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Remarks on Thermodynamic Properties of a Double Ring-Shaped Quantum Dot at Low and High Temperatures

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Abstract

In a recent paper published in this Journal, Khordad and Sedehi (J Low Temp Phys 190(3):200, 2018) have studied the thermodynamic properties of a GaAs double ring-shaped quantum dot under external magnetic and electric fields. In that meritorious research the energy of the system was obtained by solving the Schrödinger equation. The radial equation was mapped into a confluent hypergeometric differential equation and the differential equation associated to z coordinate was mapped into a biconfluent Heun differential equation. In this paper, it is pointed out a misleading treatment on the solution of the biconfluent Heun equation. It is shown that the energy \(E_{z}\) can not be labeled with \(n_{z}\) and this fact jeopardizes the results of this system. We calculate the partition function with the correct energy spectrum and recalculate the specific heat and entropy as a function of low and high temperatures.

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Acknowledgements

The authors are indebted to the anonymous referee for an excellent and constructive review. L. B. Castro would like to thank Professor Dr. Antonio S. de Castro for useful comments and suggestions. This work was supported in part by means of funds provided by CNPq, Brazil, Grant No. 307932/2017-6 (PQ) and No. 422755/2018-4 (UNIVERSAL), São Paulo Research Foundation (FAPESP), Grant No. 2018/20577-4, FAPEMA, Brazil, Grant No. UNIVERSAL-01220/18 and CAPES, Brazil. Angel E. Obispo thanks to CNPq (grant 312838/2016-6) and Secti/FAPEMA (grant FAPEMA DCR-02853/16), for financial support.

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Authors and Affiliations

  1. Departamento de Física, Universidade Estadual Paulista (UNESP), Campus de Guaratinguetá, Guaratinguetá, SP, 12516-410, Brazil

    Luis B. Castro

  2. Departamento de Física, Universidade Federal do Maranhão, Campus Universitário do Bacanga, São Luís, MA, 65080-805, Brazil

    Andrés G. Jirón Vicente, Luis B. Castro, Angel E. Obispo & Luis E. Arroyo Meza

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  1. Andrés G. Jirón Vicente
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  2. Luis B. Castro
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  3. Angel E. Obispo
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  4. Luis E. Arroyo Meza
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Correspondence to Luis B. Castro.

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Vicente, A.G.J., Castro, L.B., Obispo, A.E. et al. Remarks on Thermodynamic Properties of a Double Ring-Shaped Quantum Dot at Low and High Temperatures. J Low Temp Phys 202, 372–381 (2021). https://doi.org/10.1007/s10909-020-02550-y

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