Abstract
The physics of semiconductor quantum rings near the band edge is often well described considering decoupled bands. There are however instances where band coupling leads to relevant changes in the electronic structure and derived properties. In this chapter we analyze two such cases. First, we focus on the heavy hole-light hole band mixing in self-assembled InAs/GaAs quantum rings, which is important for current endeavour to develop quantum information science using the spin of holes. In InAs/GaAs quantum dots, the hole ground state is known to be mainly formed by the heavy hole subband. However, there is a finite spin-orbit coupling with the light-hole subband which is critical in determining the hole spin properties. Based on k\(\cdot \)p theory, in this chapter we study the influence of hole subband mixing in quantum rings. It is shown that the inner cavity of the ring enhances the light hole component of the ground state. As the quasi-1D limit is approached, the light-hole character becomes comparable to that of the heavy hole. Strain reduces the coupling, but it is still larger than in quantum dots. Second, we study the electronic structure of monolayer MoS\(_2\) quantum dots subject to a magnetic field. Here, the coupling between conduction and valence band gives rise to mid-gap topological states which localize near the dot edge. These edge states are analogous to those of 1D quantum rings. We show they present a large, Zeeman-like, linear splitting with the magnetic field, anticross with the delocalized Fock-Darwin-like states of the dot, give rise to Aharonov-Bohm-like oscillations of the conduction (valence) band low-lying states in the K (K\(^{\prime }\)) valley, and modify the strong-field Landau levels limit form of the energy spectrum.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In graphene systems one can associate an index to each of the inequivalent valleys. Then, the Chern number can be calculated as the sum of these indexes. It is found that while the individual Chern number per inequivalent valley does not vanish, the sum is zero, so that the system is topologically trivial. However, the non-vanishing valley index allows the system to sustain edge states. Such behavior is related to graphene’s marginal topological character. In a similar sense, MoS\(_2\) is marginal as well. The marginality implies that a small perturbation in the Hamiltonian (e.g. mass term) can have a big effect on the presence or absence of the gapless modes.
References
P.Y. Yu, M. Cardona, Fundamentals of Semiconductors (Springer, Berlin, 1999)
M. Dyakonov (ed.), Spin Physics in Semiconductors (Springer, Berlin, 2010)
R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, Berlin, 2003)
L. Jacak, P. Hawrylak, A. Wójs, Quantum Dots (Springer, Berlin, 1998)
D. Brunner, B.D. Gerardot, P.A. Dalgarno, G. Wüst, K. Karrai, N.G. Stoltz, P.M. Petroff, R.J. Warburton, Science 325, 70 (2009)
A. Greilich, S.G. Carter, D. Kim, A.S. Bracker, D. Gammon, Nat. Photonics 5, 702 (2011)
