Abstract :
At a finite temperature, electron-electron interactions and
energy eigenvalues were studied using in the field of
symplectic geometry and the relativistic radial
Schrödinger equation with the expanded exponential
thermal potential (parabolic potential) representing the
strong electron-electron interaction. Electron-electron
interactions can strongly affect the effective mass, mass
spectrum, and functionality of multi-electron quantum
dots. A quanto-relativistic interaction's behavior and
effects with temperature dependence in the magnetic field
are shown to have a unique feature in semiconductor
quantum dots. These results have important implications
for lighting, quantum dot enhancement film, rational
design, edge optic, new materials, spin electronics color
filter, on-chip, visible and IR/NIR image sensor,
photovoltaic, and fabrication of quantum dot qubits with
predictable properties.
References:
[1] Singha, V. Pellegrini, A. Pinczuk, et al., Strong electron-electron interactions in Si/SiGe quantum dots, Phys. Rev. Lett. 104, 246802, 2010. https://doi.org/10.1103/PhysRevLett.104.246802
[2] Miserev and O. Sushkov, Prediction of the spin-triplet two-electron quantum dots in Si: Towards controlled quantum simulations of magnetic systems, Phys. Rev. B, 100(20), 5129, 2019, https://link.aps.org/doi/10.1103/PhysRevB.100.205129; R. Gould, Quantum electrodynamics. Electromagnetic Processes, 1st ed. Springer- Verlag, 2020, https://doi.org/10.1515/9780691215846-008.
[3] Caruso, V. Oguri, and F. Silvera, How the inter-electronic potential Ansätze affect the bound state solutions of a planar two-electron quantum dot model, Physica E: Low-dimensional Systems, 105, 182, 2019. https://doi.org/10.1016/j.physe.2018.09.017
[4] Heyong-chan, et al., New variational perturbation theory based on−deformed oscillator, International Journal of Theoretical Physics, 45, 1017, 2006. https://doi.org/10.1007/s10773-006-9094-3.
[5] Taqi, J. Diouri, A theoretical model for exciton binding energies in rectangular and parabolic spherical finite quantum dots, Semiconductor physics quantum electronics & optoelectronics, (15)4, 365, 2012. https://doi.org/10.15407/spqeo15.04.365
[6] Hartstein, Y. Hsu, K. A. Modic, et al., Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-Tc superconductors, Nature Physics, 4,2020. https://doi.org/10.1038/s41567-020-0910-0
[7] El-Said, Two-electron quantum dots in a magnetic field, Semiconductor science, and technology. 10(10),1310, 1995. https://doi.org/10.1088/0268-1242/10/10/003
[8] Tazikeh, et al., Optoelectronical Properties of a Metalloid-Doped B12N12 Nano-Cage, Journal of Optoelectronical Nanostructures, 5(1), 10, 2020. https://doi.org/20.1001.1.24237361.2020.5.1.7.2
[9] , Rushka, J. Freericks, A completely algebraic solution of the simple harmonic oscillator, Am J Phys. 88(11), 976, 2019. https://doi.org/10.1119/10.0001702
Greiner, S. Schramm, E. Stein, Quantum chromodynamics, Springer Science & Business Media; 2007.
https://link.springer.com/content/pdf/bfm%3A978-3-540-48535-3%2F1.pdf
Fujiwara, Rigorous Time Slicing Approach to Feynman Path Integrals, 1st ed. Springer International Publishing, 2017. https://doi.org/10.1007/978-4-431-56553-6
Dienykhan, G. Efimov, G. Ganbold, N. Nedelko, Oscillator representation in quantum physics (lecture notes in physics monographs), 1st ed. Springer International Publishing, 1995, https://doi.org/10.1007/978-3-540-49186-6; M. Martin Nieto, Existence of bound states in continuous 0<D<∞ dimensions, Physics Letters A, 293(1-2), 10, 2020. https://doi.org/10.1016/S0375-9601(01)00827-1
Kelley, J. Leventhal, Ladder operators for the harmonic oscillator. Problems in Classical and Quantum Mechanics, Springer International Publishing, 2017. https://doi.org/10.1007/978-3-319-46664-4
Maireche, A theoretical investigation of nonrelativistic bound state solution at finite temperature using the sum of modified Cornell plus inverse quadratic potential, Sri Lankan J Phys, 21(1), 11, 2020. https://doi.org/10.4038/sljp.v21i1.8069
Jahanshir, Relativistic modification of the exciton’s mass in monolayer TMDCs materials, Journal of Advanced Materials and Processing, 8(4), 2020. https://doi.org/20.1001.1.2322388.2020.8.4.5.0
J. Mousavi, First–Principle Calculation of the Electronic and Optical Properties of Nanolayered ZnO Polymorphs by PBE and mBJ Density Functionals, Journal of Optoelectronical Nanostructures, 2(4), 1, 2017. https://doi.org/20.1001.1.24237361. 2017.2.4.1.1.; Ghaffary, et al., Study of the spin-orbit interaction effects on energy levels and the absorption coefficients of spherical quantum dot and quantum anti-dot under the magnetic field, Journal of Optoelectronical Nanostructures, 6(2), 55, 2021. https://doi.org/10.30495/jopn.2021.27965.1222
Ciurla, J. Adamowski, B. Szafran, S. Bednare, Modelling of confinement potentials in quantum dots, Physica E, 15, 261 (2002). https://doi.org/10.1016/S1386-9477(02)00572-6.
