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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.

No description available.

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.

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.

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.

The kicked-rotor under the Aharonov-Bohm effect are studyed by using the floquet map, the energy change with different magnetic flux have also being discussed. Finally, the kicked-rotor under the time-dependent magnetic flux are discussed.

The fractional quantum Hall (FQH) effect harbors a wealth of unique phenomena, many of which remain mysterious. Of particular interest is the predicted existence of quasi-particles with unusual topological properties, especially in light of recent proposals to observe these properties using electronic interferometers. An introduction to quantum Hall physics and electronic interferometry is given in Chapter 1 of this thesis. The remaining chapters, summarized below, describe a set of experiments in which FQH systems are studied using electronic Fabry-Perot interferometry and related techniques. Since prior studies of electronic Fabry-Perot interferometers revealed unexpected behavior even in the integer quantum Hall (IQH) regime, we began our measurements there. Our initial experiment, presented in Chapter 2, disentangles signatures of Coulomb interaction effects from those of Aharonov-Bohm (AB) interference and provides the first measurement of pure AB interference in these devices. In our next experiment, presented in Chapter 3, we measure AB interference oscillations as a function of an applied dc bias, use their period to study the velocity of the interfering electrons, and study how the oscillations decay as a function of bias and magnetic field. Moving to the FQH regime, applying a similar-sized bias to a quantum point contact leads to long-lasting changes in the strengths and positions of FQH plateaus. The involvement of lattice nuclear spins in this effect, suggested by the long persistence times, is confirmed using NMR-type measurements. Although the exact physical process responsible for the effect remains unclear, its filling-factor dependence provides a striking illustration of composite fermion physics. These measurements are described in Chapter 4. In certain devices, interference oscillations associated with several FQH states are observed. Interpretation of their magnetic-field and gate-voltage periods provides a measurement of quasi-particle charge, and temperature dependence measurements suggest differences between the edge structure of IQH and FQH states. These measurements are described in Chapter 5. Finally, Chapter 6 presents some recent, not-yet-published observations that may shed light on ways to improve the visibility of existing oscillations and potentially observe interference at additional FQH states. This chapter concludes with a discussion of possible next steps toward achieving these goals. / Physics

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.