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<p>The main theme covered in this thesis is experimentalstudies of quantum dynamics and coherent control in homonuclearalkali diatomic molecules by ultrafast laser spectroscopy iththe implementation of pump-probe techniques.</p><p>A series of experiments have been performed on the Rb2molecules in a molecular beam as well as in a thermal oven. Thereal-time molecular quantum dynamics of the predissociatingelectronically excited D(3)¹Πu state of Rb₂, which couples to/intersects several otherneighbouring states, is investigated using wavepackets. Thepredissociation of the D state, explored by this wavepacketmethod, arises from two independent states, the (4)³Σ_u⁺and (1)³∆_u, for which the second corresponds to a much fasterdecay channel above a sharp energy threshold around 430 nm. Thelifetime of the D state above the energy threshold is obtained,τ ≈ 5 ps, by measuring the decay time of thewavepacket in a thermal oven. Further experimentalinvestigation performed in a molecular beam together withquantum calculations of wavepacket dynamics on the D state haveexplored new probe channels of wavepacket evolution: theD′(3)1Σu+ channel, which exhibits vibrational motionin a shelf state and the (4)³Σu+ channel, where direct build-up of thewavefunction is observed due to its spin-orbit oupling to the Dstate.</p><p>The real-time quantum dynamics of wavepackets confined totwo bound states, A¹Σ_u⁺(0_u⁺) and b³Π_u(0_u⁺), have been studied by experiment andcalculations. It is shown that these two states are fullycoupled by spin-orbit interaction, characterised by itsintermediate strength. The intermediate character of thedynamics is established by complicated wavepacket oscillationatterns and a value of 75 cm^-1is estimated for the coupling strength at thestate crossing.</p><p>The experiments on the Li₂molecule are performed by coherent control ofrovibrational molecular wavepackets. First, the Deutsch-Jozsaalgorithm is experimentally demonstrated for three-qubitfunctions using a pure coherent superposition of Li₂rovibrational eigenstates. The function’scharacter, either constant or balanced, is evaluated by firstimprinting the function, using a phase-tailored femtosecond(fs) pulse, on a coherent superposition of the molecularstates, and then projecting the superposition onto an ionicfinal state using a second fs pulse at a specific delay time.Furthermore, an amplitude-tailored fs pulse is used to exciteselected rovibrational eigenstates and collision induceddephasing of the wavepacket signal, due to Li₂-Ar collisions, is studied experimentally. Theintensities of quantum beats decaying with the delay time aremeasured under various pressures and the collisional crosssections are calculated for each well-defined rovibrationalquantum beat, which set the upper limitsfor ure dephasingcross sections.</p><p><b>Keywords:</b>Ultrafast laser spectroscopy, pump-probetechnique, predissociation, wavepacket, pin-orbit interaction,coherent control, (pure) dephasing</p>

This dissertation describes the theoretic studies of magnetic moment and spinorbit interaction in vacuum (Dirac wavepacket) and solid state systems, such as semiconductors. The semiclassical approach developed here provides a simple and intuitive picture for the origin of spin and spin-orbit coupling. In the Dirac model, the spin magnetic moment is originated from the self-rotating Dirac wavepacket with a correct g-value. The spin-orbit interaction is related to Berry connection (gauge potential) and the model is generalized to solid state systems. The Rashba effect caused by the spin-orbit coupling in a crystal with asymmetric potential in heterostructure quantum well is calculated by semiclassical spindependent scattering. The exact treatment of interface phase accumulation provides a justification of spin-dependent boundary condition at interface derived in previous treatment using Löwdin decomposition. Other spin-orbit coupling related phenomena in solid state system are also discussed in this thesis. / text

