The ultimate goal in the rapidly burgeoning field of spintronics is to realize semiconductor-based devices that utilize the spin degree of freedom of a single charge carrier (electron or hole) or an ensemble of such carriers to achieve novel and/or enhanced device functionalities such as spin based light emitting devices, spin transistors and femto-Tesla magnetic field sensors. These devices share a common feature: they all rely on controlled transport of spins in semiconductors. A prototypical spintronic device has a transistor-like configuration in which a semiconducting channel is sandwiched between two contacts (source and drain) with a gate electrode sitting on top of the channel. Unlike conventional charge-based transistors, the source electrode of a spin transistor is a ferromagnetic (or half-metallic) material which injects spin polarized electrons in the channel. During transit, the spin polarizations of the electrons are controllably rotated by a gate electric field mediated spin-orbit coupling effect. The drain contact is ferromagnetic (or half-metallic) as well and the transmission probability of an electron through this drain electrode depends on the relative orientation of electron spin polarization and the (fixed) magnetization of the drain. When the spins of the electrons are parallel to the drain magnetization, they are transmitted by the drain resulting in a large device current (ON state of spin FET). However, these electrons will be completely blocked if their spins are antiparallel to the drain magnetization, and ideally, in this situation device current will be zero (OFF state of spinFET). Thus, if we vary the gate voltage, we can modulate the channel current by controlling the spin orientations of the electrons with respect to the drain magnetization. This is how transistor action is realized (Datta-Das model). However, during transport, electrons' velocities change randomly with time due to scattering and hence different electrons experience different spin-orbit magnetic fields. As a result, even though all electrons start their journey with identical spin orientations, soon after injection spins of different electrons point along different directions in space. This randomization of initial spin polarization is referred to as spin relaxation and this is detrimental to the spintronic devices. In particular, for Datta-Das transistor, this will lead to inefficient gate control and large leakage current in the OFF state of the spinFET. The aim of this work is to understand various spin relaxation processes that are operative in semiconductor nanostructures and to indicate possible ways of minimizing them. The theoretical aspect of this work (Chapters 2-5) focuses on the D'yakonov-Perel' process of spin relaxation in a semiconductor quantum wire. This process of spin relaxation occurs because during transport electron spin precesses like a spinning top about the spin-orbit magnetic field. We show that the conventional drift-diffusion model of spin transport, which has been used extensively in literature, completely breaks down in case of a quantum confined system (e.g. a quantum wire). Our approach employs a semi-classical model which couples the spin density matrix evolution with the Boltzmann transport equation. Using this model we have thoroughly studied spin relaxation in a semiconductor quantum wire and identified several inconsistencies of the drift-diffusion formalism.The experimental side of this work (Chapters 6-8) deals with two different issues: (a) performing spin transport experiments in order to extract spin relaxation length and time in various materials (e.g. Cu, Alq3) under one-dimensional confinement, and (b) measurement of the ensemble spin dephasing time in self-assembled cadmium sulfide quantum dots using electron spin resonance technique. The spin transport experiment, as described in Chapter 7 of this dissertation, shows that the spin relaxation time in organic semiconductor (Alq3) is extremely long, approaching a few seconds at low temperatures. Alq3 is the chemical formula of tris- 8 hydroxy-quinoline aluminum, which is a small molecular weight organic semiconductor. This material is extensively used in organic display industry as the electron transport and emission layer in green organic light emitting diodes. The long spin relaxation time in Alq3 makes it an ideal platform for spintronics. This also indicates that it may be possible to realize spin based organic light emitting diodes which will have much higher internal quantum efficiency than their conventional non-spin counterparts. From spin transport experiments mentioned above we have also identified Elliott-Yafet mode as the dominant spin relaxation mechanism operative in organic semiconductors. Electron spin resonance experiment performed on self-assembled quantum dots (Chapter 8) allows us to determine the ensemble spin dephasing time (or transverse spin relaxation time) of electrons confined in these systems. In quantum dots electrons are strongly localized in space. Surprisingly, the ensemble spin dephasing time shows an increasing trend as we increase temperature. The most likely explanation for this phenomenon is that spin dephasing in quantum dots (unlike quantum wells and wires) is dominated by nuclear hyperfine interaction, which weakens progressively with temperature. We hope that our work, which elaborates on all of the above mentioned topics in great detail, will be a significant contribution towards the current state of knowledge of subtle spin-based issues operative in nanoscale device structures, and will ultimately lead to realization of novel nano-spintronic devices.

