Dinâmica de pacotes de onda em semicondutores e grafeno e de vórtices em supercondutores

• Ano de defesa: 2010
• Autor(a) principal: Chaves, Andrey
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Semicondutores; Carbono; Supercondutores
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/1096

This work has two parts. In the first one, we analyze the time evolution of wave packets in low dimensional systems. The time dependent Schrödinger equation is solved by means of the split-operator technique, which is easy to be computationally implemented and expanded to systems with more dimensions. We calculate the eigenstates and time evolution of wave packets in T-wires and quantum rings with injection channels. In the presence of an external magnetic field, the Aharonov-Bohm oscillations in the transmission and reflection coeficients of the quantum ring are verified. By analyzing the projections of the transmitted wave function on the subbands of the quantum wells describing the injection channels, we observe that the incoming and outgoing wave functions are in the same subband, although the other subband states can be accessed inside the ring region. The presence of a magnetic field induces a phase shift on these projections, which can be used for tunning the subband of the outgoing wave function. A similar effect can also be obtained by considering an asymmetric ring potential. We have also derived a variant of the split-operator method that allows one to deal with Zeeman and spin-orbit Hamiltonians. We verify that the results obtained by the method we developed are in good agreement with the analytical results for the Zeeman effect in semiconductor quantum dots. We have also adapted the split-operator method to the study of graphene-based systems, within the tight-binding and continuum (Dirac) models. First, we briefly analyze the eigenstates of graphene quantum rings, comparing the results obtained by each model. Further, we verify the existence of a trembling motion of the wave function in graphene (zitterbewegung). We observe that in the presence of a magnetic field, the zitterbewegung becomes permanent. Besides, we demonstrate that the presence of an energy gap due to a substrate-induced potential may intensify the oscillations. In both cases, the experimental detection of this effect would be improved. We also demonstrate that the effect of strain on the electrons behavior in graphene is similar to that of a pseudo-magnetic field, capable of reproducing all the features related to an external field, such as the Landau levels and the persistent zitterbewegung. Moreover, we demonstrate how such strain effects can be used to produce valley filtering in graphene. In the presence of electrostatic potential barriers, we study two interesting effects in graphene monolayers: the Klein paradox and the Snell law for the electron tunneling. In the second part of this thesis, we calculate the interaction potential between vortices in bulk superconductors within the Ginzburg-Landau (GL) theory, which is of importance for future vortex dynamics studies. We derived a set of coupled differential equations for both the vector potential and the order parameter, considering a number of fixed vortices positioned in chosen points of a plane as a constraint, where the merger of vortices into a giant-vortex is naturally allowed. We have obtained the interaction potentials between a vortex and another vortex, a giant-vortex and an antivortex, for both type-I and type-II cases. Our numerical results exhibit good agreement with the analytical expressions for larger vortex-vortex separations available in previous work in the literature. We propose new (empirical) expressions valid for any interaction distance, which are fitted to our numerical data for several values of the GL parameter. Further, using the same numerical and analytical methods described in details for single-band superconductors, we demonstrate and discuss the complexity of the resulting behavior of two Cooper pairs condensates in two-band superconductors. The properties of the coupled system depend on those of each band in a non-trivial way, and their behavior might be not only different, but even opposite to the one of the individual condensates. Therefore, we discuss the possibility of tunning this behavior as a function of the microscopical parameters and temperature, which is of relevance for the understanding of the properties of recently studied materials, such as MgB2 and the iron pnictides, of nanoscale superconductors, as well as of the futuristic artificial composites.