In the recent years, interest in TM oxides with 5d valence electrons has grown immensely due to the realization of novel spin-orbit coupled ground states. In these compounds, e.g., iridates and osmates, the intriguing situation arises where the spin-orbit and electron-electron interactions meet on the same energy scale. This has created a new window of interest in these compounds since the interplay of crystal field effects, local multiplet physics, spin-orbit couplings, and intersite hopping can offer novel types of correlated ground states and excitations. In 5d5 iridates, a spin-orbit entangled j = 1/2 Mott insulating state has been realized recently. A remarkable feature of such a ground state is that it gives rise to anisotropic magnetic interactions. The 2D honeycomb-lattice 213 iridium oxides, A2IrO3 (A=Li,Na), have been put forward to host highly anisotropic bond-dependent spin-spin interactions that resemble the Kitaev spin model, which supports various types of topological phases relevant in quantum computing. The 2D square-lattice 214 iridates Sr2IrO4 and Ba2IrO4 are, on the other hand, appealing because of their perceived structural and magnetic simi- larity to La2CuO4, the mother compound of the cuprate high-Tc superconductors. This has promoted the latter iridium oxide compounds as novel platforms for the search of high-Tc superconductivity. To put such considerations on a firm footing, it is essential to quantify the different coupling strengths and energy scales, as they for instance appear in effective Hamiltonian descriptions of these correlated systems. Moreover, it is important to correctly describe their effects. In this thesis, the electronic structure and magnetic properties of 5d5 (mainly 214 and 213) iridates are studied using wave-function-based quantum chemistry methods. These methods are fully ab initio and are capable of accurately treating the electron-electron interactions without using any ad hoc parameters. The spin-orbit entangled j = 1/2 ground state in 214, 213 and other lower symmetry Sr3CuIrO6 and Na4Ir3O8 iridates is first analyzed in detail, by studying the local electronic structure of the 5d5 Ir4+ ion. We establish that the longer-range crystal anisotropy, i.e., low-symmetry fields related to ionic sites beyond the nearest neighbor oxygen cage, strongly influence the energies of Ir d levels. The ground state in all the compounds studied is j = 1/2 like with admixture from j ≃ 3/2 states ranging from 1 – 15 %. Further, the average j ≃ 1/2 → j ≃ 3/2 excitation energy we find is around 0.6 eV. The NN magnetic exchange interactions we computed for 214 iridates are predominantly isotropic Heisenberg-like with J ~ 60 meV, 3 – 4 times smaller than found in isostructural copper oxides. However, the anisotropic interactions are an order of magnitude larger than those in cuprates. Our estimates are in excellent agreement with those extracted from experiments, e.g., resonant inelastic x-ray scattering measurements. For the 213 honeycomb-lattice Na2IrO3 our calculations show that the relevant spin Hamiltonian contains further anisotropic terms beyond the Kitaev-Heisenberg model. Nevertheless, we predict that the largest energy scale is the Kitaev interaction, 10 to 20 meV, while the Heisenberg superexchange and off-diagonal symmetric anisotropic couplings are significantly weaker. In the sister compound Li2IrO3, we find that the structural inequivalence between the two types of Ir-Ir links has a striking influence on the effective spin Hamiltonian, leading in particular to two very different NN superexchange pathways, one weakly AF (~ 1 meV) and another strongly FM (−19 meV). The latter gives rise to rigid spin-1 triplets on a triangular lattice.

NMR spectroscopy of paramagnetic solids provides detailed information about the local configuration and the chemical environment of the NMR observed center, as well as about the structural, magnetic and electronic properties of the coordianted paramagnetic centres. In the case of complex paramagnetic solids such as cathode materials for (rechargeable) batteries, NMR represents an invaluable tool to provide insight into the structural and electronic properties of the systems, which are at the base of the electrochemical performance of these materials. However, the paramagnetism makes the interpretation of the NMR data very challenging. This is primarily due to the interactions of the unpaired electrons with the NMR observed nucleus, and the interpretation of the NMR spectra often requires the aid of reliable theoretical and computational methods. Often the dominant interaction contributing to the measured isotropic shifts is the hyperfine interaction between the unpaired electrons and the observed nucleus, which results from the transfer of unpaired electrons from the paramagnetic centre(s) to the NMR observed site. In systems such as the ones studied here, in which