Long-wave Absorption of Few-Hole Gas in Prolate Ellipsoidal Ge/Si Quantum Dot: Implementation of Analytically Solvable Moshinsky Model
Abstract
:1. Introduction
2. Adiabatic Description of the Hole Gas
3. Implementation of the One-Dimensional Moshinsky Model
4. Kohn Theorem Realization
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
- Ledentsov, N.N.; Ustinov, V.M.; Shchukin, V.A.; Kop’Ev, P.S.; Alferov, Z.I.; Bimberg, D. Quantum dot heterostructures: Fabrication, properties, lasers (Review). Semiconductors 1998, 32, 343–365. [Google Scholar] [CrossRef]
- Harrison, P.; Valavanis, A. Quantum Wells, Wires and Dots; Wiley: Chichester, UK, 2016. [Google Scholar]
- Chakraborty, T. Quantum Dots: A Survey of the Properties of Artificial Atoms; Elsevier: Amsterdam, The Netherlands, 1999. [Google Scholar]
- Maksym, P.A.; Chakraborty, T. Quantum dots in a magnetic field: Role of electron-electron interactions. Phys. Rev. Lett. 1990, 65, 108–111. [Google Scholar] [CrossRef] [PubMed]
- Hüttel, A.K.; Ludwig, S.; Lorenz, H.; Eberl, K.; Kotthaus, J.P. Direct control of the tunnel splitting in a one-electron double quantum dot. Phys. Rev. B 2005, 72, 081310. [Google Scholar] [CrossRef] [Green Version]
- Haddad, H.; Nammas, F.; Al Shorman, M.; Shukri, A. Electronic structure of one electron confined in three-dimensional quantum dots. Phys. B: Condens. Matter 2017, 526, 132–135. [Google Scholar] [CrossRef]
- Gindikin, Y.; Sablikov, V.A. Electron–electron interaction effect on the singlet–triplet transitions in one-dimensional quantum dots. J. Physics: Condens. Matter 2011, 23, 175601. [Google Scholar] [CrossRef]
- Deng, K.; Calderon-Vargas, F.A.; Mayhall, N.J.; Barnes, E. Negative exchange interactions in coupled few-electron quantum dots. Phys. Rev. B 2018, 97, 245301. [Google Scholar] [CrossRef] [Green Version]
- Anisimovas, E.; Matulis, A.; Peeters, F.M. Currents in a many-particle parabolic quantum dot under a strong magnetic field. Phys. Rev. B 2004, 70, 195334. [Google Scholar] [CrossRef] [Green Version]
- Florian, M.; Steinhoff, A.; Gies, C.; Jahnke, F. Scattering-induced dephasing of many-particle transitions in semiconductor quantum dots. Appl. Phys. A 2016, 122, 6. [Google Scholar] [CrossRef]
- Efros, A.L.; Efros, A.L. Interband absorption of light in a semiconductor sphere. Soviet Phys. Semicond. USSR 1982, 16, 772–775. [Google Scholar]
- Atoyan, M.; Kazaryan, E.; Sarkisyan, H. Interband light absorption in parabolic quantum dot in the presence of electrical and magnetic fields. Phys. E Low-dimens. Syst. Nanostruct. 2006, 31, 83–85. [Google Scholar] [CrossRef]
- Sarkisyan, H.A. Electronic states in a cylindrical quantum dot in the presence of parallel electrical and magnetic fields. Mod. Phys. Lett. B 2002, 16, 835–841. [Google Scholar] [CrossRef]
- Atayan, A.K.; Kazaryan, E.M.; Meliksetyan, A.V.; Sarkisyan, H.A. Magneto-absorption in cylindrical quantum dots. Eur. Phys. J. B 2008, 63, 485–492. [Google Scholar] [CrossRef]
