Estudio de las propiedades electrónicas, ópticas y termodinámicas de anillos cuánticos en forma de diamante bajo la presencia de campos externos
Ilustraciones
- Autores:
-
Rios Álvarez, Santiago
- Tipo de recurso:
- Fecha de publicación:
- 2022
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/86672
- Palabra clave:
- 530 - Física
530 - Física::539 - Física moderna
Fisica cuantica
Teoria cuantica
Optica cuantica
Operador de Schrodinger
Anillos cuánticos
Anillos acoplados
Impureza donadora
Complejo molecular
Susceptibilidad eléctrica
Respuesta óptica
Efecto Aharanov-Bohm
Efecto Stark
Propiedades térmicas
Anti-crossing
Quantum rings
Donor impurity
Molecular complex
Electric susceptibility
Optical response
Aharanov-Bohm effect
Stark effect
Thermal properties
- Rights
- openAccess
- License
- Atribución-NoComercial-CompartirIgual 4.0 Internacional
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| dc.title.eng.fl_str_mv |
Estudio de las propiedades electrónicas, ópticas y termodinámicas de anillos cuánticos en forma de diamante bajo la presencia de campos externos |
| dc.title.translated.eng.fl_str_mv |
Study of electronic, optical and thermal properties of diamond-shaped quantum rings under the presence of external fields |
| title |
Estudio de las propiedades electrónicas, ópticas y termodinámicas de anillos cuánticos en forma de diamante bajo la presencia de campos externos |
| spellingShingle |
Estudio de las propiedades electrónicas, ópticas y termodinámicas de anillos cuánticos en forma de diamante bajo la presencia de campos externos 530 - Física 530 - Física::539 - Física moderna Fisica cuantica Teoria cuantica Optica cuantica Operador de Schrodinger Anillos cuánticos Anillos acoplados Impureza donadora Complejo molecular Susceptibilidad eléctrica Respuesta óptica Efecto Aharanov-Bohm Efecto Stark Propiedades térmicas Anti-crossing Quantum rings Donor impurity Molecular complex Electric susceptibility Optical response Aharanov-Bohm effect Stark effect Thermal properties |
| title_short |
Estudio de las propiedades electrónicas, ópticas y termodinámicas de anillos cuánticos en forma de diamante bajo la presencia de campos externos |
| title_full |
Estudio de las propiedades electrónicas, ópticas y termodinámicas de anillos cuánticos en forma de diamante bajo la presencia de campos externos |
| title_fullStr |
Estudio de las propiedades electrónicas, ópticas y termodinámicas de anillos cuánticos en forma de diamante bajo la presencia de campos externos |
| title_full_unstemmed |
Estudio de las propiedades electrónicas, ópticas y termodinámicas de anillos cuánticos en forma de diamante bajo la presencia de campos externos |
| title_sort |
Estudio de las propiedades electrónicas, ópticas y termodinámicas de anillos cuánticos en forma de diamante bajo la presencia de campos externos |
| dc.creator.fl_str_mv |
Rios Álvarez, Santiago |
| dc.contributor.advisor.none.fl_str_mv |
Marín-Cadavid, Jairo Humberto Suaza-Tabares, Yoder Alberto |
| dc.contributor.author.none.fl_str_mv |
Rios Álvarez, Santiago |
| dc.contributor.researchgroup.spa.fl_str_mv |
Materiales Cerámicos y Vítreos |
| dc.contributor.orcid.spa.fl_str_mv |
Ríos-Álvarez, Santiago [0000000303751961] |
| dc.subject.ddc.spa.fl_str_mv |
530 - Física 530 - Física::539 - Física moderna |
| topic |
530 - Física 530 - Física::539 - Física moderna Fisica cuantica Teoria cuantica Optica cuantica Operador de Schrodinger Anillos cuánticos Anillos acoplados Impureza donadora Complejo molecular Susceptibilidad eléctrica Respuesta óptica Efecto Aharanov-Bohm Efecto Stark Propiedades térmicas Anti-crossing Quantum rings Donor impurity Molecular complex Electric susceptibility Optical response Aharanov-Bohm effect Stark effect Thermal properties |
