Energy Spectra Of Exciton States In Disk-shaped Gaas-ga 1-xal Xas Quantum Dots Under Growth-direction Magnetic Fields

A theoretical study, within the effective-mass approximation, of the effects of applied magnetic fields on excitons in disk-shaped GaAs-Ga 1-xAl xAs quantum dots is presented. Magnetic fields are applied in the growth direction of the semiconductor heterostructure. The parity of the excitonic envelope function related to the simultaneous exchange of z e→-z e and z h→-z h is a good quantum number and the wave function, both the odd and even parity, can be expanded as combination of products of the quantum well electron and hole function that preserves the parity with appropriate Gaussian functions. We have simultaneously obtained the energies of the excitonic ground and excited states and discuss the behavior of these energies as a function of the magnetic field. © EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007.564303309M. Pacheco, Z. Barticevic, F. Claro, J. Phys.: Condens. Matter 5, A363 (1993)Z. Barticevic, M. Pacheco, F. Claro, Phys. Rev. B 51, 14414 (1995);Pacheco, M., Barticevic, Z., (2001) Phys. Rev. B, 64, p. 033406Janssens, K.L., Peeters, F.M., Schweigert, V.A., (2001) Phys. Rev. B, 63, p. 205311Barticevic, Z., Pacheco, M., Dnque, C.A., Oliveira, L.E., (2002) J. Phys.: Condens. Matter, 14, p. 1021Itskevich, I.E., Lyapin, S.G., Troyan, I.A., Klipstein, P.C., Eaves, L., Main, P.C., Henini, M., (1998) Phys. Rev. B, 58, pp. R4250Itskevich, I.E., Skolnick, M.S., Mowbray, D.J., Troyan, I.A., Lyapin, S.G., Wilson, L.R., Steer, M.J., Main, P.C., (1999) Phys. Rev. B, 60, pp. R2185Ma, B.S., Wang, X.D., Su, F.H., Fang, Z.L., Ding, K., Niu, Z.C., Li, G.H., (2004) J. Appl. Phys, 95, p. 933Duque, C.A., Porras-Montenegro, N., Barticevic, Z., Pacheco, M., Oliveira, L.E., (2005) Microelectr. J, 36, p. 231Pacheco, M., Barticevic, Z., (1997) Phys. Rev. B, 55, p. 10688Stier, O., Grundmann, M., Bimberg, D., (1999) Phys. Rev. B, 59, p. 5688Williamson, A.J., Wang, L.W., Zunger, A., (2000) Phys. Rev. B, 62, p. 12963Austing, D.G., Sasaki, S., Tarucha, S., Reimann, S.M., Koskinen, M., Manninen, M., (1999) Physica B, 272, p. 68Hirose, K., Wingreen, N.S., (1999) Phys. Rev. B, 59, p. 4604Wojs, A., Hawrylak, P., Fafard, S., Jacak, L., (1996) Phys. Rev. B, 54, p. 5604Rodríguez, A.H., Trallero-Giner, C., Ulloa, S.E., MarínAntuña, J., (2001) Phys. Rev. B, 63, p. 125319Song, J., Ulloa, S.E., (1995) Phys. Rev. B, 52, p. 9015Xie, W., (2000) Physica B, 279, p. 253Nötzel, R., Jahn, U., Niu, Z., Trampert, A., Fricke, J., Schönherr, H.-P., Kurth, T., Ploog, K.H., (1998) Appl. Phys. Lett, 72, p. 2002Bayer, M., Walck, S.N., Reinecke, T.L., Forchel, A., (1998) Phys. Rev. B, 57, p. 6584Xie, W., (2005) Physica B, 358, p. 109Wang, G., Guo, K., (2005) Physica E, 28, p. 14Demel, T., Heitmann, D., Grambow, P., Ploog, K., (1990) Phys. Rev. Lett, 64, p. 788M. Pacheco, Z. Barticevic, J. Phys.: Gondens. Matter 11, 1079 (1999)Barticevic, Z., Pacheco, M., Duque, C.A., Oliveira, L.E., (2003) Phys. Rev. B, 68, p. 073312Kuther, A., Bayer, M., Forchel, A., Gorbunov, A., Timofeev, V.B., Schäfer, F., Reithmaier, J.P., (1998) Phys. Rev. B, 58, pp. R7508Braskén, M., Lindberg, M., Sundholm, D., Olsen, J., (2000) Phys. Rev. B, 61, p. 7652Lorke, A., Kotthaus, J.P., Ploog, K., (1990) Phys. Rev. Lett, 64, p. 2559Palacios, J.J., Hawrylak, P., (1995) Phys. Rev. B, 51, p. 1769Partoens, B., Peeters, F.M., (2000) Phys. Rev. Lett, 84, p. 4433Wang, W., Mendez, E.E., Stern, F., (1984) Appl. Phys. Lett, 45, p. 639Li, E.H., (2000) Physica E, 5, p. 215Cohen-Tannoudji, G., Diu, B., Laloë, F., (1977) Quantum Mechanics, Complement, pp. D-VI. , Hermann and John Wiley and Sons, ParisThe absence of the inversion symmetry in the z-potential does not produced fundamental changes in the obtained results. In this case, if the Coulomb interaction is not considered, there are also electron-hole wave functions formed by different states of independent particles (of course these states will not have definite parity) and subbands associated to each, h pairs with different quantum numbers in z. The exciton energies as a function of the magnitude of an in-plane magnetic field will show anticrossings between subbands levels due to the electron-hole couplingFox, A.M., Miller, D.A.B., Livescu, G., Cunningham, J.E., Jan, W.Y., (1991) Phys. Rev. B, 44, p. 6231Alexandrou, A., Mendez, E.E., Hong, J.M., (1991) Phys. Rev, 44, p. 1934Rastelli, A., Stufler, S., Schliwa, A., Songmuang, R., Manzano, C., Constantini, G., Kern, K., Schmidt, O.G., (2004) Phys. Rev. Lett, 92, p. 166104Schildermans, N., Hayne, M., Moshchalkov, V.V., Rastelli, A., Schmidt, O.G., (2005) Phys. Rev. B, 72, p. 115312Y. Sidor, B. Partoens, F.M. Peeters, N. Schildermans, M. Hayne, V.V. Moshchalkov, A. R.astelli, O.G. Schmidt, Phys. Rev. B 73, 155334 (2006