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We have studied the electron quantum phase by fabricating low dimensional (d ≤ 2) mesoscopic interferometers in high-quality narrow-gap semiconductor (NGS) heterostructures. The low effective-mass electrons in NGS heterostructures enable observation of delicate quantum phases; and the strong spin-orbit interaction (SOI) in the systems gives us means by which we can manipulate the quantum-mechanical spin of these electrons through the orbital properties of the electrons. This enables the observation of spin-dependent phenomena otherwise inaccessible in non-magnetic systems. We have performed low temperature (0.4 K ≤ T ≤ 8 K), low noise (â V ~ 1μV ) transport measurements, and observed evidence of Aharonov-Bohm (AB) and Alâ tshuler-Aronov-Spivak (AAS) quantum oscillations in meso- scopic devices that we fabricated on these NGSs. Our measurements are unique in that we observe both AB and AAS in comparable magnitude in ballistic networks with strong SOI. We show that, with appropriate considerations, diffusive formalisms can be used to describe ballistic transport through rings, even in the presence of SOI. This work also contains an introduction to the physics of geometric phases in mesoscopic systems, and the experimental and analytic processes through which these phases are probed. A discussion of the results of our measurements presents the case that quantum interferometric measurements of geometric phases can be understood quite thoroughly, and that these measurements may have deeper utility in discovery than has yet been recognized. / Ph. D.

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Recent advances in the chemical vapor deposition method of growing graphene sheets suggest that graphene rings can grow. We may anticipate that chemical methods can be developed to construct twisted nano-ribbons to form Möbius structures in the very near future. I investigated the quantum mechanics of an electron constrained to motion on a nanoscale Möbius ring by solving the Schrdinger equation on the curved surface. The close analogy between ordinary cylindrical rings and Möbius rings is displayed by the closeness of their energy spectra. The expectation values for the angular momentum component L_z are shown to be close, but not exactly equal, to integral or half-integral multiples of hbar. The half-integer angular momentum states are present only for the nontrivial topology of Möbius rings. The effect of the curvature of the Möbius rings manifests itself in the level splitting. This can be understood in terms of representations of the discrete rotational groups C_nv. The nonzero variance of L_z will allow weak transitions between integral and half-integral angular momentum states, while preserving the unit angular momentum for photons. Again, since the topology of the system is critical for the Aharonov-Bohm effect, I investigated the AB effect on Möbius rings and found a remarkable pattern in transmission through finite-width 2D ring structures with finite-width input and output contacts attached at the periphery. The periodicity in the magnetic flux, in units of h/e, is weakly broken on 2D rings of finite width. The unusual states with half-integer values of observed on Möbius rings, investigated earlier, display a different characteristic in transmission. In view of the fascinating properties displayed by the non-trivial topology in terms of its novel two-dimensional physics, we expect that the properties of carriers on the Möbius ring that we have presented here will be relevant for practical applications.

Estudamos as teorias não-relativísticas e não-comutativas de campos de spin zero e l/2 acoplado minimamente com o campo ele Chern-Simons em 2+ 1 dimensões. Na situação comutativa o modelo escalar foi usado para simular o efeito Aharonov-Bohrn na abordagem da teoria de campos. Na teoria escalar verificamos que, contrariamente ao resultado comutativo, a inclusão ele urna auto--interação quártica do campo escalar não ó necessária para garantir a renormalização ultravioleta do modelo. Entretanto, para obter um limite comutativo analítico a presença ele uma auto-interação quártica é exigida. Mostramos para o caso ele partículas ele spin 1/2 que a contribuição em um laço para a matriz ele espalhamento contendo o termo de Pauli é puramente não--planar. O termo de Pauli desempenha a mesma função ela auto-interação quártica como no caso escalar. Para valores pequenos do parâmetro da não--comutatividade determinamos as correções para o espalhamento Aharonov-Bohm e provamos que, até ordem de um laço, os modelos são livres de singularidades ultravioleta/infravermelha. / We study noncommutative nonrelativistic theories of spin 0 and 1/2 field coupled to thc Chern-Sirnons field in 2+1 dimensions. In the commutative situation the scalar model has been used to simulate the Aharonov-Bohm effect in the field theory context. We verified that, contrarily to the commutative result, the inclusion of a quartic self-interaction of the scalar field is not necessary to secure the ultraviolet renormalization of the model. However, to obtain a smooth commutative limit the presence of a quartic gauge invariant self-interaction is required. For the case of spin 1/2 particles we show that the one-loop contributions to the that scattering matrix the which contain the Pauli\'s term are purely nonplanar. Thc Pauli\'s term plays the same role of a quartic self-interaction in the scalar case. For small values of the noncommutative parameter we fix the corrections to the Aharonov-Bohm scattering and prove that up to one-loop the models are free from dangerous infrared/ultraviolet divergences.