the paramagnetic ions are a major constituent of the lattice, the multitide of different local environments results in a complex distribution of resonances. As in the case of the Li$_x$V$_6$O$_{13}$ cathode material, a methodical investigation of the configurational stability from first principles gives insight into the preferred site configurations. The combination of experimental $^7$Li NMR spectra and hyperfine shift DFT calculations of the so-found stable Li environments allows to unravel the complex lithiation mechanism of this material. In the other case of the LiTi$_x$Mn$_{2-x}$O$_4$ cathode materials, the $^7$Li hyperfine shifts calculated from first principles for a variety of Li environments are combined in a lattice model which allows to assign the isotropic regions of the experimental $^7$Li NMR spectra, helping to resolve the complex cation ordering as a function of Mn/Ti content in the series. For paramagnetic centres with an unquenched orbital component of the electron magnetic moment(s), the spin-orbit coupling effects also contribute to the paramagnetic NMR shift and shift anisotropy. A first principles model is derived, which describes how spin-orbit coupling and the single-ion $g$-tensor are defined and calculated in periodic paramagnetic solids, and how they can be coupled with the hyperfine interaction to model their effects on the NMR spectrum. The method is applied to a series of olivine-type LiTMPO$_4$ cathode materials (with TM = Mn, Fe, Co, and Ni) and the respective $^7$Li and $^{31}$P NMR spectra are simulated and compared with the experiments. The other paramagnetic effect considered in this thesis involves the bulk magnetic susceptibility (BMS), which is particularly important for paramagnetic single crystals and solids of complex shape. The BMS effect results from the discontinuity of the bulk susceptibility at the surface of the crystal, inducing a demagnetizing field throughout the sample which changes the measured NMR shift and shift anisotropy. A method to analytically calculate the demagnetising field and the BMS shift in crystals of different shapes is derived, and it is applied to a series of LiFePO$_4$ single crystals for which the $^7$Li NMR spectra are also measured experimentally. The study confirms that, particularly for $^7$Li NMR, the macroscopic shape-dependent BMS shift can indeed be a significant contribution to the measured resonances, determining the large variation in shift measured for the crystals of different shapes.

Spin-dependent phenomena in semiconductor nanowires have recently gained a lot of attention, in special because these nanostructures can be a viable setup to study exotic states of matter like the Majorana fermions. One of the key ingredients to accommodate the Majorana zero modes is the spin-orbit coupling in the nanowires, which has been usually treated with two-band Hamiltonians. The spin-orbit coupling in semiconductors arise from two distinct sources being the bulk inversion asymmetry, when the unit cell does not present inversion symmetry, e.g. when the crystal unit cell is composed by two different atoms, and the structural inversion asymmetry, when the whole system does not have a mirror symmetry. To describe the system these effective models take as input, parameters that are dependent on the system configuration and measurement setups. Although these effective models have been successful in determine relevant physical properties, a more realistic description of the interacting energy bands is required, specially in quantum confined systems where the interplay between both sources of spin-orbit coupling can change the systems properties in non-trivial ways. For instance, in quantum wells there is an anisotropy of the g-factor due to the quantum confinement and structural inversion asymmetry. Furthermore, the in-plane g-factor also have an anisotropy which is due to the intrinsic spin-orbit coupling and it is not captured by these effective models. In this study, we use realistic multiband k &middot; p Hamiltonians, including both spin-orbit coupling mechanisms, to determine the band structure of zincblende InSb and wurtzite InAs nanowires under a transverse electric field. We analyze the effects of the lateral quantum confinement for a hexagonal cross-section geometry and of the change in growth directions, extracting the relevant physical parameters for the first conduction subband. We found that the g-factors are heavily dependent on the