A condutância de fios quânticos definidos em uma geometria de \"split gate\" varia em platôs quantizados de 2e2/h em relação à ocupação dos seus modos transversais [van Wees et al. Phys. Rev. Lett. 60, 848 (1988) & Wharam et al. J. Phys. C: solid state phys. 21, L209 (1988)]. Em gráficos da condutância esta ocupação é dada pelo potencial aplicado aos eletrodos que formam o fio. Em 1996 observou-se experimentalmente nestes gráficos [Thomas et al. Phys. Rev. Lett. 77, 135 (1996)] que quando apenas um modo transversal é ocupado a condutância exibe um platô anômalo adicional em 0.7X2e2/h. Desde então, a origem desta anomalia 0.7 é associada a fenômenos dependentes de spin, porém sua descrição teórica permanece como importante objeto de pesquisa. Recentemente, observou-se que na presença de altos campos magnéticos, cruzamentos de modos transversais de spins opostos também geram estruturas anômalas no gráfico da condutância [Graham etal. Phys. Rev. Lett. 91, 136404 (2003)]. Os análogos 0.7, assim chamados devido à semelhança com a anomalia 0.7, são usualmente relacionados ou como anti-crossings ou como transições de fase magnética. Motivado pela concordância quantitativa com experimentos de um trabalho anterior em magnetotransporte em 2DEGs e transições de fase de ferromagnetismo de efeito Hall quântico via teoria do funcional da densidade dependente de spin (SDFT) [Freire e Egues, Phys. Rev. Lett. 99, 026801 (2007) & Ferreira et al. Phys. Stat. Sol. (c) 3, 4364 (2006)], propomos aqui um modelo similar para estudar na magnetocondutância de fios quânticos. Utilizamos (i) a SDFT resolvendo as equações de Kohn-Sham autoconsistentemente dentro da aproximação de densidade local de spin para obter a estrutura eletrônica do fio quântico e (ii) o formalismo de Landauer-Büttiker para calcular a condutância do fio no regime de resposta linear. Em nosso modelo, a anomalia e os análogos 0.7 aparecem devido a transições ferromagnéticas que rearranjam de forma abrupta os modos transversais do fio quântico próximos ao nível de Fermi. Nossos resultados teóricos apresentam boa concordância com os dados de Graham et al. / At low temperatures the conductance of a quantum wires exhibits plateaus at integer multiples of 2e2/h due to the quantization of the transverse modes [van Wees et al. Phys. Rev. Lett. 60, 848 (1988) & Wharam et al. J. Phys. C: solid state phys. 21, L209 (1988)]. This conductance behavior is understood within an independent particles model. In 1996 Thomas et al.[Phys. Rev. Lett. 77, 135 (1996)] showed experimentally that when only one transverse mode is occupied, the conductance displays an additional plateau at 0.7 X 2e2/h the so-called 0.7 anomaly. Further experiments have shown that in the presence of high in-plane magnetic fields, similar structures also appear in the conductance near the crossings of spin-split transverse modes [Graham et al. Phys. Rev. Lett. 91, 136404 (2003)]. These so-called 0.7 analogs, due to their similarity to the 0.7 anomaly, are usually related to either anti-crossings or magnetic phase transitions. Motivated by the quantitative agreement with experiments of a previous theoretical work on magnetotransport in 2DEGs and quantum Hall ferromagnetic phase transitions via the Spin Density Functional Theory (SDFT) [Freire and Egues, Phys. Rev. Lett. 99, 026801 (2007) & Ferreira et al. Phys. Stat. Sol. (c) 3, 4364 (2006)], here we propose a similar model to investigate the magnetoconductance of interacting quantum wires. We use (i) the SDFT via the Kohn-Sham self-consistent scheme within the local spin density approximation to obtain the quantum wire electronic structure and (ii) the Landauer-Büttiker formalism to calculate the conductance of a quantum wire in the linear response regime. Our results show good agreement with the data of Graham et al.