Nessa tese, mostramos que a Hamiltoniana H e o operador helicidade de uma partícula de Dirac que se movimenta em duas dimensões na presença de um tubo de fluxo magnético infinitamente fino na origem admitem, cada um, uma família de quatro parâmetros de extensões auto-adjuntas. Para cada extensão correspondem condições de contorno a serem satisfeitas pelas auto-fuções na origem. Apesar dos operadores H e formalmente comutarem antes da especificação das condições de contorno, para garantirmos a conservação da helicidade, não é suficiente obtermos as mesmas condições de contorno para ambos os operadores, ou seja, não é suficiente a determinação de um domínio comum a ambos. Mostramos que, para certas relações entre os parâmetros das extensões satisfeitas, é possível a determinação dos domínios mais gerais onde ambos os operadores H e são auto-adjuntos e onde a helicidade é conservada, simultaneamente com a preservação da simetria de Aharonov-Bohm ( + 1), onde é o fluxo magnético em unidades naturais. Nossos resultados implicam que, nem a conservação da helicidade nem a simetria de Aharonov-Bohn, resolvem o problema da escolha da condição de contorno fisicamente correta. / We show that both the Hamiltonian H and the helicity operator of a Dirac particle moving in two dimension in the presence of an infinitely thin magnetic flux tube admit each a four- parameter family of self-adjoint extensions. Each extension is in one-to-one correspondence with the boundary conditions (BC\'s) to be satisfied by the eigenfunctions at the origin. Althou- gh the actions af these two operators commute before specification of boundary conditions, to ensure helicity conservation it is not sufficient to take the same BC\'s for both operators. We show that, given certain relations between the parameters of the extensions it is possible to write down the most general domain where both operators H and are self-adjoint with heli- city conservation and also Aharonov-Bohm symmetry ( + 1) preserved, where is the magnetic flux in natural units. The continuity of the dynamics is also obtained. Our results im- ply that neither helicity conservation nor Aharonov-Bohm symmetry by themselves solves the problem of choosing the \"physical \"boundary conditions for this system.

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Made available in DSpace on 2016-06-02T20:16:55Z (GMT). No. of bitstreams: 1 6767.pdf: 16621562 bytes, checksum: 66df3d9efcbf65c2d47f601b4ef3f3c0 (MD5) Previous issue date: 2015-04-01 / Universidade Federal de Sao Carlos / Quantum dots grown by epitaxial techniques for optical and transport studies are usually capped by a layer of the same material on which the QDs were grown. Recently, several studies have shown how the growth parameters and materials used in this layer significantly affect the morphological, optical and electrical properties of these nanostructures. In this work Indium Arsenide quantum dots capped with a layer of Gallium Arsenide and Antimony are studied. After the growth, a rapid thermal annealing was performed, which improved significantly the size distribution of the quantum dots, increasing the optical eficiency, and inducing a change in the band structure from a Type-I to Type-II. The investigations performed by magnetophotoluminescence have shown that the effects of the topology confinement on the band structure of these quasi zero-dimensional systems are strongly modulated by an external electric field applied parallel to the magnetic field orientation. Purely quantum effects such as Aharonov-Bohm interference and the inversion of the excitonic Landfie g-factor were observed at low temperatures and for specific values of electric fields, showing that the choice of the material and growth conditions of quantum dots capping layer leads to controlled experimental results which could not be achieved using conventional growth methods of semiconductor quantum dots. / Pontos quânticos crescidos por técnicas epitaxiais para estudos ópticos e de transporte são comumente cobertos com uma camada do mesmo material sobre o qual os pontos foram crescidos. Recentemente diversos estudos têm demonstrado como os parâmetros de crescimento e materiais utilizados nesta camada afetam significativamente as propriedades morfológicas, ópticas e elétricas destas nanoestruturas. Neste trabalho são estudados pontos quânticos tradicionais de Arseneto de Índio cobertos com uma camada de Arseneto de Gálio e Antimônio. Após o crescimento foi realizado um tratamento térmico rápido que melhorou significativamente a distribuição de tamanhos dos pontos, com um aumento na eficiência óptica e uma indução na estrutura de bandas do Tipo-I para Tipo-II. As investigações por magnetofotoluminescência revelaram que os efeitos da topologia de confinamento na estrutura de bandas deste sistema quase zero-dimensional são fortemente modulados pela aplicação de um campo elétrico externo paralelo _a orientação do campo magnético. Efeitos de caráter puramente quântico como a interferência Aharonov-Bohm e a inversão do fator-g de Landé excitônico foram observados a baixas temperaturas e para valores específicos de campo elétrico, demonstrando assim que a escolha do material e condições de deposição da camada de cobertura de pontos quânticos levam a efeitos e resultados controlados experimentalmente que não poderiam ser observados utilizando métodos convencionais de crescimento de pontos quânticos semicondutores.

