Cette thèse est consacrée à l'étude des propriétés de transport statique et dynamique du gaz d'électrons bidimensionnel supraconducteur à l'interface LaAlO3/SrTiO3. Dans un premier temps, nous étudions l'effet du désordre microscopique induit par le dopage en Chrome, sur la supraconductivité et le couplage spin-orbite en fonction de la densité de porteur modulée par effet de champ. Dans une géométrie de grille locale au-dessus du gaz, nous montrons le contrôle électrostatique de la transition supraconducteur-isolant. De même, nous analysons l'ajustement du couplage spin-orbite contrôlé par effet de champ. A l'aide de méthodes de nanofabrication par lithographie électronique, nous démontrons la première réalisation d'un point critique quantique dans LaAlO3/SrTiO3. En changeant le confinement latéral et le niveau de Fermi par effet de champ, nous sommes capables de régler le nombre de canaux conducteurs dans l'état normal et de mesurer la quantification de la conductance. Enfin, nous présentons des mesures radio-fréquence qui donnent accès aux propriétés dynamiques du gaz supraconducteur. L'évolution de la conductivité en fonction de la densité de porteurs et de la température est comparée avec la théorie standard BCS/Mattis-Bardeen d'une part, et avec la théorie BKT d'autre part. / This thesis is devoted to the study of static and dynamical transport properties of the superconducting two-dimensional electron gas at the LaAlO3/SrTiO3 interface. Under strong 2D confinement, the degeneracy of the t$_{2g}$ bands of SrTiO$_3$ is lifted at the interface, generating a rich and complex band structure. Starting from a free electron model, we derive numerically a self-consistent calculation of the potential well and the band structure (chapter 1). These simulations highlight the presence of two types of bands d$_{xy}$ and d$_{xz/yz}$ with very different transport properties. We investigate first the effect of microscopic disorder introduced by Cr doping, on superconductivity and spin-orbit coupling over a wide range of back-gate doping (chapter 3). We also describe the first implementation of a field-effect device where the superconductor-insulator transition could be continuously tuned with a top-gate. The presence of a strong spin-orbit coupling that could be controlled with the top-gate voltage is also demonstrated by analyzing the magneto-transport measurements. The gate dependence of the spin-splitting energy, of the order of a few meV, is found to be consistent with Rashba spin-orbit coupling. Going one step further in nanofabrication, we report on the first realization of a quantum point contact in LaAlO$_3$/SrTiO$_3$ using split gates (chapter 6). To go further in the understanding of the LaAlO$_3$/SrTiO$_3$ interface, we present high frequency measurements of the conductivity $\sigma$ (chapter 5). This measurement gives us access to the superfluid stiffness and to the gap energy via the BCS theory. We show that the competition between these two energy scales controls the superconducting Tc in the phase diagram.

L’objectif de ce travail de thèse est d’étudier les possibilités d’excitation, de propagation et de détection d’ondes de spin dans des couches ultraminces de Y₃Fe₅O₁₂(YIG). Pour ce faire, nous proposons d’accéder à la dynamique d’aimantation du YIG à travers l’exploitation de phénomènes de transport électronique polarisé en spin liés aux effets Hall de spin (SHE) existant au sein de métaux normaux (MN) présentant un fort couplage spin-orbite.Nous avons pour cela fait croître, par ablation laser pulsée, des films de YIG épitaxiés d’épaisseur nanométrique. En effet, le fait de pouvoir disposer de films magnétiques ultraminces est nécessaire pour ouvrir le champ d’étude du YIG à la lithographie et aux techniques de micro-fabrications de la micro-électronique en vue notamment d’applications magnoniques.L’étude de la dynamique d’aimantation de ces couches magnétiques par résonance ferromagnétique (FMR) nous a permis de quantifier la constante d’amortissement magnétique de Gilbert pour ces films. Pour les meilleurs films ayant une épaisseur de 20 nm celle-ci est de de 2*10^-4, soit une valeur comparable avec celle des films de YIG d’épaisseur micrométrique obtenus par la technique standard d’épitaxie en phase liquide et seulement un ordre de grandeur supérieure à l’amortissement du YIG massif (a=3*10^-5). Nous avons pu montrer par des mesures inductives à l’analyseur de réseau que les ondes de spin pouvaient se propager dans de tels films sur plusieurs centaines de microns, ce résultat valide la pertinence de l’emploi de couches de YIG de 20 nm d’épaisseur pour des applications magnoniques.Afin de procéder à des mesures de détection/excitation d’ondes de spin par exploitation du SHE, nous avons déposé différents métaux (Pt, Pd, CuBi) sur nos films de YIG, formant ainsi des bicouches YIG|MN. Nous avons mis en évidence la détection non locale d’ondes de spin due aux phénomènes d’effet Hall de spin inverse dans le MN et de pompage de spin dont nous avons caractérisé le paramètre de mixing conductance g à partir d’analyse de résonance ferromagnétique.Afin d’apporter un élément de réponse sur l’origine d’effets de la magnétorésistance observés dans des bicouches YIG|MN, origine intrinsèque ou extrinsèque (induite par une polarisation magnétique du MN), nous avons effectué des mesures de dichroïsme magnétique circulaire de rayons X au niveau du seuil K du Pd dans des bicouches YIG|Pd. Ces mesures indiquent l’absence de moments magnétiques induits par le YIG dans le Pd avec un seuil de détection estimé à 10^-5µB/atome. Ce résultat, associé à des mesures de magnétotransport réalisées sur les mêmes échantillons, nous a permis de montrer que le pompage de spin entre un isolant ferromagnétique et un métal non magnétique, permettait seul (sans effets de proximité magnétique) d’expliquer les effets de magnétorésistance d’effet Hall de spin observés dans ces bicouches.Nous avons étudié la dynamique d’aimantation de nanodisques de YIG et YIG|MN par microscopie à force de résonance magnétique. Cette étude a permis de montrer que la nanostructuration de ces films ne dégrade pas les paramètres a et g et permet même, grâce au confinement géométrique des modes propres de résonance, d’annuler la contribution inhomogène (DH0) à largeur de raie.Finalement, à partir de l’injection dans le MN d’un courant électrique continu, nous avons mis en évidence la possibilité de modifier (augmenter/diminuer) la largeur de raie du mode FMR d’un microdisque de YIG|MN, exploitant ainsi le couple de transfert de spin d’un courant de spin créé dans le MN par effet de Hall de spin direct. Passé une valeur critique de courant, nous avons pu activer (en l’absence d’excitation RF) un régime d’auto oscillations de l’aimantation du YIG. Ce dernier résultat qui confirme la possibilité d’exciter la dynamique d’aimantation dans le YIG par un couple de transfert de spin est très prometteur pour l’intégration des dispositifs magnoniques au sein de circuits électroniques. / The aim of this thesis is to study the excitation, the propagation and the detection of spin waves into ultrathin Y₃Fe₅O₁₂ (YIG) films. Our approach consists in interacting with the YIG magnetization dynamics thanks to spin polarized electronic transport phenomena related to spin Hall effect (SHE) that occurs within normal metals (NM) which have a large spin orbit coupling.To do so, we first grew epitaxially, by pulsed laser deposition, nanometer thick YIG films. Having ultrathin magnetic films is indeed necessary to be able to use lithography and microfabrication technics in order to develop magnonic devices.Studying these films by ferromagnetic resonance (FMR) allowed us to quantify the Gilbert magnetic damping constant, which is down to 2∙〖10〗^(-4) for the best 20 nm thick films. This value is comparable to which is reported for micrometer thick YIG films grown by liquid phase epitaxy and is only one order of magnitude higher than the bulk YIG damping (α = 3∙〖10〗^(-5)). Inductive measurements performed with a vectorial network analyzer show that spin waves can propagate over hundreds microns through such thin films. The suitability of 20 nm thick YIG films for magnonic applications is therefore confirmed by this result.In order to detect/excite spinwave by exploiting SHE, we have deposited different metals (Pt, Pd, CuBi) on our YIG films, thus obtaining YIG|NM bilayers. We have performed a nonlocal detection of spin waves based on inverse SHE and spin pumping phenomena. From the FMR analysis, we also measured the spin mixing conductance g_(↑↓) that quantify the efficiency of spin pumping.To answer the question of the origin of magnetoresistance observed into YIG|NM