quantum confinement and nanowire orientation, with in-plane/out-of-plane anisotropies up to 3%. We also found that for zinc-blende nanowires the extrinsic spin-orbit coupling is dominant over the intrinsic one whereas, for wurztize, the opposite behavior holds. In order to assess if the nanowires could host the aforementioned Majorana zero modes we investigate under which circumstances the topological phase transition occurs, using the Bogoliubov-de Gennes formalism to couple the nanowire with a superconductor, and we found that using realistic and experimental feasible parameters, indeed, the phase transition occurs. In conclusion, our systematic investigation of nanowires shows that the spin-orbit coupling energy can be fine tuned by the external electric field in experimentally achievable setups that ultimately could guide the search for the elusive Majorana modes. Moreover, our numerical approach is not restricted to a specific material or dimensionality and can be used to study others systems to provide useful insights into the electronic and spintronic fields. / Recentemente, fenômenos dependentes de spin em nanofios semicondutores se tornaram uma área de pesquisa ativa especialmente porque essas nanoestruturas podem ser viáveis para o estudo de estados exóticos da matéria como, por exemplo, os férmions de Majorana. Um dos ingredientes chave para que esses modos de excitação possam existir em nanofios é o acoplamento spin-órbita, o qual tem sido usualmente tratado com modelos de duas bandas. O acoplamento spin-órbita em semicondutores aparece de duas fontes distintas sendo elas a assimetria de inversão no bulk, quando a célula unitária do cristal não possui simetria de inversão, por exemplo, quando é formada por dois átomos diferentes, e a assimetria de inversão estrutural, quando o sistema como um todo não possui simetria de inversão. Para descrever o sistema, os modelos efetivos de duas bandas usam como entrada parâmetros que dependem tanto do sistema específico quanto da configuração do arranjo experimental. Apesar desses modelos terem sucesso em descrever algumas das propriedades físicas relevantes, uma descrição mais realística da interação entre as bandas de energia se faz necessária, especialmente em sistemas com confinamento quântico onde a ação combinada das duas fontes de acoplamento spin-órbita muda as propriedades do sistema de maneira não-trivial. Por exemplo, o fator giromagnético em poços quânticos é anisotrópico devido aos efeitos de ambos, confinamento quântico e a assimetria de inversão estrutural. Ademais, o fator giromagnético ao longo do plano também possui uma anisotropia, a qual tem origem no acoplamento spin-órbita intrínseco do sistema e não é capturada por esses modelos efetivos. Nesse estudo, nós usamos Hamiltonianos k &middot; p multibanda, incluindo ambos os mecanismos de acoplamento spin-órbita, para determinar a estrutura de bandas de nanofios de InSb na fase blenda de zinco e InAs na fase wurtzita sob a ação de um campo elétrico transversal. Nós analisamos os efeitos do confinamento quântico lateral, para fios com seção transversal hexagonal, e diferentes direções de crescimento, extraindo parâmetros físicos relevantes para a primeira sub-banda de condução. Nós encontramos que os fatores giromagnéticos são fortemente influenciados pelo confinamento quântico e orientação dos nanofios, com anisotropias no plano e fora do plano de até 3%. Nós também encontramos que para nanofios de InSb na fase blenda de zinco, o acoplamento spin-órbita extrínseco domina o intrínseco enquanto que, em nanofios de InAs na fase wurtzita, vale o oposto. Para avaliar se os nanofios podem hospedar os modos de Majorana de energia zero nós investigamos sob quais circunstâncias a transição de fase topológica ocorre usando o formalismo de Bogoliubov-de Gennes para acoplar o nanofio a um supercondutor, e encontramos que usando nossos parâmetros e em condições experimentalmente factíveis, de fato, a transição de fase ocorre. Em conclusão, nossa investigação sistemática nos nanofios mostrou que o acoplamento spin-órbita pode ser ajustado por fontes externas, tais como um campo elétrico aplicado, e em configurações experimentais factíveis e que ultimamente pode guiar à busca dos elusivos modos de Majorana. Além do mais, nossa abordagem numérica não é restrita a esses materiais em específico e nem a nanofios, podendo ser usada para estudar outros sistemas provendo intuições úteis nos campos de eletrônica e spintrônica.