T.M. Godden, J.H. Quilter, A.J. Ramsay, Y. Wu, P. Brereton, S.J. Boyle, I.J. Luxmoore, J. Puebla-Nunez, A.M. Fox, M.S. Skolnick, Phys. Rev. Lett. 108, 017402 (2012)
K. De Greve, P.L. McMahon, D. Press, T.D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, Y. Yamamoto, Nat. Phys. 7, 827 (2011)
K. Müller, A. Bechtold, C. Ruppert, C. Hautmann, J.S. Wildmann, T. Kaldewey, M. Bichler, H.J. Krenner, G. Abstreiter, M. Betz, J.J. Finley, Phys. Rev. B 85, 241306(R) (2012)
E.A. Stinaff, M. Scheibner, A.S. Bracker, I.V. Ponomarev, V.L. Korenev, M.E. Ware, M.F. Doty, T.L. Reinecke, D. Gammon, Science 311, 636 (2006)
D. Heiss, S. Schaeck, H. Huebl, M. Bichler, G. Abstreiter, J.J. Finley, D.V. Bulaev, D. Loss, Phys. Rev. B 76, 241306(R) (2007)
B.D. Gerardot, D. Brunner, P.A. Dalgarno, P. Öhberg, S. Seidl, M. Kroner, K. Karrai, N.G. Stoltz, P.M. Petroff, R.J. Warburton, Nature 451, 441 (2008)
J. Fischer, W.A. Coish, D.V. Bulaev, D. Loss, Phys. Rev. B 78, 155329 (2008)
B. Eble, C. Testelin, P. Desfonds, F. Bernardot, A. Balocchi, T. Amand, A. Miard, A. Lemaitre, X. Marie, M. Chamarro, Phys. Rev. Lett. 102, 146601 (2009)
P. Fallahi, S.T. Yilmaz, A. Imamoglu, Phys. Rev. Lett. 105, 257402 (2010)
E.A. Chekhovich, A.B. Krysa, M.S. Skolnick, A.I. Tartakovskii, Phys. Rev. Lett. 106, 027402 (2011)
C.-Y. Lu, Y. Zhao, A.N. Vamivakas, C. Matthiesen, S. Fält, A. Badolato, M. Atatüre, Phys. Rev. B 81, 035332 (2010)
M.F. Doty, J.I. Climente, A. Greilich, M. Yakes, A.S. Bracker, D. Gammon, Phys. Rev. B 81, 035308 (2010)
J.H. Blokland, F.J.P. Wijnen, P.C.M. Christiansen, U. Zeitler, J.C. Maan, Phys. Rev. B 75, 23305 (2007)
J.I. Climente, J. Planelles, M. Pi, F. Malet, Phys. Rev. B 72, 233305 (2005)
W. Jaskólski, M. Zielinski, G.W. Bryant, Phys. Rev. B 74, 195339 (2006)
G. Bester, A. Zunger, Phys. Rev. B 72, 165334 (2005)
M.F. Doty, J.I. Climente, M. Korkusinski, M. Scheibner, A.S. Bracker, P. Hawrylak, D. Gammon, Phys. Rev. Lett. 102, 047401 (2009)
J.I. Climente, M. Korkusinski, G. Goldoni, P. Hawrylak, Phys. Rev. B 78, 115323 (2008)
T. Chwiej, B. Szafran, Phys. Rev. B 81, 075302 (2010)
A.I. Yakimov, A.A. Bloshkin, A.V. Dvurechenskii, Semicond. Sci. Technol. 24, 095002 (2009)
G. Katsaros, V.N. Golovach, P. Spathis, N. Ares, M. Stoffel, F. Fournel, O.G. Schmidt, L.I. Glazman, S. De Franceschi, Phys. Rev. Lett. 107, 246601 (2011)
F. Suarez, D. Granados, Dotor M. Luisa, J.M. Garcia, Nanotechnology 15, S126 (2004)
J. Wu, Z.M. Wang, V.G. Dorogan, S. Li, Z. Zhou, H. Li, J. Lee, E.S. Kim, Y.I. Mazur, G.J. Salamo, Appl. Phys. Lett. 101, 043904 (2012)
O. Tangmettajittakul, P. Boonpeng, P. Changmoung, S. Thainoi, S. Rattanathammaphan, S. Panyakeow, in Photovoltaics Specialists Conference 37th IEEE, vol. 002665 (2011)
Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)
A. Lorke, J. Luyken, A.O. Govorov, J.P. Kotthaus, Phys. Rev. Lett. 84, 2223 (2000)
M. Bayer, M. Korkusinski, P. Hawrylak, T. Gutbrod, M. Michel, A. Forchel, Phys. Rev. Lett. 90, 186801 (2003)
N.A.J.M. Kleemans, I.M.A. Bominaar-Silkens, V.M. Fomin, V.N. Gladilin, D. Granados, A.G. Taboada, J.M. Garcia, P. Offermans, U. Zeitler, Christianen, Maan J. C., Devreese J. T., Koenraad P. M. Phys. Rev. Lett. 99, 146808 (2007)