bilayers, intrinsic or extrinsic origin (ie. induced by the magnetic polarization of the NM), we have measured the X-ray magnetic circular dichroism of YIG|Pd bilayers at the K-edge of Pd. These measurements do not show any induced magnetic moment for YIG to Pt for a resolution of 〖10〗^(-5) μ_B/atom. Combining this result with magnetotransport measurements performed on the same samples, allowed us to show that the spin pumping between a ferromagnetic insulator and a nonmagnetic metal could explain (without any magnetic proximity effects) spin Hall magnetoresistance effects observed into these bilayers.We studied the magnetization dynamics of YIG and YIG|NM nanodisks by magnetic resonance force microscopy. This study has shown that the nanostructuration performed on these films doesn’t affect such parameters as α and g_(↑↓), the geometrical confinement even leads to suppress the linewidth inhomogeneous broadening (ΔH_0).Then, we injected a continuous electrical current through the NM. Using the spin transfer torque of the spin current thus created into the NM by direct spin Hall effect, it allowed us to modified (increased/decreased) the FMR mode’s linewidth of a YIG|NM microdisk. After reaching a critical current, we managed to enable (without any RF excitation) a regime of magnetization auto-oscillations into the YIG. This last result, which confirms the ability of exciting the YIG magnetization dynamics by spin transfer torque, is very promising for the integration of magnonic devices into electronic circuits.

L’interaction spin-orbite a permis de reproduire dans les modèles nucléaires théoriques, les nombres magiques N=28 et 50 observés dans les noyaux atomiques. Ces dernières décennies, l’étude expérimentale de noyaux exotiques a mis en évidence une évolution des nombres magiques loin de la vallée de stabilité. On peut alors se poser la question de l’évolution des potentiels d’interaction eux-mêmes, et en particulier de l’interaction spin-orbite. Si cette interaction a été historiquement incluse « à la main » dans les modèles de champ moyen « classiques », elle émerge cependant naturellement dans les modèles relativistes. La description de l’interaction spin-orbite est très similaire dans ces deux types de modèles, mais il subsiste a priori un désaccord du point de vue de sa dépendance en isospin : les modèles non-relativistes de type Hartree-Fock présentent en effet un potentiel spin-orbite dépendant fortement de l’isospin, contrairement aux modèles de type Relativistic Mean Field.En 2009, des calculs mettant en œuvre différents modèles théoriques ont prédit l’existence d’une « bulle », caractérisée par une déplétion en densité protonique centrale, dans le ³⁴Si. Ce dernier aurait une densité protonique très exotique, et bien différente de sa densité neutronique. Le ³⁴Si constituerait alors une sonde idéale de l’évolution du potentiel spin-orbite dans les systèmes présentant une forte asymétrie protons-neutrons. L’émergence d’un tel effet trouverait son origine dans la déplétion de l’orbitale protonique2s½, les orbitales s étant les seules à contribuer à la densité nucléaire centrale.Une expérience réalisée en Septembre 2012 à NSCL (MSU, Etats-Unis), a permis de mettre en évidence pour la première fois un effet de bulle nucléaire dans le ³⁴Si. L’étude des facteurs spectroscopiques des états peuplés lors des réactions d’arrachage de proton ou de neutron ³⁴Si(-1p) ³³Al et ³⁴Si(-1n) ³³Si indique que sa structure neutronique est très proche d’un système sans corrélations au-delà du champ moyen, tandis que son orbitale protonique est très faiblement occupée : n(2s½) = 0,16(4).Les réactions ³⁶S(-1p) ³⁵P et ³⁶S(-1n) ³⁵S ont été étudiées dans les mêmes conditions expérimentales. L’évolution de l’occupation n(2s½) mesurée entre le ³⁶S et le ³⁴Si, ainsi que la variation de l’écart en énergie des partenaires spin-orbite neutroniques 2p½-2p^3/2, mesurée entre ces deux noyaux dans une expérience antérieure, sont en faveur des modèles de champ moyen non-relativistes. La partie théorique de cette thèse a cependant montré que la différence de comportement de l’interaction spin-orbite entre modèles relativistes et non-relativistes est en fait un artefact causé par l’omission du terme d’échange dans les calculs de type Relativistic Mean Field. En effet, l’inclusion du terme de Fock dans les modèles relativistes permet de