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Effects of Spin Orbit Interaction (SOI) on the Thermodynamic Properties of a Quantum Pseudodot

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Abstract

We investigate the effect of spin orbit interaction (SOI) on thermodynamics quantities of a quantum pseudodot. The energy levels have been derived and thermal properties are evaluated using the Tsallis formalism. Compared to BG, Tsallis formalism consists in evaluating the thermodynamic quantities only on the accessible states. The results show that spin orbit interaction (SOI) has a great effect on entropy since it increases the number of accessible states causing the splitting on internal energy. Our results also show that chemical potential influences the spin-states in a quantum pseudodot system and creates splitting of some thermodynamic quantities. SOI and chemical potential are prominent parameters to modulate the spin alignment and perform the thermodynamics of electronic devices.

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References

  1. M.A. Kastner, The single-electron transistor. Rev. Mod. Phys. 64(3), 849 (1992)

    Article  ADS  Google Scholar 

  2. N.F. Johnson, Quantum dots: few-body, low-dimensional systems. J. Phys.: Condens. Matter 7(6), 965 (1995)

    ADS  Google Scholar 

  3. R.C. Ashoori, Electrons in artificial atoms. Nature 379(6564), 413–419 (1996)

    Article  ADS  Google Scholar 

  4. U. Woggon, Optical Properties of Semiconductor Quantum Dots (Springer, Berlin, 1997), pp. 103–157

    Google Scholar 

  5. Q. Dots (1998). L. Jacak, P. Hawrylak, and A. Wojs.

  6. D. Bimberg, M. Grundmann, N.N. Ledentsov, Quantum Dot Heterostructures (Wiley, New Jersy, 1999)

    Google Scholar 

  7. S. Mukhopadhyay, A. Chatterjee, Polaronic effects in quantum dots. Acta Phys. Pol. B 32, 473–502 (2001)

    ADS  Google Scholar 

  8. L.P. Kouwenhoven, D.G. Austing, S. Tarucha, Few-electron quantum dots. Rep. Prog. Phys. 64(6), 701 (2001)

    Article  ADS  Google Scholar 

  9. J. Kainz, S.A. Mikhailov, A. Wensauer, U. Rössler, Ground state energies of quantum dots in high magnetic fields: a new approach. Phys. E. 12(1–4), 888–891 (2002)

    Article  Google Scholar 

  10. R. Khordad, A. Ghanbari, Effect of phonons on optical properties of RbCl quantum pseudodot qubits. Opt. Quant. Electron. 49(2), 76 (2017)

    Article  Google Scholar 

  11. Y. Sun, J.L. Xiao, The magnetic field effect on the coherence time of qubit in RbCl crystal quantum pseudodot. Opt. Quant. Electron. 51(4), 1–8 (2019)

    Article  Google Scholar 

  12. J.L. Xiao, The effect of Coulomb impurity potential on the coherence time of RbCl quantum pseudodot qubit. J. Low Temp. Phys. 195(5), 442–449 (2019)

    Article  ADS  Google Scholar 

  13. J.L. Xiao, Effect of hydrogen-like impurity on a qubit in quantum pseudodot at finite temperature. Superlattices Microstruct. 125, 233–236 (2019)

    Article  ADS  Google Scholar 

  14. Y. Sun, Z.H. Ding, J.L. Xiao, The effect of phonons in RbCl quantum pseudodot qubits. J. Electron. Mater. 45(7), 3576–3580 (2016)

    Article  ADS  Google Scholar 

  15. R. Khordad, Temperature effect on the threshold frequency of absorption in a quantum pseudodot. Phys. B 406(3), 620–623 (2011)

    Article  ADS  Google Scholar 

  16. A.J. Peter, K. Navaneethakrishnan, Effects of position-dependent effective mass and dielectric function of a hydrogenic donor in a quantum dot. Phys. E 40(8), 2747–2751 (2008)

    Article  Google Scholar 

  17. J.J. Sharkey, C. Yoo, A.J. Peter, Magnetic field induced diamagnetic susceptibility of a hydrogenic donor in a GaN/AlGaN quantum dot. Superlattices Microstruct. 48(2), 248–255 (2010)

    Article  ADS  Google Scholar 

  18. R. Khordad, Pressure effect on the threshold frequency of absorption in a quantum pseudodot. Indian J. Phys. 86(7), 653–657 (2012)