| dc.subject.lemb.none.fl_str_mv |
Fisica cuantica Teoria cuantica Optica cuantica Operador de Schrodinger |
| dc.subject.proposal.spa.fl_str_mv |
Anillos cuánticos Anillos acoplados Impureza donadora Complejo molecular Susceptibilidad eléctrica Respuesta óptica Efecto Aharanov-Bohm Efecto Stark Propiedades térmicas Anti-crossing |
| dc.subject.proposal.eng.fl_str_mv |
Quantum rings Donor impurity Molecular complex Electric susceptibility Optical response Aharanov-Bohm effect Stark effect Thermal properties |
| description |
Ilustraciones |
| publishDate |
2022 |
| dc.date.issued.none.fl_str_mv |
2022-03-11 |
| dc.date.accessioned.none.fl_str_mv |
2024-07-31T21:32:54Z |
| dc.date.available.none.fl_str_mv |
2024-07-31T21:32:54Z |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/masterThesis |
| dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
| dc.type.content.spa.fl_str_mv |
Text |
| dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TM |
| status_str |
acceptedVersion |
| dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/86672 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Nacional de Colombia |
| dc.identifier.reponame.spa.fl_str_mv |
Repositorio Institucional Universidad Nacional de Colombia |
| dc.identifier.repourl.spa.fl_str_mv |
https://repositorio.unal.edu.co/ |
| url |
https://repositorio.unal.edu.co/handle/unal/86672 https://repositorio.unal.edu.co/ |
| identifier_str_mv |
Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.relation.references.spa.fl_str_mv |
Acosta, R. E. ; Morales, A. L. ; Duque, C. M. ; Mora-Ramos, M. E. ; Duque, C. A.: Optical absorption and refractive index changes in a semiconductor quantum ring: Electric eld and donor impurity e ects. In: Phys. Status Solidi B, n °4 254 (2016), S. 744-754 Aharonov, Y. ; Bohm, D.: Signi cance of Electromagnetic Potentials in the Quantum Theory. In: Phys. Rev., n °3 115 (1959), S. 485-491 Baghdasaryan, D. A. ; Hayrapetyan, D. B. ; Kazaryan, E. M. ; Sarkisyan, H. A.: Thermal and magnetic properties of electron gas in toroidal quantum dot. In: Physica E. 101 (2018), S. 1{-4 Banyai, L. ; Koch, S. W.: Semiconductor Quantum dots. Singapore : World Scienti c, 1993 Bayer, M. ; Korkusinski, M. ; Hawrylak, P. ; Gutbrod, T. ; Michel, M. ; Forchel, A.: Optical Detection of the Aharonov-Bohm Effect on a Charged Particle in a Nanoscale Quantum Ring. In: Physical Review Letters 90 (2003), S. 18{21 Bejan, D. ; Stan, C. ; Niculescu, E. C.: Optical properties of an elliptic quantum ring: Eccentricity and electric fi eld effects. In: Optical Materials 381 (2018), S. 207-219 Bejan, D. ; Stan, C.: Aharonov-Bohm effect in pseudo-elliptic quantum rings: influence of geometry, eccentricity and electric field. In: The European Physical Journal Plus 134 (2019) Bimberg, D. ; Pohl, U. W.: Quantum dots: promises and accomplish. In: Mater. Today, n°9 14 (2006), S. 388-397 Boyacioglu, A. B. et C. B. et Chatterjee: Heat capacity and entropy of a GaAs quantum dot with Gaussian con finement. In: J. Appl. Phys. 112, 083514 (2012), S. 1-6 Boyd, R. W. ; Gaeta, A. L. ; Giese, E.: Nonlinear Optics. Wiley, 2007 Dahan, P. ; Malits, P.: E ect of symmetry on the electronic properties of arbitrarily shaped quantum rings in a magnetic field. In: Physica E. 56 (2014), S. 165-171 Duque, C. M. ; Morales, A. L. ; Mora-Ramos, M. E. ; Duque, C. A.: Optical nonlinearities associated to applied electric fields in parabolic two-dimensional quantum rings. In: J. Lumin. 