rétablir la dépendance en isospin du potentiel spin-orbite observée dans le cas non-relativiste. / The spin-orbit interaction is essential for the reproduction of magic numbers N=28 and 50 in theoretical nuclear models. Over the past few decades, the experimental study of exotic nuclei has highlighted an evolution of magic numbers far from stability. One can then wonder about the evolution of nuclear potentials themselves, and in particular the one of spin-orbit interaction. Historically, this interaction was included « by hand » in mean field models, whereas it naturally arises in relativistic mean field models. The description of the spin-orbit interaction happens to be very similar in those two kinds of models, but there remains a disagreement regarding its isospin dependance. Indeed, Hartree-Fock models exhibit a spin-orbit potential which strongly depends on isospin, contrary to relativistic mean field models.In 2009, a proton bubble was predicted in ³⁴Si by means of several different nuclear models. This effect consists in a central proton central density depletion. ³⁴Si would exhibit a quite exotic proton density, and very different from its neutron density. This nucleus would then constitute an ideal probe to test the behaviour of the spin-orbit potential in systems with strong proton-neutron asymmetry. The appearance of such an effect would originate from the depletion of proton 2s½ orbitals, as s orbitals are the only ones contributing to the central density.An experiment which was performed in September 2012 at NSCL (MSU, United States) highlighted for the first time a proton bubble in ³⁴Si. The spectroscopic strengths of states populated in the knockout reactions ³⁴Si(-1p)³³Al and ³⁴Si(-1n)³³Si reveal that the neutron structure of ³⁴Si is close to the one of a system without beyond-mean-field correlations, whereas its proton orbital is only weakly occupied : n(2s½) = 0,16(4).The reactions ³⁶S(-1p)³⁵P and ³⁶S(-1n)³⁵S were studied in similar experimental conditions. The change in occupancy n(2s½) measured between ³⁶S and ³⁴Si, as well as the variation in the neutron spin-orbit splitting 2p½-2p^3/2 measured in an earlier experiment, suggest that non-relativistic models exhibit the right isospin dependance. The theoretical part of this thesis showed however that the difference in behaviour of the spin-orbit interaction between relativistic and non-relativistic model is actually an artefact caused by the omission of the exchange term in relativistic mean field calculations. Indeed, including the Fock term in relativistic models enables to restore the isospin dependance observed in the non-relativistic case.

Cette thèse porte sur l’étude de la génération, la propagation et la détection d’ondes de spin dans des nanostructures et microstructures élaborées à partir de couches ultra-minces (quelques nanomètres d’épaisseur) de Y₃Fe₅O₁₂ (YIG). Ce travail se trouve à l’interface entre deux thématiques du magnétisme : la magnonique et la spintronique. Grâce aux effets spin-orbite dans des microstrutures YIG|Pt, il a été possible d’étudier et de manipuler la dynamique d’aimantation du YIG, un matériau utilisé de longues dates sous forme de films épais ou billes pour ses très faibles pertes magnétiques. Ce travail ouvre la voie au développement de circuits magnoniques submicroniques soit pour le traitement des signaux hyperfréquences pour les applications télécom soit pour la réalisation de circuits logiques dans la perspective du remplacement de la technologie CMOS (beyond-CMOS). Ce travail repose sur une expertise dans la croissance de films de YIG développée au laboratoire. Les couches ultra-minces de YIG ont été élaborées par ablation laser pulsée. Pour les meilleurs films ayant une épaisseur de 20 nm, la constante d’amortissement de Gilbert caractérisant les pertes des films, estimée par résonance ferromagnétique, est typiquement de α=3x10⁻ 4. Cette avancée cruciale sur l’aspect matériau a ouvert au début de ma thèse un champ de possibilités pour la réalisation et l’étude de dispositifs magnoniques. En effet, la diminution des épaisseurs a permis d’ouvrir le YIG au domaine de la micro/nanofabrication, levant ainsi un verrou technologique vieux de plusieurs décennies. Nous avons donc pu montrer par des mesures inductives et optiques que la propagation d’ondes de spin dans des guides d’onde de YIG de 20 