    Article  ADS  Google Scholar 

  19. R. Khordad, H. Bahramiyan, H.R. Sedehi, Effects of strain, magnetic field and temperature on entropy of a two dimensional GaAs quantum dot under spin–orbit interaction. Opt. Quant. Electron. 50(7), 1–13 (2018)

    Article  Google Scholar 

  20. R. Khordad, H.R. Sedehi, H. Bahramiyan, Simultaneous effects of impurity and electric field on entropy behavior in double cone-like quantum dot. Commun. Theor. Phys. 69(1), 95 (2018)

    Article  ADS  Google Scholar 

  21. R. Khordad, H.R. Sedehi, Low temperature behavior of thermodynamic properties of 1D quantum wire under the Rashba spin-orbit interaction and magnetic field. Solid State Commun. 269, 118–124 (2018)

    Article  ADS  Google Scholar 

  22. R. Khordad, R. Bornaei, H.A. Mardani-Fard, Application of Tsallis formalism to study entropy and specific heat of V-groove quantum wires. Indian J. Phys. 89(6), 545–550 (2015)

    Article  ADS  Google Scholar 

  23. R. Khordad, B. Vaseghi, Magnetic properties in three electrons under Rashba spin-orbit interaction and magnetic field. Int. J. Quantum Chem. (2019). https://doi.org/10.1002/qua.25994

    Article  Google Scholar 

  24. R. Khordad, Spin-orbit interaction in a quantum pseudodot: pressure effect. J. Comput. Electron. 13(2), 383–393 (2014)

    Article  MathSciNet  Google Scholar 

  25. R. Khordad, B. Vaseghi, Effects temperature, pressure and spin–orbit interaction simultaneously on third harmonic generation of wedge-shaped quantum dots. Chin. J. Phys. 59, 473–480 (2019)

    Article  MathSciNet  Google Scholar 

  26. C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52(1–2), 479–487 (1988)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Ehrenfest, P., & Ehrenfest, T. (1990). The conceptual foundations of the statistical approach in mechanics. Courier Corporation.

  28. Y.M. Guttmann, The Concept of Probability in Statistical Physics (Cambridge University Press, 1999)

  29. G. Gallavotti, Statistical Mechanics: A Short Treatise (Springer Science & Business Media, Berlin, 2013)

    MATH  Google Scholar 

  30. B.H. Lavenda, J. Dunning-Davies, Additive Entropies of degree-q and the Tsallis Entropy (2003). https://doi.org/10.3923/jas.2005.315.322

  31. B. Das, S. Datta, R. Reifenberger, Zero-field spin splitting in a two-dimensional electron gas. Phys. Rev. B 41(12), 8278 (1990)

    Article  ADS  Google Scholar 

  32. S. Datta, B. Das, Electronic analog of the electro-optic modulator. Appl. Phys. Lett. 56(7), 665–667 (1990)

    Article  ADS  Google Scholar 

  33. R. Winkler, Rashba spin splitting in two-dimensional electron and hole systems. Phys. Rev. B 62(7), 4245 (2000)

    Article  ADS  Google Scholar 

  34. X.F. Bai, C. Han, Properties of the internal excited state of the strong-coupling magneto-bipolaron in a parabolic quantum dot. Acta PhysicaSinica 63(2), 027501 (2014)

    Google Scholar 

  35. T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, R. Huber, Coherent terahertz control of antiferromagnetic spin waves. Nat Photonics 5(1), 31–34 (2011)

    Article  ADS  Google Scholar 

  36. P. Liu, X. Lin, Y. Xu, B. Zhang, Z. Si, K. Cao, W. Zhao, Optically tunable magnetoresistance effect: from mechanism to novel device application. Materials 11(1), 47 (2018)

    Article  ADS  Google Scholar 

  37. A.R. Lima, J.S. Martins, T.J.P. Penna, Monte Carlo simulation of magnetic systems in the Tsallis statistics. Phys. A 268(3–4), 553–566 (1999)

    Article  Google Scholar 

  38. J.J.S. De Groote, J.E.M. Hornos, A.V. Chaplik, Thermodynamic properties of quantum dots in a magnetic field. Phys. Rev. B 46(19), 12773 (1992)

    Article  ADS  Google Scholar 

  39. P. Hawrylak, Single-electron capacitance spectroscopy of few-electron artificial atoms in a magnetic field: Theory and experiment. Phys. Rev. Lett. 71(20), 3347 (1993)