This thesis is devoted to optical properties of Aharonov-Bohm quantum rings in external electromagnetic fields. It contains two problems. The first problem deals with a single-electron Aharonov-Bohm quantum ring pierced by a magnetic flux and subjected to an in-plane (lateral) electric field. We predict magneto-oscillations of the ring electric dipole moment. These oscillations are accompanied by periodic changes in the selection rules for inter-level optical transitions in the ring allowing control of polarization properties of the associated terahertz radiation. The second problem treats a single-mode microcavity with an embedded Aharonov-Bohm quantum ring, which is pierced by a magnetic flux and subjected to a lateral electric field. We show that external electric and magnetic fields provide additional means of control of the emission spectrum of the system. In particular, when the magnetic flux through the quantum ring is equal to a half-integer number of the magnetic flux quantum, a small change in the lateral electric field allows tuning of the energy levels of the quantum ring into resonance with the microcavity mode, providing an efficient way to control the quantum ring-microcavity coupling strength. Emission spectra of the system are calculated for several combinations of the applied magnetic and electric fields.

In this thesis, we investigate the quantum transport properties of disordered three dimensional topological insulator (3DTI) nanostructures of BiSe and BiTe in detail. Despite their intrinsic bulk conductivity, we show the possibility to study the specific transport properties of the topological surface states (TSS), either with or without quantum confinement. Importantly, we demonstrate that unusual transport properties not only come from the Dirac nature of the quasi-particles, but also from their spin texture. Without quantum confinement (wide ribbons), the transport properties of diffusive 2D spin-helical Dirac fermions are investigated. Using high magnetic fields allows us to measure and separate all contributions to charge transport. Band bending is investigated in BiSe nanostructures, revealing an inversion from upward to downward bending when decreasing the bulk doping. This result points out the need to control simultaneously both the bulk and surface residual doping in order to produce bulk-depleted nanostructures and to study TSS only. Moreover, Shubnikov-de-Haas oscillations and transconductance measurements are used to measure the ratio of the transport length to the electronic mean free path ltr/le. This ratio is measured to be close to one for bulk states, whereas it is close to 8 for TSS, which is a hallmark of the anisotropic scattering of spin-helical Dirac fermions. With transverse quantum confinement (narrow wires or ribbons), the ballistic transport of quasi-1D surface modes is evidenced by mesoscopic transport measurements, and specific properties due to their topological nature are revealed at very low temperatures. The metallic surface states are directly evidenced by the measure of periodic Aharonov-Bohm oscillations (ABO) in 3DTI nanowires. Their exponential temperature dependence gives an unusual power-law temperature dependence of the phase coherence length, which is interpreted in terms of quasi-ballistic transport and decoherence in the weak-coupling regime. This remarkable finding is a consequence of the enhanced transport length, which is comparable to the perimeter. Besides, the ballistic transport of quasi-1D surface modes is further evidenced by the observation of non-universal conductance fluctuations in a BiSe nanowire, despite the long-length limit (L > ltr) and a high metallicity (many modes). We show that such an unusual property for a mesoscopic conductor is related to the limited mixing of the transverse modes by disorder, as confirmed by numerical calculations. Importantly, a model based on the modes' transmissions allows us to describe our experimental results, including the full temperature dependence of the ABO amplitude.