Magnetic Field Effects on Electron Eigenstates in a Concentric Triple Quantum Ring

Abstract:

In this paper, the electronic eigenstates and energy spectra of a two-dimensional system formed by three concentric, coupled, semiconductor quantum rings with a perpendicular magnetic field in the presence and the absence of a single ionized hydrogenic donor impurity are studied. It is found that the magnetic field localizes the electron wave function in the inner rings. The effects of hydrogenic donor on the electronic structure of concentric triple quantum rings are investigated in the both on- and off-center configurations. It is shown that as the donor moves away from the center of the system, the ground state energy decreases monotonically, the degeneracy is lifted and the gap between the energy levels increases. Also, the binding energy of donor impurity increases with increasing magnetic field.

• Periodical: Journal of Nano Research (Volume 10)
• Pages: 121-130
• DOI: https://doi.org/10.4028/www.scientific.net/JNanoR.10.121
• Online since: April 2010
• Authors: Hojjatollah K. Salehani, Mahdi Esmaeilzadeh, Khosrow Shakouri
• Keywords: Concentric Triple Quantum Ring, Nanostructure, Quantum Confinement, Semiconductor

References

[1] S. Tarucha, D. G. Austing, and T. Honda, R. J. van der Hage and L. P. Kouwenhoven, Spontaneous symmetry breaking in single and molecular quantum dots, Phys. Rev. Lett. 77 (1996) 5325-5328.

DOI: 10.1103/physrevlett.77.3613

[2] S. M. Reimann and M. Manninen, Electronic structure of quantum dots, Rev. Mod. Phys. 74 (2002) 1283-1342.

DOI: 10.1103/revmodphys.74.1283

[3] Y. Aharonov, D. Bohm, Significance of electromagnetic potentials in quantum theory, Phys. Rev. 115 (1959) 485-491.

DOI: 10.1103/physrev.115.485

[4] R.A. Webb, S. Washburn, C.P. Umbach, R.B. Laibowitz, Observation of h/e Aharonov-Bohm oscillations in normal-metal rings, Phys. Rev. Lett. 54 (1985) 2696-2699.

DOI: 10.1103/physrevlett.54.2696

[5] G. Timp, A.M. Chang, J.E. Cunningham, T.Y. Chang, P. Mankiewich, R. Behringer, R.E. Howard, Observation of the Aharonov-Bohm effect for 1c , Phys. Rev. Lett, 58 (1987) 2814-2817.

DOI: 10.1103/physrevlett.58.2814

[6] S. Pedersen, A.E. Hansen, A. Kristensen, C.B. SHdersen P.E. Lindelof, Observation of quantum asymmetry in an Aharonov-Bohm ring, Phys. Rev. B 61 (2000) 5457-5460.

DOI: 10.1103/physrevb.61.5457

[7] M. Pi, A. Emperador, M. Barranco, F. Garcias, K. Muraki, S. Tarucha and D. G. Austing, Dissociation of Vertical Semiconductor Diatomic Artificial Molecules, Phys Rev. Lett, 87 (2001) 066801-4.

DOI: 10.1103/physrevlett.87.066801

[8] M. Marlo, A. Harju, and R.M. Nieminen, Role of interactions in the far-infrared spectrum of a lateral quantum-dot molecule, Phys. Rev. Lett. 91 (2003) 187401-4.

DOI: 10.1103/physrevlett.91.187401

[9] S. Viefers, P. Koskinen, P.S. Deo and M. Manninen, Quantum rings for beginners: energy spectra and persistent currents, Physica E 21 (2004) 1-35.

DOI: 10.1016/j.physe.2003.08.076

[10] B.C. Lee, O. Voskoboynikov and C.P. Lee, III-V semiconductor nano-rings, Physica E 24 (2004) 87-91.

[11] I. Neder, M. Heiblum, Y. Levinson, D. Mahalu and V. Umansky, Unexpected Behavior in a Two-Path Electron Interferometer, Phys. Rev. Lett. 96 (2006) 016804-4.

DOI: 10.1103/physrevlett.96.016804

[12] T. Chwiej and B. Szafran, Few-electron artificial molecules formed by laterally coupled quantum rings, Phys Rev. B 78 (2008) 245306-17.

DOI: 10.1103/physrevb.78.245306

[13] T. Kuroda, T. Mano, T. Ochiai, S. Sanguinetti, K. Sakoda, G. Kido, and N. Koguchi, Optical transitions in quantum ring complexes, PhysRev. B. 72 (2005) 205301-8.

DOI: 10.1103/physrevb.72.205301

[14] T. Mano, T. Kuroda, S. Sanguinetti, T. Ochiai, T. Tateno, J. Kim, T. Noda, M. Kawabe, K. Sakoda, G. Kido, and N. Koguchi, Self-assembly of concentric quantum double rings, Nano Lett. 5 (2005) 425-428.

DOI: 10.1021/nl048192+

[15] A. Fuhrer, S. Lüscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegschneider, and M. Bichler, Energy spectra of quantum rings, Nature 413 (2001) 822-825.

