 29, St. Petersburg, 195251, Russia

    H. A. Sarkisyan

Authors
  1. V. L. Derbov
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  2. A. A. Gusev
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  3. O. Chuluunbaatar
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  4. L. L. Hai
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  5. S. I. Vinitsky
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  6. E. M. Kazaryan
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  7. H. A. Sarkisyan
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Corresponding author

Correspondence to A. A. Gusev .

Editor information

Editors and Affiliations

  1. Institute for Theoretical Physics, University of Wroclaw, Wroclaw, Poland

    David Blaschke

  2. Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    Dmitry Firsov

  3. Institute for Physical Research of National Academy of Sciences of Armenia, Ashtarak, Armenia

    Aram Papoyan

  4. Russian-Armenian University, Yerevan, Armenia

    Hayk A. Sarkisyan

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Derbov, V.L. et al. (2022). Crossing Points in Spectra and Light Absorption in Spheroidal and Cone-Shaped Quantum Dots. In: Blaschke, D., Firsov, D., Papoyan, A., Sarkisyan, H.A. (eds) Optics and Its Applications. Springer Proceedings in Physics, vol 281. Springer, Cham. https://doi.org/10.1007/978-3-031-11287-4_11

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