We present in this thesis a series of studies on the physical properties of some one dimensional systems. In particular we study the low energy properties of various spin chains and a junction of Luttinger wires. For spin chains we specifically look at the role of perturbations like frustrating interactions and dimerisation in a nearest neighbour chain and the formation of magnetisation plateaus in two kinds of models; one purely theoretical and the other motivated by experiments. In our second subject of interest we study using a renormalisation group analysis the effect of spin dependent scattering at a junction of Luttinger wires. We look at the physical effects caused by the interplay of electronic interactions in the wires and the scattering processes at the junction. The thesis begins with an introductory chapter which gives a brief glimpse of the ideas and techniques used in the specific problems that we have worked on. Our work on these problems is then described in detail in chapters 25. We now present a brief summary of each of those chapters. In the second chapter we look at the ground state phase diagram of the mixed-spin sawtooth chain, i.e a system where the spins along the baseline are allowed to be different from the spins on the vertices. The spins S1 along the baseline interact with a coupling strength J1(> 0). The coupling of the spins on the vertex (S2) to the baseline spins has a strength J2. We study the phase diagram as a function of J2/J1 [1]. The model exhibits a rich variety of phases which we study using spinwave theory, exact diagonalisation and a semi-numerical perturbation theory leading to an effective Hamiltonian. The spinwave theory predicts a transition from a spiral state to a ferrimagnetic state at J2S2/2J1S1 = 1 as J2/J1 is increased. The spectrum has two branches one of which is gapless and dispersionless (at the linear order) in the spiral phase. This arises because of the infinite degeneracy of classical ground states in that phase. Numerically, we study the system using exact diagonalisation of up to 12 unit cells and S1 = 1 and S2 =1/2. We look at the variation of ground state energy, gap to the lowest excitations, and the relevant spin correlation functions in the model. This unearths a richer phase diagram than the spinwave calculation. Apart from revealing a possibility of the presence of more than one kind of spiral phases, numerical results tell us about a very interesting phase for small J2. The spin correlation function (for the spin1/2s) in this region have a property that the nextnearest-neighbour correlations are much larger than the nearest neighbour correlations. We call this phase the NNNAFM (nextnearest neighbour antiferromagnet) phase and provide an understanding of this phase by deriving an effective Hamiltonian between the spin1/2s. We also show the existence of macroscopic magnetisation jumps in the model when one looks at the system close to saturation fields. The third chapter is concerned with the formation of magnetisation plateaus in two different spin models. We show how in one model the plateaus arise because of the competition between two coupling constants, and in the other because of purely geometrical effects. In the first problem we propose [2] a class of spin Hamiltonians which include as special cases several known systems. The class of models is defined on a bipartite lattice in arbitrary dimensions and for any spin. The simplest manifestation of such models in one dimension corresponds to a ladder system with diagonal couplings (which are of the same strength as the leg couplings). The physical properties of the model are determined by the combined effects of the competition between the ”rung” coupling (J’ )and the ”leg/diagonal” coupling (J ) and the magnetic field. We show that our model can be solved exactly in a substantial region of the parameter space (J’ > 2J ) and we demonstrate the existence of magnetisation plateaus in the solvable regime. Also, by making reasonable assumptions about the spectrum in the region where we cannot solve the model exactly, we prove the existence of first order phase transitions on a plateau where the sublattice magnetisations change abruptly. We numerically investigate the ladder system mentioned above (for spin1) to confirm all our analytical predictions and present a phase diagram in the J’/J - B plane, quite a few of whose features we expect to be generically valid for all higher spins. In the second problem concerning plateaus (also discussed in chapter 3) we study the properties of a compound synthesised experimentally [3]. The essential feature of the structure of this compound which gives rise to its physical properties is the presence of two kinds of spin1/2 objects alternating with each other on a helix. One kind has