143 (2013), S. 81-88 Esaki, L. ; Tsu, R.: Superlattice and Negative Differential Conductivity in Semiconductors. (1970), S. 61-65 Fomin, V.: Physics of Quantum Dots. 2018 Fuhrer, A. ; Luscher, S. ; Ihn, T. ; Heinzel, T. ; Ensslin, K. ; Wegscheider, W. ; Bichler, M.: Energy spectra of quantum rings. In: Nature 413 (2001), S. 822-825 García, J. M. ; Medeiros-Ribeiro, G. ; Schmidt, K. ; Ngo, T. ; Feng, J. L. ; Lorke, A. ; Kotthaus, J. ; Petroff, P. M.: Intermixing and shape changes during the formation of InAs self-assembled quantum dots. In: Appl. Phys. Lett. 71 (1997), S. 2014-2016 Grynberg, G. ; Aspect, A. ; Fabre, C.: Introduction to Quantum Optics. Cambridge, 2010 Gumber, S. ; Kumar, M. ; Gambhir, M. ; Mohan, M. ; Kumar-Jha, P.: Thermal and magnetic properties of cylindrical quantum dot with asymmetric con nement. In: Can. J. Phys. 93 (2015), S. 1264{1268 Harrison, P. ; Valavanis, A.: Quantum Wells, Wires and Dots. Leeds : Wiley, 2016 Hernández, N. ; López, R. ; Álvarez, J. A. ; Marín, J.H. ; Fulla, M. R. ; Tobón, H.: Optical absorption computation of a D+2 arti cial molecule in GaAs/Ga1-xAlxAs nanometer-scale rings. In: Optik 245 (2021), S. 1-4 Huang, S. ; Niu, Z. ; Fang, Z. ; Ni, H. ; Zheng, G. ; Xia, J.: Complex quantum ring structures formed by droplet epitaxy. In: Appl. Phys. Lett., n 389(2006); S;89-91 Huang, S. ; Niu, Z. C. ; Xia, J.: Self-Assembled GaAs Quantum Rings by MBE Droplet Epitaxy. In: Solid State Phenom., n 3 121-123 (2007), S. 541-544 Jacak, L. ; W., Hawrylak A.: Quantum Dots. 2013 Jewell, J. L. ; Lee, Y. H. ; Warren, M. ; Gibbs, H. M. ; Peyghambarian, N. ; Gossard, A. C. ; Wiegmann, W.: 82 - MHz optical logic gates in a room temperature GaAs/AlGaAs multiple quantum well etalon. In: Appl. Phys. Lett, n °10 46 (1985), S. 918-920 Karabulut, I. ; Baskoutas, S.: Linear and nonlinear optical absorption coe cients and refractive index changes in spherical quantum dots: Effects of impurities, electric field, size, and optical intensity. In: J. Appl. Phys. 103, 073512 (2008), S. 1-5 Khordad, R. ; Rastegar Sedehi, H. R.: Thermodynamic Properties of a Double Ring-Shaped Quantum Dot at Low and High Temperatures. In: Journal of Low Tem- perature Physics 190 (2018), S. 200-212 Kirak, M.: Magnetic and thermodynamic properties of GaAs quantum dot confi ned by parabolic-inverse square plus gaussian potential. In: Journal of Magnetism and Magnetic Materials 536 (2021), S. 1-10 Kiravittaya, S. ; Rastelli, A. ; Schmidt, O. G.: Advanced quantum dot con figurations. In: Rep. Prog. Phys. 72 (2009), S. 1-34 Lafaurie-Ponce, L. G. ; Suaza, Y. A. ; Pérez, J. A. ; Ávila, A. ; Rincón, M. ; Marín, J. H.: Thermal Properties of a Hydrogen Molecular Ion in Quantum Rings Under Electric and Intense Laser Fields. In: SSRN 1 (2021) Lampert, M. A.: Mobile and Immobile Effective-Mass-Particle Complexes in Nonmetallic Solids. In: Phys. Rev. Lett., n 12 1 (1958), S. 450{453 Lee, C. M. ; Li, J. Q. ; Ruan, W. Y. ; Lee, R. C. H.: Optical spectra and intensities of a magnetic quantum ring bound to an off-center neutral donor D0. In: Physical Review B. 73 (2006), S. 212407- 212411 Liang, S. ; W., Xie ; Shen, H.: Optical properties in a two-dimensional quantum ring: Con nement potential and Aharonov Bohm effect. In: Optics Communications 284 (2011), S. 5818-5828 Lima, R. P. A. ; M., Amado: Electronic states of on- and off-center donors in quantum rings of nite width. In: J. Lumin., n° 5-6 128 (2021), S. 858-861 Lorke, A. ; Johannes-Luyken, R. ; Govorov, A. O. ; Kotthaus, J. P. ; Garcia, J. M. ; Petroff, P. M.: Spectroscopy of Nanoscopic Semiconductor Rings. In: Phys. Rev. Lett., n°10 84 (2000), S. 2223-2226 