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.

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.

Cette thèse est dédiée à l'étude théorique de phases exotiques dans un gaz dilué de bosons avec deux composantes (spins) en présence d'un couplage spin-orbite (SOC) entre ces deux états internes. En ajoutant ce dernier couplage à une description de type champs classiques de notre système, nous montrons que cette méthode permet de prédire le diagramme de phase à température finie de manière quantitative, efficace et fiable. Notre étude porte particulièrement sur un système de bosons bidimensionnels avec SOC dont nous dessinons le diagramme de phase en fonction de l'anisotropie du couplage spin-orbite ainsi que des interactions. Dans le cas d'un SOC anisotrope, une transition de phase de type Berenzinskii-Kosterlitz-Thouless sépare une phase dite normale d'une phase superfluide à plus basse température. L'ordre des spins du quasi-condensat dans la phase superfluide est alors guidé par les interactions de contact dépendantes du spin. Elles favorisent l'apparition soit d'un état onde plane avec moment non-nul (PW) soit d'une superposition linéaire de deux ondes planes appelée état de bande (SP). Pour des interactions indépendantes du spin des particules, nos simulations indiquent une fractionalisation du quasi-condensat. Les états PW et SP restent alors dégénérés. Dans le cas d'un SOC isotrope, nos calculs n'indiquent aucune transition de phase à la limite thermodynamique et à température finie. Un changement de comportement non critique subsiste pour un nombre important mais fini d'atomes. / In this thesis, we theoretically study the occurrence of exotic phases in a dilute two component (spin) Bose gas with artificial spin-orbit coupling (SOC) between the two internal states. Including spin-orbit coupling in classical field Monte Carlo calculations, we show that this method can be used for reliable, quantitative predictions of the finite temperature phase diagram. In particular, we have focused on SOCed bosons in two spatial dimensions and established the phase diagram for isotropic and anisotropic SOC and interparticle interactions. In the case of anisotropic SOC, the system undergoes a Berenzinskii-Kosterlitz-Thouless transition from a normal to a superfluid state at low temperature. The spin order of the quasicondensate in the low temperature superfluid phase is driven by the spin dependence of the interparticle interaction, favoring either the occurence of a single plane wave state at non-vanishing momentum (PW) or a linear sperposition of two plane waves with opposite momenta, called stripe phase (SP). For spin-independent interparticle interaction, our simulations indicate a fractionalized quasicondensate where PW and SP remain degenerate. For isotropic SOC, our calculations indicate that no true phase transition at finite temperature occurs in the thermodynamic limit, but a cross-over behavior remains visible for large, but finite number of atoms.

<div>The quantum phase transitions and exotic excitations are exciting and important topics of nowadays condensed matter theory. Topologically protected excitations are of great interest for potential applications in quantum computing. This Thesis explores two examples of exotic topologically protected excitations, Majorana fermions and parafermions in hybrid superconductor/semiconductor systems.</div><div><br></div><div>In the first part of the thesis, after a brief review of ideas on Majorana zero modes in solid state systems obtained by researchers over the past decade, I present our study of the emergence of Majorana fermions in charge carrier holes doped quantum wires. Study of Majorana modes in this system requires understanding Luttinger holes in low dimensions, which is also crucial for numerous spin-dependent phenomena, emerging field of spintronics and nanotechnology. We find that hole-doped quantum wires that are proximity coupled to a conventional s-wave superconductor is a promising system for the observation of Majorana fermions. We advanced understanding of Luttinger holes in quantum wells and quantum wires. We have shown that the vast majority of earlier treatments of Luttinger holes ignored an important effect, a mutual transformation of heavy and light holes at the heteroboundaries. We have derived the effective hole Hamiltonians in the ground size-quantized sub-bands of quantum wells and quantum wires. The effect of mutual transformation of holes is crucial for understanding Zeeman and spin-orbit coupling, and results in several spin-orbit terms linear in momentum in hole-doped quantum wires. We discuss the criterion for realizing Majorana modes in charge carrier hole systems and show that GaAs or InSb hole wires shall exhibit stronger topological superconducting pairing, providing additional opportunities for its control compared to intensively studies InSb and InAs electron systems.</div><div><br></div><div>In the second part of the thesis, I first introduce the basic facts of the current theoretical understanding of the fractional quantum Hall effect and a theoretical model of parafermion excitations. Parafermion zero modes are promising for universal quantum computing. However, physical systems that are predicted to host these exotic excitations are rare and difficult to realize in experiments. I present our work on modeling domain walls on the boundary between gate-induced polarized and unpolarized domains of the fractional quantum Hall effect system near the spin transitions, and the emergence of the parafermion zero modes when such domain wall is proximity coupled to an s-wave superconductor. Exact diagonalization of the Hamiltonian in a disk and torus geometries proves formation of the counter-propagating edge states with different spin polarizations at the boundaries between areas of the electron liquid in polarized and unpolarized filling factor $\nu=2/3$ phases. By analytical and numerical methods we find the conditions for emergence of parafermion zero modes in hybrid fractional quantum Hall/s-wave superconductor system. The phase diagram indicates that the parafermionic phase, which is represented by the six-fold ground state degeneracy, is separated from other phases by a topological phase transition. Such parafermion modes are experimentally feasible. They present a vital step toward the realization of Fibonacci anyons that allow a full universal set of quantum operations with topologically protected quasiparticles.</div><div><br></div>

