Abstract.
We present a theoretical study of the energy spectrum of single electron and hole states in quantum dots of annular geometry under a high magnetic field along the ring axis in the frame of uncorrelated electron-hole theory. We predict the periodic disappearance of the optical emission of the electron-hole pair as the magnetic field increases, as a consequence of the finite height of the barriers. The model has been applied to semiconductor rings of various internal and external radii, giving as limiting cases the disk and antidot.
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References
Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)
L. Lévy, G. Dolan, J. Duinsmuir, H. Bouchiat, Phys. Rev. Lett. 64, 2074 (1990)
D. Mailly, C. Chapelier, A. Benoit, Phys. Rev. Lett. 70, 2020 (1991)
A. Fuhrer, S. Lüscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, M. Bichler, Nature 413, 822 (2001)
M. Büttiker, Y. Imry, R. Landauer, Phys. Lett. A 96, 365 (1983)
N. Byers, C.N. Yang, Phys. Rev. Lett. 7, 46 (1961)
Y. Gefen, Y. Imry, M.Ya. Azbel, Phys. Rev. Lett. 52, 129 (1984)
V. Halonen, T. Chakraborty, P. Pietiläinen, Phys. Rev. B 45, 5980 (1992)
A.V. Chaplik, JETP Lett. 62, 900 (1995)
R.A. Römer, M.E. Raikh, Phys. Rev. B 62, 7045 (2000)
M. Bayer, M. Korkusinski, P. Hawrylak, T. Gutbrod, M. Michel, A. Forchel, Phys. Rev. Lett. 90, 186801 (2003)
E. Ribeiro, A.O. Govorov, W. Carvalho, G. Medeiros-Ribeiro, Phys. Rev. Lett. 92, 126402 (2004)
C. Shulhauser, R.J. Warburton, A. Högele, A.O. Govorov, K. Karrai, J.M. Garcia, B.D. Gerardot, P.M. Petroff, Physica E 21, 184 (2004)
A. Lorke, R.G. Luyken, A.O. Govorov, J.P. Kotthaus, J.M. Garcia, P.M. Petroff, Phys. Rev. Lett. 84, 2223 (2000)
A.V. Kalameitsev, V.M. Kovalev, A.O. Govorov, JETP Lett. 68, 669 (1998)
A.O. Govorov, S.E. Ulloa, K. Karrai, R.J. Warburton, Phys. Rev. B 66, 081309 (2002)
S.E. Ulloa, A.O. Govorov, A.V. Kalameitsev, R.J. Warburton, K. Karrai, Physica E 12, 790 (2002)
A.O. Govorov, A.V. Kalameitsev, R.J. Warburton, K. Karrai, S.E. Ulloa, Physica E 13, 297 (2002)
J. Song, S.E. Ulloa, Phys. Rev. B 63, 125302 (2001)
H. Hu, J.L. Zhu, D.J. Li, J.J. Xiong, Phys. Rev. B 63, 195307 (2001)
F. Palmero, J. Dorgnac, J.C. Eilbeck, R.A. Römer, Phys. Rev. B 72, 075343 (2005)
Y. Aharonov, A. Casher, Phys. Rev. Lett. 53, 319 (1984)
A.A. Zvyagin, JETP 76, 167 (1993)
A.A. Zvyagin, T.V. Bandos, JETP 82, 135 (1996)
A.V. Maslov, D.S. Citrin, Phys. Rev. B 67, 121304 (2003)
L.G.G. V. Dias da Silva, S.E. Ulloa, T.V. Shahbazyan, Phys. Rev. B 72, 125327 (2005)
Z. Barticevic, M. Pacheco, J. Simonin, C.R. Proetto, Phys. Rev. B 73, 165311 (2006)
K.L. Janssens, B. Partoens, F.M. Peeters, Phys. Rev. B 64, 155324 (2001)
K.L. Janssens, B. Partoens, F.M. Peeters, Phys. Rev. B 66, 075314 (2002)
D. Haft, C. Shulhauster, A.O. Govorov, R.J. Warburton, K. Karrai, J.M. Garcia, W. Schoenfeld, P.M. Petroff, Physica E 13, 165 (2002)
A. Rastrelli, S. Stufler, R. Songmuang, C. Manzano, G. Costantini, K. Kern, A. Zrenner, D. Bimberg, O.G.Schmidt, Phys. Rev. Lett. 92, 166104 (2004)
Y. Sidor, B. Partoens, F.M. Peeters, N. Shildermans, M. Hayne, V.V. Moshchalkov, A. Rastrelli, O.G. Schmidt, Phys. Rev. B 73, 155334 (2006)
K. Maschke, T. Meier, P. Thomas, S.W. Koch, Eur. Phys. J. B 19, 599 (2001)
W.C. Tan, J.C. Inkson, Phys. Rev. B 53, 6947 (1995)
V. Fock, Z. Phys. 47, 446 (1928)
L. Landau, E. Lifschitz, Quantum mechanics (Mir, Moscow, 1996)
M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, Natl. Bur. Stand. Appl. Math. Ser. No. 55, (U.S. GPO, Washington, D.C.,1970)
K. Nishibayashi, T. Okuno, Y. Masumoto, H.-W. Ren, Phys. Rev. B 68, 035333 (2003)
M. Robnik, J. Phys. A. 19, 3619 (1986)
A. Müller, H.A. Weidenmüller, C.H. Lewenkopf, Europhys. Lett. 22, 193 (1993)
T. Chakraborty, P. Pietiläinen, Phys. Rev. B 50, 8460 (1994)
R.A. Römer, A. Punnoose, Phys. Rev. B 52, 14809 (1995)
A.A. Zvyagin, I.V. Krive, Sov. J. Low Temp. 21, 533 (1995)
B.I. Halperin, Phys. Rev. B 25, 2185 (1981)
C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum mechanics, (Wiley, New York, 1977)
C.S. Lent, Phys. Rev. B 43, 4179 (1991)
A. Groshev, I.Z. Kostadinov, I. Dobrianov, Phys. Rev. B 45, 6279 (1992)
R. Courant, D. Hilbert, Methods of Mathematical Physics, (Interscience Publications, John Wiley and Sons, New York, USA, 1953)
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Bandos, T., Cantarero, A. & García-Cristóbal, A. Finite size effects on the optical transitions in quantum rings under a magnetic field. Eur. Phys. J. B 53, 99–108 (2006). https://doi.org/10.1140/epjb/e2006-00351-2
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DOI: https://doi.org/10.1140/epjb/e2006-00351-2