an axis of anisotropy at an inclination to the helical axis (which essentially makes it an Ising spin) whereas the other is an isotropic spin1/2 object. These two spin1/2 objects interact with each other but not with their own kind. Experimentally, it was observed that in a magnetic field this material exhibits magnetisation plateaus one of which is at 1/3rd of the saturation magnetisation value. These plateaus appear when the field is along the direction of the helical axis but disappear when the field is perpendicular to that axis. The model being used for the material prior to our work could not explain the existence of these plateaus. In our work we propose a simple modification in the model Hamiltonian which is able to qualitatively explain the presence of the plateaus. We show that the existence of the plateaus can be explained using a periodic variation of the angles of inclination of the easy axes of the anisotropic spins. The experimental temperature and the fields are much lower than the magnetic coupling strength. Because of this quite a lot of the properties of the system can be studied analytically using transfer matrix methods for an effective theory involving only the anisotropic spins. Apart from the plateaus we study using this modified model other physical quantities like the specific heat, susceptibility and the entropy. We demonstrate the existence of finite entropy per spin at low temperatures for some values of the magnetic field. In chapter 4 we investigate the longstanding problem of locating the gapless points of a dimerised spin chain as the strength of dimerisation is varied. It is known that generalising Haldane’s field theoretic analysis to dimerised spin chains correctly predicts the number of the gapless points but not the exact locations (which have determined numerically for a few low values of spins). We investigate the problem of locating those points using a dimerised spin chain Hamiltonian with a ”twisted” boundary condition [4]. For a periodic chain, this ”twist” consists simply of a local rotation about the zaxis which renders the xx and yy terms on one bond negative. Such a boundary condition has been used earlier for numerical work whereby one can find the gapless points by studying the crossing points of ground states of finite chains (with the above twist) in different parity sectors (parity sectors are defined by the reflection symmetry about the twisted bond). We study the twisted Hamiltonian using two analytical methods. The modified boundary condition reduces the degeneracy of classical ground states of the chain and we get only two N´eel states as classical ground states. We use this property to identify the gapless points as points where the tunneling amplitude between these two ground states goes to zero. While one of our calculations just reproduces the results of previous field theoretic treatments, our second analytical treatment gives a direct expression for the gapless points as roots of a polynomial equation in the dimerisation parameter. This approach is found to be more accurate. We compare the two methods with the numerical method mentioned above and present results for various spin values. In the final chapter we present a study of the physics of a junction of Luttinger wires (quantum wires) with both scalar and spin scattering at the junction ([5],[6]). Earlier studies have investigated special cases of this system. The systems studied were two wire junctions with either a fully transmitting scattering matrix or one corresponding to disconnected wires. We extend the study to a junction of N wires with an arbitrary scattering matrix and a spin impurity at the junction. We study the RG flows of the Kondo coupling of the impurity spin to the electrons treating the electronic interactions and the Kondo coupling perturbatively. We analyse the various fixed points for the specific case of three wires. We find a general tendency to flow towards strong coupling when all the matrix elements of the Kondo coupling are positive at small length scales. We analyse one of the strong coupling fixed points, namely that of the maximally transmitting scattering matrix, using a 1/J perturbation theory and we find at large length scales a fixed point of disconnected wires with a vanishing Kondo coupling. In this way we obtain a picture of the RG at both short and long length scales. Also, we analyse all the fixed points using lattice models to gain an understanding of the RG flows in terms of specific couplings on the lattice. Finally, we use to bosonisation to study one particular case of scattering (the disconnected wires) in the presence of strong interactions and find that sufficiently strong interactions can stabilise a multichannel fixed point which is unstable in the weak interaction limit.

