The heat capacity of a semiconductor quantum dot in magnetic fields
https://doi.org/10.17586/2220-8054-2019-10-5-530-535
Abstract
The heat capacity of two interacting electrons confined in a quantum dot presented in a magnetic field has been calculated by solving the Hamiltonian using the exact diagonalization method. The statistical average energies for confined and interacting electrons have been computed for various values of magnetic fields, confining frequency and temperature. We had investigated the dependence of the heat capacity on quantum dot Hamiltonian’s parameters and temperature. The singlettriplet transitions in the ground state of the quantum dot spectra and the corresponding jumps in the heat capacity curves had been shown. The comparisons show that our results are in very good agreement with theoretical reported works.
About the Authors
A. Shaer
Physics Department, Faculty of Science, An-Najah National University
Palestinian Territory, Occupied
Palestinian Territory, Occupied
Ayham Shaer
Nablus, West Bank
M. K. Elsaid
Physics Department, Faculty of Science, An-Najah National University
Palestinian Territory, Occupied
Palestinian Territory, Occupied
Mohammad K. Elsaid
Nablus, West Bank
E. Hjaz
Physics Department, Faculty of Science, An-Najah National University
Palestinian Territory, Occupied
Palestinian Territory, Occupied
Eshtiaq Hjaz
Nablus, West Bank
References
1. Ashoori R.C., Stormer H.L., Weiner J.S., Pfeiffer L.N., Baldwin K.W., West K.W. N-electron ground state energies of a quantum dot in magnetic field. Physical review letters, 1993, 71(4), P. 613–616.
2. Ciftja O. Understanding electronic systems in semiconductor quantum dots. Physica Scripta, 2013, 88(5), P. 058302.
3. Kastner M.A. The single-electron transistor. Reviews of modern physics, 1992, 64(3), P. 849–858.
4. Loss D., DiVincenzo D.P. Quantum computation with quantum dots. Physical Review A, 1998, 57(1), P. 120–126.
5. Burkard G., Loss D. and DiVincenzo D.P. Coupled quantum dots as quantum gates. Physical Review B, 1999, 59(3), P. 2070–2078.
6. Maksym P.A. and Chakraborty T. Quantum dots in a magnetic field: Role of electron-electron interactions. Physical Review Letters, 1990, 65(1), P. 108–111.
7. Wagner M., Merkt U. and Chaplik A.V. Spin-singlet–spin-triplet oscillations in quantum dots. Physical Review B, 1992, 45(4), P. 1951–1954.
8. Taut M. Two electrons in a homogeneous magnetic field: particular analytical solutions. Journal of Physics A: Mathematical and General, 1994, 27(3), P. 1045–1055.
9. Ciftja O. and Kumar A.A. Ground state of two-dimensional quantum-dot helium in zero magnetic field: Perturbation, diagonalization, and variational theory. Physical Review B, 2004, 70(20), P. 205326.
10. Ciftja O. and Faruk M.G. Two-dimensional quantum-dot helium in a magnetic field: Variational theory. Physical Review B, 2005, 72(20), P. 205334.
11. Kandemir B.S. Variational study of two-electron quantum dots. Physical Review B, 2005, 72(16), P. 165350.
12. El-Said M. Spectroscopic structure of two interacting electrons in a quantum dot by the shifted 1/N expansion method. Physical Review B, 2000, 61(19), P. 13026–13031.
13. De Groote J.J.S., Hornos J.E.M. and Chaplik A.V. Thermodynamic properties of quantum dots in a magnetic field. Physical Review B, 1992, 46(19), P. 12773–12776.
14. Nguyen N.T. and Peeters F.M. Magnetic field dependence of the many-electron states in a magnetic quantum dot: The ferromagneticantiferromagnetic transition. Physical Review B, 2008, 78(4), P. 045321.
15. Boyacioglu B. and Chatterjee A. Heat capacity and entropy of a GaAs quantum dot with Gaussian confinement. Journal of applied physics, 2012, 112(4), P. 083514.
16. Helle M., Harju A. and Nieminen, R.M. Two-electron lateral quantum-dot molecules in a magnetic field. Physical Review B, 2005, 72(20), P. 205329.
17. Nguyen N.T. and Sarma S.D. Impurity effects on semiconductor quantum bits in coupled quantum dots. Physical Review B,2011, 83(23), P. 235322.
18. DybalskiW. and Hawrylak P. Two electrons in a strongly coupled double quantum dot: From an artificial helium atom to a hydrogen molecule. Physical Review B, 2005, 72(20), P. 205432.
19. Mikhailov S.A. Quantum-dot lithium in zero magnetic field: Electronic properties, thermodynamics, and Fermi liquid–Wigner solid crossover in the ground state. Physical Review B, 2002, 65(7), P. 115312.
20. Müller, H.M. and Koonin, S.E. Phase transitions in quantum dots. Physical Review B, 1996, 54(20), P. 14532.
21. Sharma H.K., Boda A., Boyacioglu B. and Chatterjee A. Electronic and magnetic properties of a two-electron Gaussian GaAs quantum dot with spin-Zeeman term: A study by numerical diagonalization. Journal of Magnetism and Magnetic Materials, 2019, 469, P. 171–177.
22. Shaer A., Elsaid M.K. and Elhasan M. Variational calculations of the heat capacity of a semiconductor quantum dot in magnetic fields. Chinese journal of physics, 2016, 54(3), P. 391–397.
23. Al Shorman M.M., Nammas F.S., Haddad H. and Shukri A.A. Heat capacity and entropy of two electrons quantum dot in a magnetic field with parabolic interaction. Chinese journal of physics 2018, 56(3), P. 1057–1063.
24. Nammas F.S. Thermodynamic properties of two electrons quantum dot with harmonic interaction. Physica A: Statistical Mechanics and its Applications, 2018, 508, P. 187–198.
25. Shaer A., Elsaid M.K. and Elhasan M. Magnetization of GaAs parabolic quantum dot by variation method. J. Phys. Sci. Appl 2016, 6(2), P. 39–46.
Review
For citations:
Shaer A., Elsaid M.K., Hjaz E. The heat capacity of a semiconductor quantum dot in magnetic fields. Nanosystems: Physics, Chemistry, Mathematics. 2019;10(5):530-535. https://doi.org/10.17586/2220-8054-2019-10-5-530-535
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