    Article  ADS  Google Scholar 

  40. B. Boyacioglu, A. Chatterjee, Heat capacity and entropy of a GaAs quantum dot with Gaussian confinement. J. Appl. Phys. 112(8), 083514 (2012)

    Article  ADS  Google Scholar 

  41. Y.Y. Liao, Orientation and heat capacity of horizontally adsorbed molecules in electric fields. Phys. Rev. A 89(2), 022510 (2014)

    Article  ADS  Google Scholar 

  42. B. Tang, Y.T. Wang, X.L. Peng, L.H. Zhang, C.S. Jia, Efficient predictions of Gibbs free energy for the gases CO, BF, and gaseous BBr. J. Mol. Struct. 1199, 126958 (2020)

    Article  Google Scholar 

  43. C.O. Edet, A.N. Ikot, M.C. Onyeaju, U.S. Okorie, G.J. Rampho, M.L. Lekala, S. Kaya, Thermo-magnetic properties of the screened Kratzer potential with spatially varying mass under the influence of Aharanov-Bohm (AB) and position-dependent magnetic fields. Phys. E: Low-Dimensional Syst. Nanostruct. 131, 114710 (2021)

    Article  Google Scholar 

  44. C.S. Jia, R. Zeng, X.L. Peng, L.H. Zhang, Y.L. Zhao, Entropy of gaseous phosphorus dimer. Chem. Eng. Sci. 190, 1–4 (2018)

    Article  Google Scholar 

  45. C.O. Edet, P.O. Amadi, M.C. Onyeaju, U.S. Okorie, R. Sever, G.J. Rampho, A.N. Ikot, Thermal properties and magnetic susceptibility of hellmann potential in Aharonov-Bohm (AB) flux and magnetic fields at zero and finite temperatures. J. Low Temp. Phys. 202(1), 83–105 (2021)

    Article  ADS  Google Scholar 

  46. K. Kash, A. Scherer, J.M. Worlock, H.G. Craighead, M.C. Tamargo, Optical spectroscopy of ultrasmall structures etched from quantum wells. Appl. Phys. Lett. 49(16), 1043–1045 (1986)

    Article  ADS  Google Scholar 

  47. A. Boda, B. Boyacioglu, U. Erkaslan, A. Chatterjee, Effect of Rashba spin–orbit coupling on the electronic, thermodynamic, magnetic and transport properties of GaAs, InAs and InSb quantum dots with Gaussian confinement. Phys. B 498, 43–48 (2016)

    Article  ADS  Google Scholar 

  48. M.K. Elsaid, E. Hijaz, Magnetic susceptibility of coupled double GaAs quantum dot in magnetic fields. Acta Phys. Pol. A 131(6), 1491–1496 (2017)

    Article  ADS  Google Scholar 

  49. B.S. Kandemir, D. Akay, Tuning the pseudo-Zeeman splitting in graphene cones by magnetic field. J. Magn. Magn. Mater. 384, 101–105 (2015)

    Article  ADS  Google Scholar 

  50. B.S. Kandemir, D. Akay, The effect of electron-phonon coupling in spin–orbit-coupled graphene. Phil. Mag. 97(25), 2225–2235 (2017)

    Article  ADS  Google Scholar 

  51. J.W. Yin, W.P. Li, Y.F. Yu, J.L. Xiao, The Rashba effect on the bound polaron in a parabolic quantum dot. J. Low Temp. Phys. 163(1–2), 53–59 (2011)

    Article  ADS  Google Scholar 

  52. K.J. Oyewumi, B.J. Falaye, C.A. Onate, O.J. Oluwadare, W.A. Yahya, Thermodynamic properties and the approximate solutions of the Schrödinger equation with the shifted Deng-Fan potential model. Mol. Phys. 112(1), 127–141 (2014)

    Article  ADS  Google Scholar 

  53. X.L. Peng, R. Jiang, C.S. Jia, L.H. Zhang, Y.L. Zhao, Gibbs free energy of gaseous phosphorus dimer. Chem. Eng. Sci. 190, 122–125 (2018)

    Article  Google Scholar 

  54. C.S. Jia, C.W. Wang, L.H. Zhang, X.L. Peng, H.M. Tang, R. Zeng, Enthalpy of gaseous phosphorus dimer. Chem. Eng. Sci. 183, 26–29 (2018)