La théorie de Landau des liquides de Fermi prévoit que la charge et la chaleur sont transportées par les mêmes objets: les quasi-particules fermionics de Landau. De façon très général, ceci est vrai, si l'écrantage parmi les particules dans le système est assez fort pour pouvoir continuer à considérer le système comme composé de particules indépendantes. C'est le cas, par exemple, pour la mer d'électrons dans un métal ordinaire. L'existence d'un même responsable pour le transport de la charge et de la chaleur est exprimé par la lois de Wiedemann-Franz (WF) qui affirme que le rapport entre la conductivité thermique et électrique dépend de la température par une constante qui est plus au moins la même pour plusieurs métaux. La constante de proportionnalité est appelé nombre de Lorenz. <br /> Que se passe-t-il si les conditions concernant l'écrantage que nous avons mentionnées ne sont plus satisfaites, comme par exemple dans les systèmes à dimensionalité réduite, ou des système à basse densité électronique? <br /> Le travail de thèse est divisé en deux parties. Dans la première partie, nous avons étudié le transport thermique et électrique dans un fil quantique désordonné; dans la deuxième, l'influence des fluctuations supraconductives sur la conductivité thermique dans un métal granulaire.<br /><br /> -)Fils Quantiques: <br /><br /> Généralement, on appelle fil quantique un conducteur uni-dimensionel. Aujourd'hui, il est possible de réaliser des conducteurs qui présentent de très forts potentielles de confinement le long de un ou deux des dimensions linéaire. En particulier, les fils quantiques se comportent comme des véritables guides d'onde pour les électrons car ils peuvent avoirs des diamètres qui sont comparable à la longueur d'onde de Fermi. <br /> A cause de la basse dimensionalité, des tels systèmes sont étudiés dans le contexte de la théorie des liquides de Luttinger qui permet de bien prendre en compte les effets d'interaction parmi les particules. <br /> Pour un fil quantique propre connecté à deux réservoirs, la conductance électrique n'est pas renormalisée, alors que celle thermique l'est fortement à cause de la présence des connexions aux réservoirs. La présence d'un faible désordre renormalise aussi la conductance électrique. Ceci était déjà connu. <br /> Nous avons évalué la renormalisation due aux impuretés pour la conductance thermique. Cela nous a permis de pouvoir évaluer la correction au nombre de Lorenz. <br /> A très basses températures, la correction est nulle, alors que à hautes température elle ne l'est jamais. Nous pouvons affirmer qu'un fil quantique avec impuretés n'est pas dans un état type liquide de Fermi.<br /><br /> -) Métaux Granulaires: <br /> <br /> Dans un métal normal en présence d' interactions de type BCS, les électrons peuvent former des pairs de Cooper même à une température plus élevé que la température critique. Dans ce cas, les propriétés de transport du métal normal se mélangent avec celle de l'état supraconducteur. Cela donne lieu à des contributions qui déterminent le transport de la charge et de l'énergie. <br /> Notamment, sont trois les termes qui contribuent: la contribution Aslamazov -Larkin (AL), la contribution Maki-Thomson (MT), et la contribution Densité d'état (DOS). <br /> La première prend en compte la facilité des électrons formants un pair de Cooper à se propager à travers le système. Cette contribution est aussi appelé paraconductivité; les électrons formants des pairs de Cooper ne sont plus disponibles pour le transport à une seul particule. Cela est pris en compte par la contribution DOS. Le terme MT prend en compte la diffusion cohérent des électrons formants un pair de Cooper sur la même impureté.<br /> Pour un système massif, il a été démontré que les contributions DOS et MT se compense exactement. Il ne reste que le terme AL qui n'est pas singulier dans la température. <br /> Un métal granulaire peut être considéré comme un ensemble D-dimensionel the grains metallics plongé dans un milieux isolant. Les grains communiquent entre eux par effet tunnel.<br /> C'est raisonnable imaginer que la présence de l'effet tunnel renormalise les propriétés de transport. En effet, un comportement dépendant de la température émerge. Les contributions AL et MT sont d'ordre supérieur par rapport au terme DOS.<br /> On peut distinguer deux régions différentes: loin et près de la température critique. Loin de la température critique, le tunneling parmi les grains n'est pas efficace, et la structure granulaire l'emporte; une suppression de la correction à la conductivité thermique est retrouvée. Près de la température critique, le tunneling est efficace est la structure massive est retrouvée. Le signe de la correction n'est pas défini de manière univoque. Il dépend de la transparence de la barrière et de la compétition parmi les différentes contributions.<br /> Dans les deus différents régimes, la lois de WF est violée.