The 5d transition metal oxides have drawn substantial interest for predictions of being suitable candidates for hosting exotic electronic and magnetic states, including unconventional superconductors, magnetic skyrmions, topological insulators, and Weyl semimetals. In addition to the electron-electron correlation notable in high-temperature 3d transition metal superconductors, the 5d oxides contain a large spin-orbit interaction term in their ground state, which is largely responsible for the intricate phase diagram of these materials. Iridates, or compounds containing 5d iridium bonded with oxygen, are of particular interest for their spin-orbit split Jeff = 1/2 state, which is partially filled without the presence of any additional electron correlation. However, the comparable energetics between a small, finite electron correlation energy and the spin-orbit interaction make the band structure of iridates amenable to small perturbations of the crystalline lattice and ideal for exploring the interplay between these two interactions. While altering the spin-orbit interaction strength of iridium is tenably not feasible, the electron correlation energy can be tuned using a variety of experimental techniques. In this dissertation, the electronic and magnetic properties of iridates at various electron correlation energies are studied by altering the epitaxial lattice strain, dimensionality, and the radius size of the A-site cation. These parameters tune the effective electronic bandwidth of the system, which is inversely proportional to the effective electron correlation energy. The lattice strain and the cationic radius size achieve this by altering the Ir-O-Ir bond angle between nearest neighbor Ir ions. In the case of dimensionality tuning, the effective bandwidth is controlled via the coordination number of each Ir ion. In the first study, a metal-to-insulator transition is observed in thin films of the semi-metallic SrIrO3 as in-plane compressive lattice strain is increased. This observation is consistent with the expectation of compressive lattice strain increasing the effective correlation energy; however, optical spectroscopy spectra reveal the increase is not sufficient for opening an insulating Mott gap. In the second part, the effective correlation energy is adjusted using a dimensional confinement of the layered iridate Sr2IrO4. Here, the coordination number of each Ir ion is reduced using an a-axis oriented superlattice of one-dimensional IrO2 quantum stripes, where several emergent features are revealed in its insulating Jeff = 1/2 state. In the final study, the effective correlation is tuned in a series of mixed-phase pyrochlore iridate thin films, where the Ir atoms take a corner-shared tetrahedral configuration. Here, a transition between conducting to insulating magnetic domain walls is revealed as the correlation energy is increased via A-site chemical doping. Each of these studies sheds light on the pronounced role the effective correlation energy plays in determining the local subset of phases predicted for iridates and related systems featuring strong spin-orbit interactions.

acase@tulane.edu

The problem of spin manipulation via the spin-orbit interaction in nonmagnetic semiconductors in the absence of magnetic fields is investigated in this work. We begin with a review of the literature on spin dynamics in semiconductors, then discuss the semi-empirical k ⋅ p method of calculating direct-gap semiconductor properties, which we use to estimate material parameters significant for manipulation of spin even in the absence of a magnetic field. The total effective magnetic fields and precession lengths are calculated for a variety of quantum well orientations, and a class of devices are proposed that will allow for all-electric arbitrary manipulation of spin orientations. The strain- and momentum-dependent spin splitting coefficient C3 has been calculated using a fourteen band Kane k⋅p model for a variety of III-V semiconductors as well as ZnSe and CdSe. It is observed that the spin-splitting parameters C3 and γ, corresponding to the strain-induced spin-orbit interaction and Dresselhaus coefficient, are sensitive to the value of the inter-band spin-orbit coupling Δ− between the p valence and p̄ second conduction band in all cases. The value of Δ− has therefore been recalculated in these materials using a tight-binding model and modern experimental values of the valence and second conduction band spin-orbit splittings. The total effective magnetic field and precession length of spins in strained quantum wells in the (001), (110), and (111) planes are derived with consideration for all known effective magnetic fields except those due to interface effects in non- common-atom heterostructures (native inversion asymmetry). The orientation of the k-linear Dresselhaus field and the strain-dependent fields vary strongly with the growth axis of the quantum well. The precession length in the (110) and (001) cases can achieve infinite anisotropy, while the precession length of (111) quantum wells is always isotropic. We find that the electronic spin rotation induced by drift transport around a closed path in a wide variety of nonmagnetic semiconductors at zero magnetic field depends solely on the physical path taken. Physical paths that produce any possible spin rotation due to transport around a closed path are constructed for electrons experiencing strain or electric fields in (001), (110), or (111)-grown zinc blende semiconductor quantum wells. Spin decoherence due to travel along the path is negligible compared to the background spin decoherence rate. The small size of the designed paths (< 100 nm scale in GaAs) may lead to applications in nanoscale spintronic circuits.

No description available.

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. 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)3Σu+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. The real-time quantum dynamics of wavepackets confined totwo bound states, A1Σu+(0u+) and b3Πu(0u+), 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. 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. <b>Keywords:</b>Ultrafast laser spectroscopy, pump-probetechnique, predissociation, wavepacket, pin-orbit interaction,coherent control, (pure) dephasing

No description available.