Energy states and exchange energy of coupled double quantum dot in a magnetic field

Document Type : Reasearch Paper


Department of Physics, An-Najah National University, Nablus,West Bank, Jordan


The ground state energies of two interacting electrons confined in a coupled double quantum dot (DQD) presented in a magnetic field has been calculated by solving the relative Hamiltonian using variational and exact diagonalization methods. The singlet-triplet transitions in the angular momentum and spin of the quantum dot ground state had been shown .We have studied the magnetic field versus confining frequency and magnetic field versus potential barrier height phase diagram of DQD .Furthermore, we have investigated the dependence of the exchange energy of two electron double quantum dot on the confining frequency, potential height barrier, barrier width and magnetic field strength. The comparisons show that our results are in very good agreement with reported works.


Main Subjects

[1] Ashoori R. C., Stormer H. L., Weiner J. S., Pfeiffer L. N., Baldwin K. W., West K. W., (1993), N-electron ground state energies of a quantum dot in a magnetic field. Phys. Rev. Let. 71: 613-616.
[2] Ciftja C., (2013), Understanding electronic systems in semiconductor quantum dots. Physica Scripta. 72: 058302-058306.
[3] Kastner M. A., (1992), The single electron transistor. Rev. Mod. Phys. 64: 849-858.
[4] Burkard G., Loss D., Divincenzo D. P, (1999), Coupled quantum dot as a quantum gate. Phys. Rev. B. 59: 2070-2078.
[5] Wagner M., Merkt M. U., Chaplik A. V., (1992), Spin-singlet-triplet oscillations in quantum dots. Phys. Rev. B. 45: 1951-1954.
[6] Taut M., J. Phys., (1994), Two electrons in a homogeneous magnetic field: Particular analytic solution. J. Phys: Math. Gen. 27: 1045-1055.
[7] Ciftja C., Kumar A. A., (2004), Gound-state of two-dimensional quantum dot helium in zero magnetic fields. Phys. Rev. B. 70: 205326-205331.
[8] Ciftja O., Golam Faruk M., (2005), Two-dimensional quantum-dot helium in a magnetic field: Variational theory.  Phys. Rev. B. 72: 205334-205339.
[9] Kandemir B. S., (2005), Variational study of two-electron quantum dots. Phys. Rev. B. 72: 165350-165355.
[10] Elsaid M., (2000), Spectroscopic structure of two interacting electrons in a quantum dot by 1/N expansion method. Phys. Rev. B. 61: 13026-13030.
[11] Elsaid M., Al-Nafa M. A., Zugail S. J., (2008), Spin singlet-triplet splitting in the ground state of a quantum dot with magnetic fields: Effects of dimensionality. J. Comput. Theor. Nanosci. 5: 677-680.
[12] Maksym P. A., Chakraborty T., (1990), Quantum dots in a magnetic field: Role of electron-electron interactions. Phys. Rev. Lett. 65: 108-111.
[13] De Groote J. J. S., Hornos J. E. M., Chaplik A. V., (1992), Thermodynamic properties of quantum dots in a magnetic field. Phys. Rev. B. 46: 12773-12776.
[14] Nguyen N. T. T., Peeters F. M., (2008), Magnetic field dependence of many electron states in a magnetic quantum dot: The ferromagnetic-antiferromagnetic transition.  Phys. Rev. B. 78: 045321-045326.
[15] Nammas F. S, Sandouqa A. S; Ghassib H. B., Al Sugheir M. K., (2011), Thermodynamic properties of two-dimensional of few-electrons quantum dot using the static fluctuation approximation (SFA). Physica B. 406: 4671-4677.
[16] Boyacioglu B., Chatterjee A., (2012), Heat capacity and entropy of a GaAs quantum dot with a Gaussian confinement. J. Appl. Phys. 112: 083514-083518.
[17] Helle M., Harju A., Nieminen R. M., (2005), Two-electron quantum dot molecule in a magnetic field. Phys. Rev. B. 72: 205329-205336.
[18] Räsänen E., Saarikoski H., Stavrou V. N., Harju A., Puska M. J., Nieminen R. M., (2003), Electronic structure of quantum dots. Phys. Rev. B. 67: 235307-23511.
[19] Schwarz M. P., Grundler D., Wilde M., Heyn Ch., Heitmann D., (2002), Magnetization of semiconductor quantum dot. J. Appl. Phys. 91: 6875-6877.
[20] Dybalski W., Hawrylak P., (2005), Two electrons in a strongly coupled double quantum dots: From an artificial helium atom to hydrogen molecule. Phys. Rev. B. 72: 205432-205436.
[21] Abdollahi M., Telebian Darzi M. A., Hosein Kani H., Raghbani Rizi H., (2012), The effect of first order magnetic field in a GaAs/AlGaAs spherical quantum dot with hydrogenic impurity. Int. J. Nano. Dimens. 3: 149-154.
[22] Kyriakidis J., Pioro-Ladiere M., Ciorga M., Sachrajda A. S., Hawrylak P., (2002), Voltage-tunable singlet-triplet transitions in lateral quantum dots. Phys. Rev. B. 66: 035320-035320.
[23] Climente J. I., Planelles J., Movilla J. L., (2004), Magnetization of nanoscopic quantum ring and quantum dot. Phys Rev. B. 70: 081301-081306.
[24] Avetisyan S., Chakraborty T., Pietiläinen P., (2016), Magnetization of interacting electrons in anisotropic quantum dots with Rashba spin-orbit interaction. Physica E. 81: 334-338.
[25] Nguyen N. T. T., Das Sarma S., (2011), Impurity effects of semiconductor quantum bits in coupled quantum dots. Phys. Rev. B. 83: 235322-235326.
[26] Rachid N., Ben Salem E., Jaziri S., Bennaceu R., (2009), Magnetization for the spin-orbit strength evaluation in laterally coupled double quantm dots. Physica E. 41: 568-573.