A condutância de fios quânticos definidos em uma geometria de \"split gate\" varia em platôs quantizados de 2e2/h em relação à ocupação dos seus modos transversais [van Wees et al. Phys. Rev. Lett. 60, 848 (1988) & Wharam et al. J. Phys. C: solid state phys. 21, L209 (1988)]. Em gráficos da condutância esta ocupação é dada pelo potencial aplicado aos eletrodos que formam o fio. Em 1996 observou-se experimentalmente nestes gráficos [Thomas et al. Phys. Rev. Lett. 77, 135 (1996)] que quando apenas um modo transversal é ocupado a condutância exibe um platô anômalo adicional em 0.7X2e2/h. Desde então, a origem desta anomalia 0.7 é associada a fenômenos dependentes de spin, porém sua descrição teórica permanece como importante objeto de pesquisa. Recentemente, observou-se que na presença de altos campos magnéticos, cruzamentos de modos transversais de spins opostos também geram estruturas anômalas no gráfico da condutância [Graham etal. Phys. Rev. Lett. 91, 136404 (2003)]. Os análogos 0.7, assim chamados devido à semelhança com a anomalia 0.7, são usualmente relacionados ou como anti-crossings ou como transições de fase magnética. Motivado pela concordância quantitativa com experimentos de um trabalho anterior em magnetotransporte em 2DEGs e transições de fase de ferromagnetismo de efeito Hall quântico via teoria do funcional da densidade dependente de spin (SDFT) [Freire e Egues, Phys. Rev. Lett. 99, 026801 (2007) & Ferreira et al. Phys. Stat. Sol. (c) 3, 4364 (2006)], propomos aqui um modelo similar para estudar na magnetocondutância de fios quânticos. Utilizamos (i) a SDFT resolvendo as equações de Kohn-Sham autoconsistentemente dentro da aproximação de densidade local de spin para obter a estrutura eletrônica do fio quântico e (ii) o formalismo de Landauer-Büttiker para calcular a condutância do fio no regime de resposta linear. Em nosso modelo, a anomalia e os análogos 0.7 aparecem devido a transições ferromagnéticas que rearranjam de forma abrupta os modos transversais do fio quântico próximos ao nível de Fermi. Nossos resultados teóricos apresentam boa concordância com os dados de Graham et al. / At low temperatures the conductance of a quantum wires exhibits plateaus at integer multiples of 2e2/h due to the quantization of the transverse modes [van Wees et al. Phys. Rev. Lett. 60, 848 (1988) & Wharam et al. J. Phys. C: solid state phys. 21, L209 (1988)]. This conductance behavior is understood within an independent particles model. In 1996 Thomas et al.[Phys. Rev. Lett. 77, 135 (1996)] showed experimentally that when only one transverse mode is occupied, the conductance displays an additional plateau at 0.7 X 2e2/h the so-called 0.7 anomaly. Further experiments have shown that in the presence of high in-plane magnetic fields, similar structures also appear in the conductance near the crossings of spin-split transverse modes [Graham et al. Phys. Rev. Lett. 91, 136404 (2003)]. These so-called 0.7 analogs, due to their similarity to the 0.7 anomaly, are usually related to either anti-crossings or magnetic phase transitions. Motivated by the quantitative agreement with experiments of a previous theoretical work on magnetotransport in 2DEGs and quantum Hall ferromagnetic phase transitions via the Spin Density Functional Theory (SDFT) [Freire and Egues, Phys. Rev. Lett. 99, 026801 (2007) & Ferreira et al. Phys. Stat. Sol. (c) 3, 4364 (2006)], here we propose a similar model to investigate the magnetoconductance of interacting quantum wires. We use (i) the SDFT via the Kohn-Sham self-consistent scheme within the local spin density approximation to obtain the quantum wire electronic structure and (ii) the Landauer-Büttiker formalism to calculate the conductance of a quantum wire in the linear response regime. Our results show good agreement with the data of Graham et al.