- Khordad, R.; Sadeghzadeh, M.; Jahan-Abad, A.M. Specific heat of a parabolic cylindrical quantum dot in the presence of magnetic field. Superlattices Microstruct. 2013, 58, 11–19. [Google Scholar] [CrossRef]
- Aghekyan, N.; Amirkhanyan, S.; Kazaryan, E.; Sarkisyan, H. Spin magnetic moment and persistent orbital currents in cylindrical nanolayer. Superlattices Microstruct. 2014, 69, 87–98. [Google Scholar] [CrossRef] [Green Version]
- Chuu, D.-S.; Hsiao, C.M.; Mei, W.N. Hydrogenic impurity states in quantum dots and quantum wires. Phys. Rev. B 1992, 46, 3898–3905. [Google Scholar] [CrossRef] [Green Version]
- Porras-Montenegro, N.; Pérez-Merchancano, S.T.; Latge, A. Binding energies and density of impurity states in spherical GaAs?(Ga,Al)As quantum dots. J. Appl. Phys. 1993, 74, 7624–7626. [Google Scholar] [CrossRef]
- Safarpour, G.; Barati, M.; Zamani, A.; Niknam, E. Binding energy and optical properties of an off-center hydrogenic donor impurity in a spherical quantum dot placed at the center of a cylindrical nano-wire. J. Lumin. 2014, 145, 990–996. [Google Scholar] [CrossRef]
- Portacio, A.; Rodríguez, B.A.; Villamil, P. Influence of the position of a donor impurity on the second-order nonlinear optical susceptibility in a cylindrical quantum dot. Superlattices Microstruct. 2018, 113, 550–557. [Google Scholar] [CrossRef]
- Pfannkuche, D.; Gerhardts, R.R.; Maksym, P.A.; Gudmundsson, V. Theory of quantum dot helium. Phys. B Condens. Matter 1993, 189, 6–15. [Google Scholar] [CrossRef]
- Pfannkuche, D.; Gudmundsson, V.; Maksym, P.A. Comparison of a Hartree, a Hartree-Fock, and an exact treatment of quantum-dot helium. Phys. Rev. B 1993, 47, 2244–2250. [Google Scholar] [CrossRef]
- Reinisch, G.; Gudmundsson, V. Nonlinear Schrödinger–Poisson theory for quantum-dot Helium. Phys. D Nonlinear Phenom. 2012, 241, 902–907. [Google Scholar] [CrossRef] [Green Version]
- Pino, R. Exact solution of the Thomas-Fermi two-dimensional N -electron parabolic quantum dot. Phys. Rev. B 1998, 58, 4644–4648. [Google Scholar] [CrossRef]
- Pino, R. Two-dimensional Thomas-Fermi parabolic quantum dot in a weak magnetic field. Eur. Phys. J. B 2000, 13, 723–730. [Google Scholar] [CrossRef]
- Peeters, F.M. Magneto-optics in parabolic quantum dots. Phys. Rev. B 1990, 42, 1486–1487. [Google Scholar] [CrossRef] [PubMed]
- Govorov, A.O.; Chaplik, A.V. Magnetoabsorption at quantum points. JETP Lett. 1990, 52, 31–33. [Google Scholar]
- Barker, J.; O’Reilly, E.P. The influence of inter-diffusion on electron states in quantum dots. Phys. E Low-dimens. Syst. Nanostruct. 1999, 4, 231–237. [Google Scholar] [CrossRef]
- Galitski, V.; Karnakov, B.; Kogan, V.; Galitski, J.V. Exploring Quantum Mechanics; Oxford University Press (OUP): Oxford, UK, 2013. [Google Scholar]
- Hayrapetyan, D.B. Direct interband light absorption in strongly oblate semi-ellipsoidal quantum dots’ ensemble. Photonics Micro- Nano- Struct. Mater. 2011, 8414, 84140. [Google Scholar] [CrossRef] [Green Version]