Ding F., Li B., Akopian N., Perinetti U., Chen Y. H., Peeters F. M., Rastelli A., Zwiller V., and Schmidt O. G., J. Nanoelectron. and Optoelectron. 6, 51 (2011); Ding F., Akopian N., Li B., Perinetti U., Govorov A., Peeters F. M., Bof Bufon C. C., Deneke C., Chen Y. H., Rastelli A., Schmidt O. G., and Zwiller V., Phys. Rev. B 82, 075309 (2010)
J.I. Climente, J. Planelles, W. Jaskolski, Phys. Rev. B 68, 075307 (2003)
L.G.G.V. Dias da Silva, S.E. Ulloa, A.O. Govorov, Phys. Rev. B 70, 155318 (2004)
V.M. Fomin, V.N. Gladilin, S.N. Klimin, J.T. Devreese, Phys. Rev. B 76, 235320 (2007)
N. Cukaric, M. Tadic, F.M. Peeters, Superlattice Microst. 48, 491 (2010)
A.O. Govorov, S.E. Ulloa, K. Karrai, R.J. Warburton, Phys. Rev. B 66, 081309(R) (2002)
B. Li, F.M. Peeters, Phys. Rev. B 83, 115448 (2011)
E. Waltersson, E. Lindroth, I. Pilskog, J.P. Hansen, Phys. Rev. B 79, 115318 (2009)
M. Szopa, E. Zipper, J. Phys.: Conf. Series 213, 012006 (2006)
C. Segarra, J.I. Climente, J. Planelles, J. Phys.: Condens. Matter 24, 115801 (2012)
J. Planelles, F. Rajadell, J.I. Climente, J. Phys. Chem. C 114, 8337 (2010)
J.I. Climente, J. Planelles, J. Nanoelectron. Optoelectron. 6, 81 (2011)
Burt M. G., J. Phys.: Condens. Matter 4, 6651 (1992); ibid. 11, R53 (1999)
B.A. Foreman, Phys. Rev. B 48, 4964 (1993)
P.C. Sercel, K.J. Vahala, Phys. Rev. B 42, 3690 (1990)
J.M. Luttinger, W. Kohn, Phys. Rev. 97, 869 (1955); J.M. Luttinger, ibid.102, 1030 (1956)
L. Voon, M. Willatzen, The k\(\cdot \)p Method: Electronic Properties of Semiconductors (Springer, Berlin, 2009)
F. Rajadell, M. Royo, J. Planelles, J. Appl. Phys. 111, 014303 (2012)
P. Offermans, P.M. Koenraad, J.H. Wolter, D. Granados, J.M. Garcia, Appl. Phys. Lett. 87, 131902 (2005)
I. Vurgaftman, J.R. Meyer, L.R. Ram-Mohan, J. Appl. Phys. 89, 5815 (2001)
M. Tadic, F.M. Peeters, K.L. Janssens, M. Korkusiński, P. Hawrylak, J. Appl. Phys. 92, 5819 (2002)
J.A. Barker, R.J. Warburton, E.P. O’Reilly, Phys. Rev. B 69, 035327 (2004)
R. Blossey, A. Lorke, Phys. Rev. E 65, 021603 (2002)
C. Pryor, Phys. Rev. B 57, 7190 (1998)
W. Sheng, J.P. Leburton, Phys. Stat. Sol. 237, 394 (2003)
M. Tadic, N. Cukaric, V. Asoski, F.M. Peeters, Phys. Rev. B 84, 125307 (2011)
C.Y.P. Chao, S.L. Chuang, Phys. Rev. B 46, 4110 (1992)
N.A.J.M. Kleemans, J.H. Blokland, A.G. Taboada, H.C.M. van Genuchten, M. Bozkurt, V.M. Fomin, V.N. Gladilin, D. Granados, M.J.C. Christianen, J.T. Devreese, P.M. Koenraad, Phys. Rev. B 80, 155318 (2009)
C. Pryor, Phys. Rev. Lett. 80, 3579 (1998)
S.E. Economou, J.I. Climente, A. Badolato, A.S. Bracker, D. Gammon, M.F. Doty, Phys. Rev. B 86, 085319 (2012)
T. Flissikowski, I.A. Akimov, A. Hundt, F. Henneberger, Phys. Rev. B 68, 0161309(R) (2003)
M. Koperski, M.R. Molas, A. Arora, K. Nogajewski, A.O. Slobodeniuk, C. Faugeras, M. Potemski, Nanophotonics 6, 1289 (2017)
M. Koperski, K. Nogajewski, A. Arora, V. Cherkez, P. Mallet, J.Y. Veuillen, J. Marcus, P. Kossacki, M. Potemski, Nat. Nanotechnol. 10, 503 (2015)