Die Ergänzung der konventionellen Elektronik durch die quantenmechanischen Spin Eigenschaften der Elektronen ermöglicht die Entwicklung von schnellen und effizienten Rechnersystemen. Ein bekannter Baustein für solch ein System ist der Datta-Das Spin-Transistor. In dieser Arbeit wird ein akustisch angetriebener Spin-Transistor untersucht, basiert auf Quantendrähten definiert mittels Molekularstrahlepitaxie. Diese Quantendrähte (QWRs: quantum wires) bilden sich während des epitaktischen Überwachsens an den Flanken von Barrenstrukturen auf GaAs (001) Substraten. Elektronen (Löcher), die optisch in den QWR injiziert werden, sind lateral durch eine Potenzialbarriere von 25.4 meV (4.8 meV) zum umgebenden Qauntum Well eingesperrt. Die Verwendung einer akustischen Oberflächenwelle (AOW) ermöglicht den Transport von Elektronen und Löchern über große Entfernungen von bis zu 90 micron. Die akustische Transportdauer der QWR Ladungsträger entspricht der Dauer, die man aufgrund der akustischen Geschwindigkeit erwartet, d.h. dass die Ladungsträger sehr effizient transportiert werden. Im Fall von niedrigen akustischen Leistungen führen unbeabsichtigte Einfangzentren zu zusätzlichen Hotspots der Ladungsträgerrekombination auf dem Transportweg. Die intrinsischen Spinlebenszeiten der QWR Ladungsträger betragen ungefähr 2 ns bis 3 ns. Akustischer Spintransport im QWR wird über Entfernungen von mindestens 15 micron beobachtet. Es wird gezeigt, dass für Ladungsträger im QWR das Spin-Bahn Feld, um welches die Spins während des Transportes rotieren, stark von der akustischen Leistung abhängt. Daher stellen Flanken-QWRs auf GaAs (001) Substraten ein vielversprechendes Konzept für die Verwendung in einem akustisch betriebenen Spin-Transistor dar. / Fast and efficient computation devices can be developed by complementing conventional electronics with quantum mechanical spin. A common example for such a building block is the Datta-Das spin transistor. In this thesis, an acoustically driven spin transistor based on acoustic spin transport in quantum wires is investigated. These quantum wires (QWRs) are defined by molecular-beam epitaxy growth. They form on the sidewalls of ridges on GaAs (001) substrates. The edges of the ridges contain deviations from a straight line, originating from the photolithography process. Optically injected electrons and holes in the QWR are laterally confined by a potential barrier between the QWR and the surrounding QW of 25.4 meV and 4.8 meV, respectively. The application of a surface acoustic wave (SAW) enables the transport of electrons and holes over long distances along the QWR. For high acoustic powers, the charge carriers are transported by the strong SAW potential over distances up to 90 micron. The acoustic transport time of QWR corresponds to the one expected from the acoustic velocity, indicating a high transport efficiency. For lower acoustic powers, unintentional trapping centers lead to hotspots of carrier recombination along the transport path. The intrinsic spin lifetimes of the QWR carriers are approximately 2 ns to 3 ns. Acoustic spin transport in the QWR is observed over distances of at least 15 micron. It is shown that the spin-orbit field, around which the spins rotate during transport, strongly depends on the acoustic power for the QWR carriers. For high acoustic powers, the QWR spin precession frequency is enhanced by 3.5 times with respect to the intrinsic one. The results presented in this thesis demonstrate that the strain field of a SAW acts as a strain gate for QWR spins which are transported over a fixed distance. Therefore, the sidewall quantum wire on GaAs (001) substrates is a promising concept to be used in an acoustically driven spin transistor.

