This dissertation focuses on the study of spin-dependent transport in systems with strong spin-orbit coupling within their band structure. In particular we focus on the anomalous Hall effect, the spin Hall effect, and the Aharonov-Casher effect whose origins, are linked to the presence of spin-orbit coupling. Given the theoretical controversy surrounding these effects we further simplify our studies to semiconductor systems where the band structure is much simpler than in metallic systems with heavy elements. To obtain finite analytical results we focus on reduced dimensions (two and one dimensions) which can be explored experimentally. To set the stage, we discuss the origins of the strong spin-orbit coupling in semiconductors deriving the effective interaction from the Dirac equation. We discuss in detail the skew scattering contribution to the anomalous Hall effect in two-dimensional systems, which is dominant for systems with low impurity concentrations, and find that it is reduced when the two chiral subbands are partially occupied in an electron gas and vanishes for a hole gas, regardless of the band filling. We also present calculations for all contributing mechanisms. We propose a device to test this prediction and study the crossover from the intrinsic to the extrinsic anomalous Hall effect. We calculate all contributions to the anomalous Hall effect in electron systems using the Kubo-Streda formalism. We find that all contributions vanish when both subbands are occupied and that the skew scattering contribution dominates when only the majority subband is occupied. We calculate the interference effects due to spin-orbit interaction in mesoscopic ring structures patterned from HgTe quantum wells related to the Aharonov-Casher effect and the spin Hall effect. We find that the transport properties are affected by the carrier density as well as the spin orbit interaction. We find that the conductivity is larger in hole gas systems. We also show that devices with inhomogenous spin orbit interaction exhibit an electrically controlled spin-flipping mechanism.

We present studies of edge states induced by the Aharonov-Casher vector potential or Rashba-type spin-orbit interaction using quantum transport in InGaAs/InAlAs herterostructures. The Aharonov-Casher effect is electromagnetically dual to the Aharonov-Bohm effect and is predicted to lead to edge states in a parabolic confinement at two-dimensional sample edges. As a narrow gap material, InGaAs has a low effective mass, high mobility, and strong spin-orbit interaction, which indicate that it can be used as a good material to detect the Aharonov-Casher effect or SOI interaction. Using InGaAs, we measured the magnetoresistance in a quantum antidot in narrow short channels in a tilted magnetic field. The fine structure (mT spacing) observed in the magnetoresistance indicate a probable energy spacing between AC edge states. We also fabricated side-gate channel structures in InGaAs/InAlAs quantum wells and investigated the values of the Rashba spin-orbit coupling constant α using the weak antilocalization analysis as a function of the side-gate voltage. We take the effect of the finite width into account and find the corrected values. With the simulation of electric fields in the wide channel and narrow channel, we found that the electric field components can be changed using side-gate voltages. While our results do not indicate which electric field component is responsible, the data indicate that the deduced spin-orbit strength values in a narrow channel are tunable by the side-gate voltage. / Ph. D.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-16T16:53:51Z No. of bitstreams: 1 FRANKBELSON DOS SANTOS AZEVEDO – DISSERTAÇÃO (PPGFísica) 2015.pdf: 1064778 bytes, checksum: c929ffea2d7e7c51359bf2dfc237fbf9 (MD5) / Made available in DSpace on 2018-10-16T16:53:51Z (GMT). No. of bitstreams: 1 FRANKBELSON DOS SANTOS AZEVEDO – DISSERTAÇÃO (PPGFísica) 2015.pdf: 1064778 bytes, checksum: c929ffea2d7e7c51359bf2dfc237fbf9 (MD5) Previous issue date: 2015-09-24 / Capes / Este trabalho tem por objetivo estudar a dinâmica quântica planar de partículas neutras de spin-1/2 na presença de campos elétricos. A priori uma partícula com carga nula não devia interagir com campos eletromagnéticos, mas ao admitir partículas possuindo momento de dipolo magnético, vemos que a interação é possível. Tal estudo acontece através da equação de Dirac com acoplamento não mínimo, onde o termo de interação leva em conta o momento de dipolo magnético, spin da partícula e campo eletromagnético. A partir dessa equação, derivamos e resolvemos duas equações diferenciais de primeira ordem, mostrando que as soluções estão atreladas ao spin. As soluções para o efeito Aharonov-Casher é discutida em detalhes pela primeira vez neste trabalho. Também derivamos uma equação diferencial de segunda ordem, a partir da qual obtivemos o níveis de energia para uma partícula movimentando-se em um caminho circular de raio constante. Além disso, usando o método de extensão auto-adjunta, encontramos funções de onda de estados ligados e níveis de energia para o espaço completo, incluindo a região r = 0. Os níveis de energia obtidos são análogos aos níveis de Landau, e mostram uma dependência com o parâmetro projeção de spin. Por fim, tomamos o limite não relativístico para o espaço completo. / This work aims to study the planar quantum dynamics of neutral particles of spin- 1/2 in the presence of electric fields. A priori a particle with null charge should not interact with electromagnetic fields, but to admit particles having magnetic dipole moment, we see that the interaction is possible. Such study happen through the Dirac equation with non-minimal coupling, where the interaction term takes into account the magnetic dipole moment, spin of the particle and electromagnetic field. From this equation, we derive and solve two differential equations of first order, showing that the solutions is linked to spin. The solutions to the Aharonov-Casher effect is discussed in detail for the first time in this study. We also derive a differential equation of second order, from which we obtained the energy levels for a particle moving in a constant radius circular path. In addition, using the self-adjoint extension method, we find wave functions of bound states and energy levels to the full space, including the region r = 0. The Energy levels obtained are analogous to Landau levels, and show a dependence on the spin projection parameter. Finally, we take the non-relativistic limit for the full space.

Made available in DSpace on 2015-05-14T12:14:05Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 5046450 bytes, checksum: bd56c31f5c1b1739dfc96f350ac77b34 (MD5) Previous issue date: 2010-10-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we discuss the importance of the quantum phases using the Aharonov-Bohm Effect for charged particles and neutral particles with magnetic dipole moment(Aharonov- Casher Effect) and electric dipole moment(He-McKellar-Wilkens Effect) and atoms with electric quadrupole moment. It takes advantage of the initial study of such systems to show the emergence of Landau levels in the dynamics of a particle in two situations: when the particle is charged and when it is neutral. In the case of a neutral particle is considered that it possesses electric dipole moment. In addition it is the first time which is approached a neutral atom with electric quadrupole moment. / Neste trabalho discutimos a importância das fases quânticas usando o Efeito Aharonov-Bohm para partículas carregadas e partículas neutras com momento de dipolo magnético (Efeito Aharonov-Casher) e momento de dipolo elétrico (Efeito He-McKellar-Wilkens), e átomos com momento de quadrupolo elétrico. Tira-se vantagem do estudo inicial de tais sistemas para mostrar a emersão de níveis de Landau na dinâmica de uma partícula em duas situações: quando a partícula está carregada e quando ela é neutra. No caso de uma partícula neutra é considerado que esta possui momento de dipolo elétrico. Além disso é a primeira vez que é abordado um átomo neutro com momento de quadrupolo elétrico.