Lucjan, J. ; Pawel, H. ; Arkadiusz, W.: Quantum Dots. 2014 Michler, P.: Single Semiconductor Quantum Dots. 2009 Nasri, D.: On the eccentricity effects on the intraband optical transitions in two dimensional quantum rings with and without donor impurity. In: Phys. B Condens. Matter 540 (2021), S. 51-57 Patrick Tung, K. H. ; Huang, J. ; Danner, A.: Periodic Two-Dimensional GaAs and InGaAs Quantum Rings Grown on GaAs (001) by Droplet Epitaxy. In: Journal of Nanoscience and Nanotechnology 16(6) (2016), S. 6465-6469 Radhouene, M. ; Najjara, M. ; Kumar-Chhipa, M. ; Robinsond, S. ; Suthar, B.: Novel design of ring resonator based temperature sensor using photonics technology. In: Journal of Applied Physics, n°103 7 (2017), S. 311-1316 Radhouene, M. ; Najjara, M. ; Kumar-Chhipa, M. ; Robinsond, S. ; Suthar, B.: Design and analysis a thermo-optic switch based on photonic crystal ring resonator. In: Optik 172 (2018), S. 924-929 Radu, A. ; Kirakosyan, A. A. ; Laroze, D. ; Baghramyan, H. M. ; Barseghyan, M. G.: Electronic and intraband optical properties of single quantum rings under intense laser field radiation. In: Appl. Phys. 116 (2014) Radu, A. ; Kirakosyan, A. A. ; Laroze, D. ; Barseghyan, M. G.: The effects of the intense laser and homogeneous electric fields on the electronic and intraband optical properties of a GaAs/Ga0.7Al0.3As quantum ring. In: Semicond. Sci. Technol. 30 (2015) Rahmatullaha ; Abbas, M. ; Ziauddin ; Qamar, S.: Spatially structured transparency and transfer of optical vortices via four-wave mixing in a quantum-dot nanostructure. In: Physical Review A. 023821 101 (2020), S. 1-8 Salazar-Santa, J. D. ; Fonnegra-García, D. ; Marín, J. H.: Entropy and electronic properties of an off-axis hydrogen-like impurity in non-uniform height quantum ribbon with structural and geometrical azimuthal potential barriers. In: Opt. Quantum Electron, n°4 53 (2021), S. 176 Salazar-Santa, J. D. ; Fonnegra-García, D. ; Marín, J. H.: Entropy and electronic properties of an off-axis hydrogen-like impurity in non-uniform height quantum ribbon with structural and geometrical azimuthal potential barriers. In: Opt. Quant. Electron. 53 (2021), S. 176 Salinas, S. R. A.: Introduction to Statistical Physics. Springer, 2007 Shuai, K. ; Yi-Ming, L ; Ting-Yun, S.: H+2 Like impurities con ned by spherical quantum dots: a candidate for charge qubits. In: Commun Theor. Phys, n°3 50 (2008), S. 767-770 Vinasco, J. A. ; Radu, A. ; Kasapoglu, E. ; Restrepo, R. L. ; Morales, A. L. ; Feddi, E. ; Mora-Ramos, M. E. ; Duque, C. A.: Effects of Geometry on the Electronic Properties of Semiconductor Elliptical Quantum Rings. In: Sci. Rep. 8 (2018), S. 13299 Wang, Z. M.: Self-Assembled Quantum Dots. 2008 Wood, T. H. ; Burrus, C. A. ; Miller, D. A. B. ; Chemia, D. S. ; Damen, T. C. ; Gossard, A. C. ; Wiegmann, W.: High - speed optical modulation with GaAs/GaAlAs quantum wells in a p-diode structure. In: Appl. Phys. Lett, n 11 44 (1984), S. 16-18 Wu, X. ; S., Gray ; Pelton, M.: Quantum-dot-induced transparency in a nanoscale plasmonic resonator. In: Optics Express, n°23 18 (2010), S. 23633-23645 Xie, W.: Effect of an electric eld on the nonlinear optical recti cation of a quantum ring. In: Phys. B Condens. Ma 443 (2014), S. 60-62 Yun, K. ; Sheng, W. ; Li-Xianli, J.: Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field. In: Semicond. 36 (2015), S. 032003 |
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Universidad Nacional de Colombia |
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Medellín - Ciencias - Maestría en Ciencias - Física |
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Facultad de Ciencias |