This thesis presents the work done on electronic transport in various interacting and non-interacting systems in one and two dimensions. The systems under study are: an interacting quantum dot [1], a non-interacting quantum wire and a ring in which time-dependent potentials are applied [2], an interacting quantum wire and networks of multiple quantum wires with resistive regions [3, 4], one-dimensional edge stages of a two-dimensional topological insulator [5], and a hybrid system of two-dimensional surface states of a three-dimensional topological insulator and a superconductor [6]. In the first chapter, we introduce a number of concepts which are used in the rest of the thesis, such as scattering theory, Landauer conductance formula, quantum wires, bosonization, topological insulators and superconductor. In the second chapter, we study transport through a quantum dot with interacting electrons which is connected to two reservoirs. The quantum dot is modeled by two sites within a tight-binding model with spinless electrons. Using the Lippman-Schwinger method, we write down an exact two-particle wave function for the dot-reservoir system with the interaction localized in the region of the dot. We discuss the phenomena of two-particle resonance and rectification. In the third chapter, we study pumping in two kinds of one-dimensional systems: (i) an infinite line connected to reservoirs at the two ends, and (ii) an isolated ring. The infinite line is modeled by the Dirac equation with two time-independent point-like backscatterers that create a resonant barrier. We demonstrate that even if the reservoirs are at the same chemical potential, a net current can be driven through the channel by the application of one or more time-dependent point-like potentials. When the left-right symmetry is broken, a net current can be pumped from one reservoir to the other by applying a time-varying potential at only one site. For a finite ring, we model the system by a tight-binding model. The ring is isolated in the sense that it is not connected to any reservoir or environment. The system is driven by one or more time-varying on-site potentials. We develop an exact method to calculate the current averaged over an infinite amount of time by converting it to the calculation of the current carried by certain states averaged over just one time period. Using this method, we demonstrate that an oscillating potential at only one site cannot pump charge, and oscillating potentials at two or more sites are necessary to pump charge. Further we study the dependence of the pumped current on the phases and the amplitudes of the oscillating potentials at two sites. In the fourth chapter, we study the effect of resistances present in an extended region in a one-dimensional quantum wire described by a Tomonaga-Luttinger liquid model. We combine the concept of a Rayleigh dissipation function with the technique of bosonization to model the dissipative region. In the DC limit, we find that the resistance of the dissipative patch adds in series to the contact resistance. Using a current splitting matrix M to describe junctions, we study in detail the conductances of: a three-wire junction with resistances and a parallel combination of resistances. The conductance and power dissipated in these networks depend in general on the resistances and the current splitting matrices that make up the network. We also show that the idea of a Rayleigh dissipation function can be extended to couple two wires; this gives rise to a finite transconductance analogous to the Coulomb drag. In the fifth chapter, we study the effect of a Zeeman field coupled to the edge states of a two-dimensional topological insulator. These edge states form two one-dimensional channels with spin-momentum locking which are protected by time-reversal symmetry. We study what happens when time-reversal symmetry is broken by a magnetic field which is Zeeman-coupled to the edge states. We show that a magnetic field over a finite region leads to Fabry-P´erot type resonances and the conductance can be controlled by changing the direction of the magnetic field. We also study the effect of a static impurity in the patch that can backscatter electrons in the presence of a magnetic field. In the sixth chapter, we use the Blonder-Tinkham-Klapwijk formalism to study trans-port across a line junction lying between two orthogonal topological insulator surfaces and a superconductor (which can have either s-wave or p-wave pairing). The charge and spin conductances across such a junction and their behaviors as a function of the bias voltage applied across the junction and various junction parameters are studied. Our study reveals that in addition to the zero conductance bias peak, there is a non-zero spin conductance for some particular spin states of the triplet Cooper pairs. We also find an unusual satellite peak (in addition to the usual zero bias peak) in the spin conductance for a p-wave symmetry of the superconductor order parameter.