    Article  Google Scholar 

  55. A.N. Ikot, C.O. Edet, P.O. Amadi, U.S. Okorie, G.J. Rampho, H.Y. Abdullah, Thermodynamic properties of Aharanov-Bohm (AB) and magnetic fields with screened Kratzer potential. Eur. Phys. J. D 74(7), 1–13 (2020)

    Article  Google Scholar 

  56. G.J. Rampho, A.N. Ikot, C.O. Edet, U.S. Okorie, Energy spectra and thermal properties of diatomic molecules in the presence of magnetic and AB fields with improved Kratzer potential. Mol. Phys. 119(5), 1821922 (2021)

    Article  ADS  Google Scholar 

  57. C.S. Jia, L.H. Zhang, X.L. Peng, J.X. Luo, Y.L. Zhao, J.Y. Liu, L.D. Tang, Prediction of entropy and Gibbs free energy for nitrogen. Chem. Eng. Sci. 202, 70–74 (2019)

    Article  Google Scholar 

  58. C.O. Edet, A.N. Ikot, Effects of topological defect on the energy spectra and thermo-magnetic properties of \(CO\) diatomic molecule. J. Low Temp. Phys. 203(1), 84–111 (2021)

    Article  ADS  Google Scholar 

  59. C.O. Edet & U.S. Okori (2020). G, Osobonye, AN Ikot, GJ Rampho and R. Sever. Journal of Mathematical Chemistry, 58, 989.

  60. A.N. Ikot, U.S. Okorie, G. Osobonye, P.O. Amadi, C.O. Edet, M.J. Sithole, R. Sever, Superstatistics of Schrödinger equation with pseudo-harmonic potential in external magnetic and Aharanov-Bohm fields. Heliyon 6(4), 03738 (2020)

    Article  Google Scholar 

  61. C.O. Edet, P.O. Amadi, U.S. Okorie, A. Tas, A.N. Ikot, G. Rampho, Solutions of Schrodinger equation and thermal properties of generalized trigonometric Poschl-Teller potential. Revista Mexicana de Física 66(6), 824–839 (2020)

    Article  MathSciNet  Google Scholar 

  62. U.S. Okorie, C.O. Edet, A.N. Ikot, G.J. Rampho, R. Sever, Thermodynamic functions for diatomic molecules with modified Kratzer plus screened Coulomb potential. Indian J. Phys. 95(3), 411–421 (2020)

    Article  ADS  Google Scholar 

  63. R. Khordad, A. Avazpour, A. Ghanbari, Exact analytical calculations of thermodynamic functions of gaseous substances. Chem. Phys. 517, 30–35 (2019)

    Article  Google Scholar 

  64. A.N. Ikot, U.S. Okorie, G.J. Rampho, P.O. Amadi, C.O. Edet, I.O. Akpan, R. Horchani, Klein-Gordon equation and nonrelativistic thermodynamic properties with improved screened kratzer potential. J. Low Temp. Phys. 202(3), 269–289 (2021)

    Article  ADS  Google Scholar 

  65. B. Donfack, F. Fotio, A. Fotue, L.C. Fai, Cumulative effects of temperature, magnetic field and Spin orbit Interaction (SOI) on the properties of magnetopolaron in RbCl quantum well. Chinese J. Phys. 66, 573–579 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  66. A. Cetin, A quantum pseudodot system with a two-dimensional pseudoharmonic potential. Phys. Lett. A 372(21), 3852–3856 (2008)

    Article  ADS  MATH  Google Scholar 

  67. R. Khordad, Effect of pressure on spin–orbit interaction in a quantum wire with V-shaped cross section. Solid State Sci. 19, 63–68 (2013)

    Article  ADS  Google Scholar 

  68. D. Najafi, B. Vaseghi, G. Rezaei, R. Khordad, Thermodynamics of mono-layer quantum wires with spin-orbit interaction. Eur. Phys. J. Plus 133(8), 302 (2018)

    Article  Google Scholar 

  69. R. Khordad, B. Mirhosseini, Internal energy and entropy of a quantum pseudodot. Phys. B 420, 10–14 (2013)

    Article  ADS  Google Scholar 

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  1. Mesoscopic and Multilayers Structures Laboratory, Department of Physics, Faculty of Science, University of Dschang, P.O. Box 479, Dschang, Cameroon

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Donfack, B., Fotue, A.J. Effects of Spin Orbit Interaction (SOI) on the Thermodynamic Properties of a Quantum Pseudodot. J Low Temp Phys 204, 206–222 (2021). https://doi.org/10.1007/s10909-021-02604-9

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