- Hayrapetyan, D.B.; Kazaryan, E.M.; Sarkisyan, H.A. On the possibility of implementation of Kohn’s theorem in the case of ellipsoidal quantum dots. J. Contemp. Phys. Armen. Acad. Sci. 2012, 48, 32–36. [Google Scholar] [CrossRef]
- Hayrapetyan, D.; Kazaryan, E.; Sarkisyan, H. Implementation of Kohn’s theorem for the ellipsoidal quantum dot in the presence of external magnetic field. Phys. E Low-dimensional Syst. Nanostruct. 2016, 75, 353–357. [Google Scholar] [CrossRef]
- Ghaltaghchyan, H.T.; Hayrapetyan, D.B.; Kazaryan, E.M.; Sarkisyan, H.A. Few-body magneto-absorption in prolate ellipsoidal quantum dot. Phys. At. Nucl. 2017, 80, 769–773. [Google Scholar] [CrossRef]
- Ghaltaghchyan, H.T.; Hayrapetyan, D.B.; Kazaryan, E.M.; Sarkisyan, H.A. Few-body absorption in prolate ellipsoidal quantum dot. J. Phys. Conf. Ser. 2016, 673, 012012. [Google Scholar] [CrossRef]
- Sofronov, A.N.; Balagula, R.; Firsov, D.A.; Vorobjev, L.E.; Tonkikh, A.A.; Sarkisyan, H.A.; Hayrapetyan, D.B.; Petrosyan, L.S.; Kazaryan, É.M. Absorption of Far-Infrared Radiation in Ge/Si Quantum Dots. Semiconductors 2018, 52, 59–63. [Google Scholar] [CrossRef]
- Sarkisyan, H.A.; Hayrapetyan, D.; Petrosyan, L.S.; Kazaryan, E.M.; Sofronov, A.N.; Balagula, R.; Firsov, D.A.; Vorobjev, L.E.; Tonkikh, A.A. Realization of the Kohn’s Theorem in Ge/Si Quantum Dots with Hole Gas: Theory and Experiment. Nanomaterials 2019, 9, 56. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Moshinsky, M. How Good is the Hartree-Fo ck Approximation. Am. J. Phys. 1968, 36, 52. [Google Scholar] [CrossRef]
- Johnson, N.; Payne, M. Exactly solvable model of interacting particles in a quantum dot. Phys. Rev. Lett. 1991, 67, 1157. [Google Scholar] [CrossRef]
- Bouvrie, P.; Majtey, A.P.; Plastino, A.R.; Moreno, P.S.; Dehesa, J.S. Quantum entanglement in exactly soluble atomic models: The Moshinsky model with three electrons, and with two electrons in a uniform magnetic field. Eur. Phys. J. D 2012, 66, 15. [Google Scholar] [CrossRef]
- Brey, L.; Johnson, N.F.; Halperin, B.I. Optical and magneto-optical absorption in parabolic quantum wells. Phys. Rev. B 1989, 40, 10647–10649. [Google Scholar] [CrossRef]
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Hayrapetyan, D.B.; Kazaryan, E.M.; Mkrtchyan, M.A.; Sarkisyan, H.A. Long-wave Absorption of Few-Hole Gas in Prolate Ellipsoidal Ge/Si Quantum Dot: Implementation of Analytically Solvable Moshinsky Model. Nanomaterials 2020, 10, 1896. https://doi.org/10.3390/nano10101896
Hayrapetyan DB, Kazaryan EM, Mkrtchyan MA, Sarkisyan HA. Long-wave Absorption of Few-Hole Gas in Prolate Ellipsoidal Ge/Si Quantum Dot: Implementation of Analytically Solvable Moshinsky Model. Nanomaterials. 2020; 10(10):1896. https://doi.org/10.3390/nano10101896
Chicago/Turabian StyleHayrapetyan, David B., Eduard M. Kazaryan, Mher A. Mkrtchyan, and Hayk A. Sarkisyan. 2020. "Long-wave Absorption of Few-Hole Gas in Prolate Ellipsoidal Ge/Si Quantum Dot: Implementation of Analytically Solvable Moshinsky Model" Nanomaterials 10, no. 10: 1896. https://doi.org/10.3390/nano10101896