Mohebbifar, Study of the Quantum Efficiency of Semiconductor Quantum Dot Pulsed Micro-Laser, Journal of Optoelectronical Nanostructures, 6(1), 59, 2021. https://doi.org/10.30495/jopn.2021.4544.
Dharma-wardana, et al., Correlation functions in electron-electron and electron-hole double quantum wells: temperature, density and barrier-width dependence, arXiv:1901.00895v1 [cond.mat. mes-hall] 2019, https://doi.org/110.1103/PhysRevB.99.035303; A. Tanveer Karim, et al., Temperature dependency of excitonic effective mass and charge carrier conduction mechanism in CH3NH3PbI3−xClx thin films, Scientific Reports, 11,10772, 2021. https://doi.org/10.1038/s41598-021-90247-x
Ciftja, Understanding electronic systems in semiconductor quantum dots, Physica Scri. 88(5), 058302, 2013. https://doi.org/10.1088/0031-8949/88/05/058302
Jahanshir, A. Tarasenko, Computational method for determining the bound state oscillator, Math. Comp. Sci. Journal, 1(3), 16-22, 2021, https://doi.org/10.30511/mcs.2021.526310.1018.
Abu Alia, et al., Effect of tilted electric field and magnetic field on the energy levels, binding energies and heat capacity of a donor impurity in GaAs quantum dot, Indian Journal of Pure & Applied Physics 59, 365, 2021. http://nopr.niscair.res.in/handle/123456789/57471
Abu Alia, K. M. Elsaid and A. Shaer, Magnetic properties of GaAs parabolic quantum dot in the presence of donor impurity under the influence of external tilted electric and magnetic fields, Journal of Taibah University for Science, 13(1), 687, 2019. https://doi.org/10.1080/16583655.2019.1622242
Bozour, M. Elsaid, K, Ilaiwi, The effects of pressure and temperature on the energy levels of a parabolic two-electron quantum dot in a magnetic field, Journal of King Saud University, 33(7), 2017. https://doi.org/10.1016/j.jksus.2017.01.001
Chaudhuri, Two-electron quantum dot in a magnetic field: Analytic solution for a finite potential model, Physica E: Low-dimensional Systems and Nanostructures, 128, 114571, 2021. https://doi.org/10.1016/j.physe.2020.114571.
Jirovec, Dynamics of hole singlet-triplet qubits with large g-factor differences, arXiv:2111.05130v1 [cond-mat. mes-hall], 2021. https://arxiv.org/abs/2111.05130v1
Scappucci, et al., The germanium quantum information route, Nat. Rev. Mater, 6, 926-943, 2021. https://doi.org/10.1038/s41578-020-00262-z
Loss, D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A57, 120–126, 1998. https://doi.org/10.1103/PhysRevA.57.120.
Wagner, U. Merkt, A.V. Chaplik, Spin-singlet–spin-triplet oscillations in quantum dots, Phy. Rev.B45, 1951, 1992. https://doi.org/ 10.1103/PhysRevB.45.1951
D. Landau, E.M. Lifschitz, Quantum Mechanics nonrelativistic Theory, 3st ed Pergamon Oxford, 1977.
http://power1.pc.uec.ac.jp/~toru/notes/LandauLifshitz-QuantumMechanics.pdf
J. Prado, S. J. Prado, Zeeman effect and magnetic field induced spin-hybridization in semiconductor quantum dots, Journal of Physics-Condensed Matter 16(39), 6949, 2004. https://doi.org/10.1088/0953-8984/16/39/027.
Stano, g-factor of electrons in gate-defined quantum dots in a strong in-plane magnetic field, Phys. Rev. B98, 195314, 2018. https://doi.org/10.1103/PhysRevB.98.195314.