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Medellín, Colombia |
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Universidad Nacional de Colombia - Sede Medellín |
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Atribución-NoComercial-CompartirIgual 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Marín-Cadavid, Jairo Humbertoe39ce6b53fb59ca137ea0668b5e5f1c0Suaza-Tabares, Yoder Albertoe1ca88e77c0c039103a8170b98502ff4Rios Álvarez, Santiago0527c3ce0c4eebc94d4314995a72ed22Materiales Cerámicos y VítreosRíos-Álvarez, Santiago [0000000303751961]2024-07-31T21:32:54Z2024-07-31T21:32:54Z2022-03-11https://repositorio.unal.edu.co/handle/unal/86672Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/IlustracionesIn the present thesis, a exhaustive analysis of the electronic, optical and thermal properties of diamond-shaped semiconductor quantum rings with elliptical crater was performed by varying both the morphology and the external elds to which the systems are exposed. First, an electron con ned in a GaAs/Ga0.7Al0.3As quantum ring was considered, whose shape resembles quantum dots obtained by various growth techniques. The Lamé curve was used to represent the outer contour of the quantum ring in a more realistic way. Topological parameters associated with the size of the ring, the proportions of the crater and the shape of the contour were assigned. To carry out this study, a Schrödinger equation was proposed to show the interaction with external elds and geometrical con nement, being able to observe phenomena such as the Stark effect, the Aharonov-Bohm effect and the formation of anticrossing points. The Hamiltonian approach is based on the effective mass approximation, and then resorts to nite element computational methods to solve the differential equation. The analysis performed from the variations and parametric sweeps in both morphologies and external elds were taken to different situations, such as the topological analysis as an alternative to predict the properties of the quantum ring, the behavior of the nanostructure when it con nes an atomic system with a donor impurity, the manipulation of the thermal properties from the conformation of a statistical assembly with the electronic states and the optical responses of the proposed systems due to fluctuations in the probability densities caused by the topological and external eld variations.En la presente tesis se realizó un análisis exhaustivo de las propiedades electrónicas, ópticas y térmicas de anillos cuánticos semiconductores con forma de diamante y con cráter elíptico, variando tanto la morfología como los campos externos a los que se exponen los sistemas. En primer lugar, se consideró un electrón confi nado en un anillo cuántico de GaAs/Ga0.7Al0.3As, cuya forma se asemeja a los puntos cuánticos obtenidos mediante diversas técnicas de crecimiento. Se utilizó la curva de Lamé para representar el contorno externo del anillo cuántico de una forma más realista. Se asignaron parámetros topológicos asociados con el tamaño del anillo, las proporciones del cráter y la forma del contorno. Para llevar a cabo dicho estudio, se planteó una ecuación de Schrödinger que dé muestra de la interacción con campos externos y con el con namiento geométrico, pudiendo observar fenómenos como el efecto Stark, el efecto Aharonov-Bohm y la formaci on de puntos de anti-crossing. El planteamiento del Hamiltoniano se fundamenta en la aproximación de masa efectiva, para luego recurrir a métodos computacionales por elementos finitos para resolver la ecuación diferencial. El análisis realizado a partir de las variaciones