Ávalos Morales, Roberto E. (2019) Efectos de la interacción de intercambio en una cinta hall / Effects of exchange interaction in a hall bar. Maestría en Ciencias Físicas, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En este trabajo se han estudiado los efectos de la interacción electrónica de Hartree y de intercambio en gases bidimensionales de electrones (2DEG), en el régimen del efecto Hall cuántico entero (IQHE). La particularidad del trabajo es que se consideraron sistemas semiconductores de GaAs=AlᵪGa1 _ ᵪAs con bordes en la geometría de la cinta Hall. Para estos sistemas y con un campo magnético aplicado en la dirección de confinamiento, se estudiaron los efectos de la interacción de Hartree y de intercambio en el régimen del IQHE. Para el estudio de los 2DEGs se consideró la aproximación de Thomas-Fermi (TF) como una primera aproximación a un cálculo más elaborado empleando la teoría de la funcional densidad (DFT). Usando la aproximación TF y la interacción de Hartree se calculó numéricamente los factores de llenado ѵ para sistemas con la geometría de cinta Hall. Los resultados mostraron regiones de la cinta donde el factor de llenado ѵ es constante, estas regiones espaciales son denominadas plateaus. Con estas consideraciones los plateaus aparecen solamente para valores de ѵ pares, esto se debe a que solamente se consideró la interacción de Hartree y se supuso una ocupación degenerada por el espín. En la realidad el IQHE causa que aparezcan plateaus para todos los valores enteros en el factor de llenado, pares e impares. La originalidad de este trabajo está en considerar la interacción de intercambio y aplicarla en la aproximación TF dependiente del espín. En particular se consideró la aproximación de densidad local de espín (LSDA) para el potencial de intercambio. Con estas consideraciones se obtuvieron plateaus también para factores de llenado ѵ impares, además de que se discutió la relación entre la formación de los plateaus impares y la interacción de intercambio desde una perspectiva física. Se exploró la relevancia del campo magnético, la temperatura y el ancho de la cinta Hall en el comportamiento que tiene el factor de llenado del sistema, discutiendo además en que regímenes se manifiesta el IQHE.
Resumen en inglés
In this work we have studied the effects of Hartree’s electronic and exchange interaction in two-dimensional electron gases (2DEG), in the regime of the integer quantum Hall effect (IQHE). The particularity of the work is that we considered semiconductor systems of GaAs=AlᵪGa1_ ᵪAs with borders in a Hall bar geometry. For these systems and with a magnetic field applied in the confinement direction, the effects of the Hartree and the exchange interaction in the IQHE regime were studied. For the study of the 2DEGs the Thomas-Fermi (TF) approximation was considered as a first approach to a more elaborated calculation employing the density functional theory (DFT). Using the TF approximation and Hartree interaction, the filling factors ѵ were calculated numerically for systems with Hall bar geometry. The results showed regions of the bar where the filling factor ѵ is constant, these spatial regions are called plateaus.With these considerations plateaus only appeared for even values of ѵ, this is because only Hartree’s interaction was considered and we assumed a degenerated spin occupation. In reality the IQHE causes plateaus to appear for all integer values in the filling factor, even and odds. The originality of this work is that we considered the exchange interaction and applied it in the spin dependent TF approximation. In particular, the spin local density approximation (LSDA) was considered for the exchange potential. With these considerations, plateaus were also obtained for odd filling factors ѵ, also the relation between odd plateaus formation and exchange interaction was discussed from a physical perspective. It was explored the relevance of magnetic field, temperature and width of the Hall bar in the behaviour that the filling factor of the system has, further discussing in which regimes the IQHE manifests.
| Tipo de objeto: | Tesis (Maestría en Ciencias Físicas) |
|---|---|
| Palabras Clave: | Hall effect; Efecto hall; [Exchange; Intercambio; Landau levels; Niveles de Landau; Quantum hall effect; Efecto hall cuántico] |
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| Materias: | Física > Materia condensada |
| Divisiones: | Gcia. de área de Investigación y aplicaciones no nucleares > Gcia. de Física > Materia condensada > Bajas temperaturas |
| Código ID: | 884 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 19 Abr 2021 12:40 |
| Última Modificación: | 19 Abr 2021 12:40 |
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