Neste trabalho apresentamos a determinação autoconsistente da constante de interação spin-órbita em heteroestruturas com duas sub-bandas. Como recentemente proposto, ao obter o hamiltoneano de um sistema com duas sub-bandas na aproximação de massa efetiva, constata-se a presença de um acoplamento inter-subbanda que não se anula mesmo em heteroestruturas simétricas. Apresentamos aqui as deduções teóricas que levaram à proposição desse novo acoplamento e mostramos o cálculo autoconsistente da intensidade do acoplamento e a comparamos com a intensidade do acoplamento Rashba, já amplamente estudado. Discutimos o método k.p e a Aproximação da Função Envelope e mostramos a obtenção do modelo de Kane 8x8 para semicondutores com estrutura zincblende. Aplicamos o método do \"folding down\'\' ao hamiltoneano de Kane isolando o setor correspondente à banda de condução. Escrevemos dessa forma um hamiltoneano efetivo para a banda de condução no contexto de um poço quântico com uma barreira. Através da projeção desse hamiltoneano nos dois primeiros estados da parte orbital verifica-se o surgimento de um acoplamento inter-subbanda. Finalmente escrevemos o hamiltoneano efetivo 4x4 que descreve as duas primeiras subbandas de um poço quântico e obtivemos seus autoestados e autoenergias. Finalmente fizemos o cálculo autoconsistente das funções de onda e energias de um gás de elétrons em poços quânticos simples e duplos através da aproximação de Hartree e a partir desses resultados determinamos o valor da constante de acoplamento Rashba e da nova constante inter-subbanda. Entre os resultados obtidos destacam-se o controle elétrico da constante de acoplamento inter-subbanda através de um eletrodo externo e um efeito de renormalização da massa efetiva que pode chegar até 5% em algumas estruturas. / In this work we present the self-consistent determination of the spin-orbit coupling constant in heterostructure with two subbands.As recently proposed, the effective hamiltonian for the conduction band in the effective mass approximation contains an inter-subband spin-orbit coupling which is non-zero even for symmetric heterostructures. We present the theoretical derivation which leads to this proposal and show a selfconsistent determination of the coupling constant. We also compare the magnitude of the new coupling constant with the usual Rashba coupling. Starting with a discussion of the k.p method and the Envelope Function Approximation (EFA) we show the derivation of the 8x8 Kane model for semiconductors with zincblende structure. We then apply the \"folding down\'\' method, isolating the conduction band sector of the EFA hamiltonian. By projecting this hamiltonian in the first two states of the orbital part, we find an effective 4x4 hamiltonian that contains an inter-subband spin orbit coupling. The eingenvalues and eigenvectors of this hamiltonian are shown and, specializing the model for single and double quantum wells, we self-consistently determine the inter-subband and Rashba coupling constants in the Hartree approximation. The results indicate the possibility of electrical control of the coupling constant and show an effective mass renormalization effect that can be up to 5% in some cases.

A partir da teoria de resposta linear (formalismo de Kubo) calculamos a condutividade de spin $\\sigma_^$ para um gás bidimensional de elétrons formado num poço quântico com duas subbandas devido a atuação de um novo tipo de interação spin-órbita [Bernardes et al. \\textit{Phys. Rev. Lett.} \\textbf, 076603 (2007) \\& Calsaverini \\textit{et al}. \\textit{Phys. Rev. B} \\textbf, 155313 (2008)]. Este novo termo é não-nulo mesmo em estruturas simétricas e surge devido ao acoplamento entre os estados confinados no poço de paridades diferentes. Encontramos um valor para $\\sigma_^$ não-nulo e não-universal (dependente da intensidade do acoplamento $\\eta$) quando somente uma das subbandas está ocupada, ao contrário de Rashba. Para encontrarmos valores realistas para $\\sigma_^$, determinamos $\\eta$ via cálculo autoconsistente. Esse cálculo é executado para diferentes valores de densidade eletrônica em poços simples e duplos. Obtivemos que $\\sigma_^$ possui um comportamento não-monótono e sofre inversão de sinal como função da energia de Fermi (densidade de elétrons) conforme ela varia entre as duas subbandas. Contudo nossos resultados indicam que a condutividade Hall de spin é muito pequena $\\left(``\\ll \\frac{8\\pi}\"ight)$ nesses sistemas (poços simples e duplos) e possivelmente não mensurável. / Using the Kubo linear response theory, we investigate spin Hall conductivity $\\sigma_^$ in a two-dimensional electron gas in quantum wells with two subbands, when intersubband-induced spin-orbit coupling is operative [Bernardes et al. \\textit{Phys. Rev. Lett.} \\textbf, 076603 (2007) \\& Calsaverini \\textit{et al}. \\textit{Phys. Rev. B} \\textbf, 155313 (2008)]. This new spin-orbit term is non-zero even in symmetric structures and it arises from the distinct parity of the confined states. We find non-zero and non-universal $\\sigma_^$ (dependent on spin-orbit coupling strength $\\eta$) when only one of the subbands is occupied. This is in contrast to the Rashba spin-orbit interaction for which $\\sigma_^$ is identically zero. To obtain realistic values for $\\sigma_^$, we develop a self-consistent scheme to calculate $\\eta$. We performed this calcultion for different values of the eletronic density in single and double wells. We find that $\\sigma_^$ shows a non-monotonic behavior and a sign change as the Fermi energy (carrier density) varies between the two subband edges. However, our results indicate that $\\sigma_^$ is extremely small $\\left(``\\ll \\frac{8\\pi}\"ight)$ and possibly not measurable.