nm d’épaisseur pouvait être faite sur plusieurs dizaines de microns. Prouvant que la structuration des films de YIG n’altère pas la propagation des ondes de spin ouvrant la voie vers la réalisation de circuits magnoniques plus complexes. En structurant ces films de YIG pour obtenir des cristaux magnoniques, il est possible de générer une modulation spatiale du potentiel vu par les ondes de spin, se traduisant par l’apparition de bande interdite (ou gap) dans la transmittance de fréquences. L’étude de la propagation des ondes de spin dans un cristal a montré l’apparition d’un gap par des mesures BLS, accompagnée par une augmentation de l’atténuation pour la longueur d’onde de Bragg. Pour la première fois dans des films ultra-minces de YIG, ce gap montre la possibilité de réaliser une fonctionnalité de filtrage fréquentiel. La preuve de concept a été validée pour un cristal magnonique adapté pour l’intégration à des dispositifs magnoniques. Afin de manipuler et exciter la dynamique d’aimantation du YIG, nous avons dans une deuxième partie réalisée des microstructures à base de bicouche YIG|Pt. L’injection d’un courant électrique dans le Pt donne naissance, grâce à l’effet Hall de spin, à une accumulation de spin qui se couple à l’interface avec l’aimantation du YIG et permet ainsi d’exercer un couple de transfert de spin (STT) et de générer une dynamique d’aimantation du YIG. Nous avons mis en évidence la modulation d’un facteur cinq de la longueur d’atténuation des ondes de spin se propageant dans une piste YIG|Pt grâce à l’amplification des ondes de spin par STT. Ce contrôle efficace de l’atténuation s’avère très intéressant pour le transport d’information porté par les ondes de spin, afin d’amplifier ou supprimer les ondes de spin et donc sélectionner l’information transmise. Par ailleurs, au-delà d’un courant critique d’injection, nous avons pu observer des auto-oscillations de l’aimantation du YIG à la fois dans des plots ou des pistes. Ce résultat confirme la possibilité d’exciter électriquement la dynamique d’aimantation du YIG par STT. Une étude rigoureuse de ce régime a été effectuée dans des microdisques YIG|Pt pour déterminer le comportement des auto-oscillations et imager les modes d’ondes de spin excités dans le YIG. / The aim of this thesis is to study the generation, propagation and detection of spin waves in nanostructures and microstrutures based on ultrathin (a few nanometers thickness) Y₃Fe₅O₁₂ (YIG) films. This work is at the interface between two fields of magnetism: magnonics and spintronics. Thanks to spin-orbit effects in YIG|Pt microstructures, it has been possible to study and manipulate YIG magnetization dynamic, a material known and used for a long time as thick films or spheres due to its very low magnetic losses. This work opens the path towards the development of submicronic magnonic circuits either for processing radiofrequency signals of for the realization of spin waves logic devices for a future beyond-CMOS technology. Prior to the present work, a significant efforts have been made in the lab to grow epitaxial nanometer thick YIG films by pulsed laser deposition (PLD). It was possible to reduce the film thickness down to a few nanometers while preserving excellent magnetic properties. For the best YIG films having a thickness of 20 nm, ferromagnetic resonance measurements yield a Gilbert magnetic damping of α=3x10⁻ 4 . This value is comparable to micrometer thick YIG films grown by liquid phase epitaxy (LPE). This important step forward on the material aspect opened new possibilities for the realization of magnonic devices that can have a large impact on the ICT industry. Indeed, microfabrication of YIG is now possible thanks to the advent of high quality nanometer thick YIG films. Thus, we have observed the propagation of spin waves in 20-nm thick, 2.5 µm wide YIG waveguides over large distances using inductive and optical detection. Spin-wave propagation characteristics are not affected by microstructuration opening the path to the reliable design of complex magnonic circuits.By structuring YIG films to obtain magnonic crystals, it is possible to generate spatial modulation of the potential seen by spin waves, resulting in the appearance of gaps in the transmittance in frequency. To do so, magnonic crystals implemented in form of microscopic waveguides whose width