DOI: 10.1038/35101552

[16] U. F. Keyser, C. Fu¨hner, S. Borck, R. J. Haug, M. Bichler, G. Abstreiter, W. Wegscheider, Kondo effect in a few-electron quantum ring, Phys. Rev. Lett. 90 (2003) 196601-4.

DOI: 10.1103/physrevlett.90.196601

[17] G. Fuster, M. Pacheco, and Z. Barticevic, Electronic Properties of Coupled Quantum Rings in the Presence of a Magnetic Field, Brazilian Journal of Physics 34(2B) (2004) 666-668.

DOI: 10.1590/s0103-97332004000400037

[18] B. Szafran, and F. M. Peeters, Few-electron eigenstates of concentric double quantum rings, Phys Rev. B 72 (2005) 155316-9.

DOI: 10.1103/physrevb.72.155316

[19] J. Planelles, and J.I. Climente, Semiconductor concentric double rings in a magnetic field, Eur. Phys. J. B 48 (2005) 65-70.

DOI: 10.1140/epjb/e2005-00384-y

[20] J. I. Climente, J. Planelles, M. Barranco, F. Malet, and M. Pi, Electronic structure of fewelectron concentric double quantum rings, Phys Rev. B 73 (2006) 235327-6.

DOI: 10.1103/physrevb.73.235327

[21] F.J. Culchac, N. Porras-Montenegro, J.C. Granada, A. Latge, Energy spectrum in a concentric double quantum ring of GaAs-(Ga, Al)As under applied magnetic fields, Microelectronics Journal 39 (2008) 402-406.

DOI: 10.1016/j.mejo.2007.07.063

[22] J.I. Climente and J. Planelles, Far-infrared absorption of vertically coupled self-assembled quantum rings, Phys. Rev. B 72 (2005) 155322-5.

DOI: 10.1103/physrevb.72.155322

[23] F. Malet, M. Barranco, E. Lipparini, R. Mayol, and M. Pi, Vertically coupled double quantum rings at zero magnetic field, Phys. Rev. B 73 (2006) 245324-7.

DOI: 10.1103/physrevb.73.245324

[24] J. Planelles, F. Rajadell, J.I. Climente, M. Royo and J.L. Movilla, Electronic states of laterally coupled quantum rings, Journal of Physics, Conference Series 61 (2007) 936-941.

DOI: 10.1088/1742-6596/61/1/186

[25] C. M. Lee, J. Q. Li, W. Y. Ruan, and R. C. H. Lee, Energy spectra of a magnetic quantum ring with an off-center Impurity, Commun. Theor. Phys. 45 (2006) 737-740.

DOI: 10.1088/0253-6102/45/4/032

[26] C. M. Lee, J. Q. Li, W. Y. Ruan, and R. C. H. Lee, Optical spectra and intensities of a magnetic quantum ring bound to an off-center neutral donor D0, Phys Rev. B 73 (2006) 212407.

DOI: 10.1103/physrevb.73.219902

[27] G. Wang and P. Zhang, Hydrogenic impurity binding energy in self-assembled GaAs/Ga 1−x AlxAs quantum rings, Appl Phys Lett. 103 (2008) 063713-6.

DOI: 10.1063/1.2887994

[28] M. Amado, R. P. A. Lima, C. G. Santander and F. D. Adame, Donor-bound electrons in quantum rings under magnetic fields, Phys Rev. B 76 (2007) 073312-4.

DOI: 10.1103/physrevb.76.073312

[29] R. P.A. Lima, M. Amado, Electronic states of on- and off-center donors in quantum rings of finite width, Journal of Luminescence 128 (2008) 858-861.

DOI: 10.1016/j.jlumin.2007.11.022

[30] G.Y. Chen, Y.N. Chen, D.S. Chuu, The Aharonov-Bohm effect in concentric quantum double rings, Solid State Communications 143 (2007) 515-518.

DOI: 10.1016/j.ssc.2007.07.020

[31] C. Somaschini, S. Bietti, S. Sanguinetti and N. Koguchi, Fabrication of GaAs Concentric Multiple Quantum Rings by Droplet Epitaxy, E-MRS 2009 Spring Meeting, Strasbourg, France, June 8 - 12, (2009).

DOI: 10.1088/1757-899x/6/1/012008

[32] W.C. Tan and J.C. Inkson, Electron states in a two-dimensional ring-an exactly soluble model, Semicond. Sci. Technol. 11 (1996) 1635-1641.

DOI: 10.1088/0268-1242/11/11/001

[33] W.E. Arnoldi, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quart. J. Applied Mathematics 9 (1951) 17-29.

DOI: 10.1090/qam/42792

[34] Y. Saad, Numerical Methods for large ScaleEigenvalue Problems, Halsted Press, New York, (1992).

[35] R.B. Morgan, On restarting the Arnoldi method for large nonsymmetric eigenvalue problems, Math. Comput, Math. Comp. 65 (1996) 1213-1230.

DOI: 10.1090/s0025-5718-96-00745-4