Miravet Martínez, Daniel (2019) Efectos de la interacción electrón-electrón y campos magnéticos en gases bidimensionales de electrones. / Effect of electron-electron interaction and magnetic fields in two dimensional electron gas. Tesis Doctoral en Física, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En este trabajo hemos estudiado los efectos de la interacción electrón-electrón y campos magnéticos en gases cuasi-bidimensionales de electrones (q2DEGs). Para estos sistemas, con un campo magnético aplicado en la dirección de cuantización, se estudiaron los efectos de las interacciones electrónicas en el régimen del efecto Hall cuántico entero. En una primera etapa, se usó la aproximación de Hartree-Fock variacional para estudiar los posibles cruces de niveles de Landau en un sistema de tres láminas semiconductoras acopladas. A partir de este estudio se determinó en que situaciones los niveles de Landau se ¨anti-cruzan¨ (estados ¨easy-axis¨) o se mezclan (estados ¨easy-plane¨), al coincidir sus energías con el potencial químico μ. Se demuestra que este comportamiento es una consecuencia de la competencia entre las interacciones de Hartree e intercambio. Para el estudio de los q2DEGs dentro del marco de la teoría de funcional densidad (DFT), se desarrolló el formalismo de intercambio exacto para estos sistemas con campo magnético aplicado. Se obtuvo un funcional para la energía de intercambio que se minimiza de manera no analítica en los valores enteros del factor de llenado ν. Se encontró una solución analítica para el potencial de intercambio exacto en el régimen de una subbanda ocupada. Este potencial presenta discontinuidades en los valores entero de ν, que pueden ser inducidas incluso a densidad constante, variando el campo magnético. Estos funcionales de intercambio exacto presentan notables diferencias con los correspondientes en la aproximación de densidad local. Por último, dentro de la DFT, utilizando el esquema de Kohn-Sham (KS) y respuesta lineal se calculó la resistividad longitudinal ρxx para dos sistemas de interés desde el punto de vista experimental. Se evidenció en los cálculos la importancia de las interacciones, principalmente en las regiones donde se cruzan varios niveles de Landau. Los resultados obtenidos son bastante cercanos a los experimentos
Resumen en inglés
In this work we have studied the effects of electron-electron interaction and magnetic fields in quasi-two-dimensional electron gases (q2DEGs). For these systems with an applied perpendicular magnetic field, the effects of electronic interactions on the integer quantum Hall effect regime were studied. In a first stage, a variational Hartree-Fock approximation was used to study the possible crossings of Landau levels in a system of three coupled semiconductor layers. We has determined in which situations the Landau levels present a "anti-crossing" behavior (easy-axis states) or they are mixed (easy-plane states), when their energies coincide with the chemical potential μ. It is shown that this behavior is a consequence of the competition between Hartree and exchange interactions. For the study of q2DEGs within the framework of the density functional theory (DFT), the exact exchange formalism was developed for these systems with an applied magnetic field. A functional for the exchange energy was obtained that is minimized non-analytically at the integer values of the filling factor ν. We found an analytical solution for the exact exchange potential in the one occupied subband regime. This potential has discontinuities at the integer values of ν, which can be induced even at constant density, varying the magnetic field. These exact exchange functionals show notable differences with the corresponding ones in the local density approximation. Finally, within the DFT framework, using the Kohn-Sham (KS) scheme and linear response, the longitudinal resistivity ρxx was calculated for two systems of interest from the experimental point of view. The importance of interactions was evidenced in the calculations, mainly in the regions where several Landau levels cross. The results obtained are quite close to the experiments.
| Tipo de objeto: | Tesis (Tesis Doctoral en Física) |
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| Palabras Clave: | Hall effect; Efecto hall; Quantum wells; Pozos cuánticos; [Density functional theory; Teoría de funcional densidad; Exact exchange; Intercambio exacto] |
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| Materias: | Física > Materia condensada |
| Divisiones: | Gcia. de área de Investigación y aplicaciones no nucleares > Gcia. de Física > Materia condensada > Teoría de sólidos |
| Código ID: | 807 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 05 Mar 2021 09:05 |
| Última Modificación: | 05 Mar 2021 09:05 |
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