A. Srivastava, M. Slider, A.V. Allain, D.S. Lembke, A. Kis, A. Imamoglu, Nat. Nanotechnol. 10, 491 (2015)
Y.M. He, G. Clark, J.R. Schaibley, Y. He, M.C. Chen, Y.J. Wei, X. Ding, Q. Zhang, W. Yao, X. Xu, Nat. Nanotechnol. 10, 497 (2015)
C. Chakraborty, L. Kinnischtzke, K.M. Goodfellow, R. Beams, A.N. Vamivakas, Nat. Nanotechnol. 10, 507 (2015)
P. Tonndorf, R. Schmidt, R. Schneider, J. Kern, M. Buscema, G.A. Steele, A. Castellanos-Gomez, H.S.J. van der Zant, S.M. de Vasconcellos, R. Bratschitsch, Optical 2, 347 (2015)
S. Kumar, A. Kaczmarczyk, B.D. Gerardot, Nano Lett. 15, 7567 (2015)
A. Branny, G. Wang, S. Kumar, C. Robert, B. Lassagne, X. Marie, B.D. Gerardot, B. Urbaszek, Appl. Phys. Lett. 108, 142101 (2016)
G. Wei, D.A. Czaplewski, E.J. Lenferink, T.K. Stanev, I.W. Jung, N.P. Stern, Sci. Rep. 7, 3324 (2017)
L. Lin, Y. Xu, S. Zhang, I.M. Ross, A.C. Ong, D.A. Allwood, ACS Nano 7, 8214 (2013)
T.T. Tran, K. Bray, M.J. Ford, M. Toth, I. Aharonovich, Nat. Natotechnol. 11, 37 (2016)
S. Tongay, J. Suh, C. Ataca, W. Fan, A. Luce, J.S. Kang, J. Liu, C. Ko, R. Raghunathanan, J. Zhou, F. Ogletree, J. Li, J.C. Grossman, J. Wu, Sci. Rep. 3, 2657 (2013)
W. Zhou, X. Zou, S. Najmaei, Z. Liu, Y. Shi, J. Kong, J. Lou, P.M. Ajayan, B.I. Yakobson, J.C. Idrobo, Nano Lett. 13, 2615 (2013)
A. Kormanyós, V. Zóyomi, N.D. Drummond, G. Burkard, Phys. Rev. X 4, 011034 (2014)
M. Brooks, G. Burkard, Phys. Rev. B 95, 245411 (2017)
A.C. Dias, J. Fu, L. Villegas-Lelovsky, F. Qu, J. Phys.: Condens. Matter 28, 375803 (2016)
F. Qu, A.C. Dias, J. Fu, L. Villegas-Lelovsky, D.L. Azevedo, Sci. Rep. 7, 41044 (2017)
M.V. Bollinger, J.V. Lauritsen, K.W. Jacobsen, J.K. Norskov, S. Helveg, F. Besenbacher, Phys. Rev. Lett. 87, 196803 (2001)
H. Pan, Y.W. Zhang, J. Mater. Chem. 22, 7280 (2012)
E. Erdogan, I.H. Popov, A.N. Enyashin, G. Seifert, Eur. Phys. J. B 85, 33 (2012)
S. Pavlovic, F.M. Peeters, Phys. Rev. B 91, 155410 (2015)
D. Davelou, G. Kopidakis, G. Kioseoglou, I.N. Remediakis, Solid State Commun. 192, 42 (2014)
C.G. Peterfalvi, A. Kormanyos, G. Burkard, Phys. Rev. B 92, 245443 (2015)
C. Segarra, J. Planelles, S.E. Ulloa, Phys. Rev. B 93, 085312 (2016)
A. Kormanyos, G. Burkard, M. Gmitra, J. Fabian, V. Z’olyomi, N.D. Drummond and V. Fal’ko, 2D Mater. 2, 022001 (2015)
E. Ridolfi, L.R.F. Lima, E.R. Mucciolo, C.H. Lewenkopf, Phys. Rev. B 95, 035430 (2017)
A. Kormanyos, V. Z’olyomi, N.D. Drummond, P. Rakyta, G. Burkard, V.I. Fal’ko, Phys. Rev. B 88, 045416 (2013)
Acknowledgements
Support from MINECO project CTQ2017-83781-P and UJI project B2017-59 is acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Segarra, C., Planelles, J., Climente, J.I. (2018). Band Mixing Effects in InAs/GaAs Quantum Rings and in MoS\(_2\) Quantum Dots Ring-Like Behaving. In: Fomin, V. (eds) Physics of Quantum Rings. NanoScience and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-95159-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-95159-1_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-95158-4
Online ISBN: 978-3-319-95159-1
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)