y los barridos param etricos tanto en las morfologías como en los campos externos se llevaron a distintas situaciones, como el análisis topológico como alternativa para predecir las propiedades del anillo cuántico, el comportamiento de la nanoestructura cuando con na un sistema atómico con una impureza donadora, la manipulación de las propiedades térmicas a partir de la conformación de un ensamble estadístico con los estados electrónicos y las respuestas ópticas de los sistemas propuestos a raíz de las fluctuaciones en las densidades de probabilidad provocadas por las variaciones topológicas y de campos externos.MaestríaMagíster en Ciencias - FísicaSistemas de baja dimensionalidadÁrea Curricular en Física108 páginasapplication/pdfengUniversidad Nacional de ColombiaMedellín - Ciencias - Maestría en Ciencias - FísicaFacultad de CienciasMedellín, ColombiaUniversidad Nacional de Colombia - Sede Medellín530 - Física530 - Física::539 - Física modernaFisica cuanticaTeoria cuanticaOptica cuanticaOperador de SchrodingerAnillos cuánticosAnillos acopladosImpureza donadoraComplejo molecularSusceptibilidad eléctricaRespuesta ópticaEfecto Aharanov-BohmEfecto StarkPropiedades térmicasAnti-crossingQuantum ringsDonor impurityMolecular complexElectric susceptibilityOptical responseAharanov-Bohm effectStark effectThermal propertiesEstudio de las propiedades electrónicas, ópticas y termodinámicas de anillos cuánticos en forma de diamante bajo la presencia de campos externosStudy of electronic, optical and thermal properties of diamond-shaped quantum rings under the presence of external fieldsTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAcosta, R. E. ; Morales, A. L. ; Duque, C. M. ; Mora-Ramos, M. E. ; Duque, C. A.: Optical absorption and refractive index changes in a semiconductor quantum ring: Electric eld and donor impurity e ects. In: Phys. Status Solidi B, n °4 254 (2016), S. 744-754Aharonov, Y. ; Bohm, D.: Signi cance of Electromagnetic Potentials in the Quantum Theory. In: Phys. Rev., n °3 115 (1959), S. 485-491Baghdasaryan, D. A. ; Hayrapetyan, D. B. ; Kazaryan, E. M. ; Sarkisyan, H. A.: Thermal and magnetic properties of electron gas in toroidal quantum dot. In: Physica E. 101 (2018), S. 1{-4Banyai, L. ; Koch, S. W.: Semiconductor Quantum dots. Singapore : World Scienti c, 1993Bayer, M. ; Korkusinski, M. ; Hawrylak, P. ; Gutbrod, T. ; Michel, M. ; Forchel, A.: Optical Detection of the Aharonov-Bohm Effect on a Charged Particle in a Nanoscale Quantum Ring. In: Physical Review Letters 90 (2003), S. 18{21Bejan, D. ; Stan, C. ; Niculescu, E. C.: Optical properties of an elliptic quantum ring: Eccentricity and electric fi eld effects. In: Optical Materials 381 (2018), S. 207-219Bejan, D. ; Stan, C.: Aharonov-Bohm effect in pseudo-elliptic quantum rings: influence of geometry, eccentricity and electric field. In: The European Physical Journal Plus 134 (2019)Bimberg, D. ; Pohl, U. W.: Quantum dots: promises and accomplish. In: Mater. Today, n°9 14 (2006), S. 388-397Boyacioglu, A. B. et C. B. et Chatterjee: Heat capacity and entropy of a GaAs quantum dot with Gaussian con finement. In: J. Appl. Phys. 112, 083514 (2012), S. 1-6Boyd, R. W. ; Gaeta, A. L. ; Giese, E.: Nonlinear Optics. Wiley, 2007Dahan, P. ; Malits, P.: E ect of symmetry on the electronic properties of arbitrarily shaped quantum rings in a magnetic field. In: Physica E. 56 (2014), S. 165-171Duque, C. M. ; Morales, A. L. ; Mora-Ramos, M. E. ; Duque, C. A.: Optical nonlinearities associated to applied electric fields in parabolic two-dimensional quantum rings. 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