Apresento neste trabalho uma derivação alternativa da hamiltoniana efetiva para um elétron na banda de condução de uma heteroestrutura semicondutora de rede Zincblende. Partindo do modelo de Kane 8 × 8 e da aproximação das funções envelope, esta hamiltoniana efetiva foi obtida com a linearização dos denominadores (dependentes das autoenergias) presentes na equação para a banda de condução, sob a hipótese de que o gap de energia seja muito maior que todas as demais diferenças de energia envolvidas (verdade para a maioria das estruturas Zincblende). A partir de um procedimento introduzido previamente1,3, desenvolvi um procedimento mais geral que implementa sistematicamente esta linearização até segunda ordem no inverso do gap de energia e que corrige a normalização do spinor da banda de condução usando as bandas de valência. Este procedimento é idêntico à expansão em série de potência no inverso da velocidade da luz utilizada para se obter aproximações relativísticas da equação de Dirac. Uma vantagem deste procedimento é a arbitrariedade na forma dos potenciais, o que implica na validade da hamiltoniana resultante para poços, fios e pontos quânticos. Evidencio também as consequências de cada termo desta hamiltoniana efetiva para os autoestados eletrônicos em poços retangulares, incluindo termos independentes de spin inéditos (Darwin e interação momento linearcampo elétrico). Estes resultados estão de acordo com os estudos anteriores4. A fim de estudar transições ópticas dentro da banda de condução, mostro que o acoplamento mínimo pode ser realizado diretamente na hamiltoniana de Kane se os campos externos variam tão lentamente quanto as funções envelope. Repetindo a linearização dos denominadores de energia, derivo uma hamiltoniana efetiva para a banda de condução com acoplamentos elétron-fótons. Um destes acoplamentos, induzido exclusivamente pela banda de valência, origina transições mediadas pelo spin eletrônico. Estas transições assistidas por spin possibilitam mudanças, opticamente induzidas, na orientação do spin eletrônico, um fato que talvez possa ser útil na construção de dispositivos spintrônicos. Por fim, as taxas de transição deste acoplamento apresentam saturação e linhas de máximos e mínimos no espaço recíproco. Espero que estas acoplamentos ópticos possam auxiliar na observação dos efeitos dos acoplamentos spin-órbita intra (Rashba) e intersubbandas. / In this work, I present an alternative derivation of the conduction band effective hamiltonian for Zincblende semiconductor heterostructures. Starting from the 8×8 Kane model and envelope function approximation, this effective hamiltonian was obtained by means of a linearization in the eigenenergy-dependent denominators present the conduction band equation, under the hypothesis that the energy gap is bigger than any other energy difference in the system (true for mostly every Zincblende semiconductor bulk or heterostructure). Based on a previous procedure1,3, I have developed a more general procedure that implements sistematicaly (i) this linearization and (ii) renormalizes the conduction band spinor using the valence bands, both (i) and (ii) up to second order in the inverse of the energy gap. This procedure is identical to the expansion in power series of the inverse of the light speed used to derive non-relativistic approximations of the Dirac equation. One advantage of this procedure is the generality of the potentials adopted in our derivation: the same results hold for quantum wells, wires and dots. I show the consequences of each term of this hamiltonian for the electron eigenstates in retangular wells, including novel spin-independent terms (Darwin and linear momentumelectric field couplings). These resulties agree with previous works4. In order to study conduction band optical transitions, I show that the minimal substitution can be performed directly in the Kane hamiltonian if the external fields vary slowly (at least, as slowly as the envelope functions). Repeating the linearization of the energy denominators, I derive a new effective hamiltonian, up to second order in the inverse of the energy gap, with electron-photons couplings. One of these couplings, induced exclusively by the valence bands, gives rise to optical transitions mediated by the electron spin. This spin-assisted coupling enable optically-induced spin flipps in conduction subband transitions, which can be useful in the construction of spintronic devices. Finaly, the spin-assisted transitions rates show saturation and lines of maxima and minima in the reciprocal lattice. I hope that these optical couplings can be of any help in the observation of interesting effects induced by the intra and intersubband spin-orbit coupling.