is periodically varied, were fabricated. The study of spin-wave propagation showed the appearance of a gap accompanied by an increase of the spin-wave attenuation length due to Bragg reflection. For the first time in ultrathin YIG films, this gap shows the possibility to realize radiofrequency filtering. In order to manipulate and excite YIG magnetization dynamics, we have designed YIG|Pt microstructures either stripes or microdisks. Thanks to the spin Hall effect, an electrical current passing in Pt generates a transverse spin accumulation coupled at the interface to the YIG’s magnetization making it possible to exert spin transfer torque (STT). We have highlighted an efficient modulation, by a factor of five, of the spin-wave attenuation length. This control on the decay constant proves to be very interesting for the transport of information using spin waves as data carriers, in order to be able to amplify or suppress spin waves and to select transmitted information. In addition, beyond a critical current, we have induced auto-oscillations of YIG magnetization, either in stripes of microdisks, confirming the possibility to electrically excite YIG magnetization dynamics using STT. A rigorous study of this nonlinear regime has been carried out in YIG|Pt microdisks to determine auto-oscillations behavior and to observe directly dynamic modes excited in YIG.

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.

Highly correlated quantum chemical methods have been appliedto study the photophysical properties of substituted benzenes.With the inclusion of spin-orbit coupling, the phosphorescencesof these molecules have been calculated usingMulti-CongurationalSelf- Consistent Field (MCSCF) quadraticresponse theory. The Herzberg-Teller approximation has beenadopted to evaluate the vibronic contributions tophosphorescence. The performance of hybrid density functional theory (DFT) atthe B3LYP level is examined in comparison to the MP2, CCSD andCCSD(T) methods for the geometry and permanent dipole moment ofp-aminobenzoic acid. The time-dependent DFT/B3LYP method isapplied to calculate the two-photon absorption of a series ofZinc-porphyrin derivatives in combination with a two-statemodel. The transitions between excited singlet and tripletstates of Zinc and Platinum based organometallic compounds havebeen computed using DFT quadratic response theory. The resultsare used to simulate the non-linear propagation of laser pulsesthrough these materials utilizing a dynamical wave propagationmethod.

No description available.

I derive and apply quantum propagator techniques to atomic and condensed matter systems. I observe many interesting features by following the evolution of a wavepacket. In atomic systems, I revisit the Stern-Gerlach effect and study the spin dynamics inside an inhomogeneous magnetic field. The results I obtained are not exactly the same as the textbook description of the effect which is usually a manifestation of a perfect space and spin entanglement. This discovery can provide insight on more reliable quantum computation device designs. In condensed matter systems, the doping concentration inhomogeneity leads to the Rashba spin-orbit interaction. This makes it possible to control the spin without the external magnetic field. By propagating the wave packet in systems exhibiting Rashba spin-orbit interactions, I discover several features such as spin separation, spin accumulation, persistent spin-helix, and ripple formation.

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」 / 京都大学 / 新制・課程博士 / 博士(工学) / 甲第24891号 / 工博第5171号 / 新制||工||1987(附属図書館) / 京都大学大学院工学研究科電子工学専攻 / (主査)教授 白石 誠司, 准教授 掛谷 一弘, 教授 小野 輝男, 教授 森山 貴広 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The experimental pieces of evidence for the existence of Majorana states in topo- logical superconductors have so far been inconclusive despite intense research in the past two decades [Zha+20; Kay+20]. Combined with promising applications in quantum computing [Nay+08; Ali+11] and the resulting technological development of society, the elusiveness of Majorana states keeps motivating theoretical and ex- perimental research to this day. Our analytical findings and numerical explorations in new topological superconducting platforms suggest several tools and solutions for their future realisation in condensed matter systems. The planar Josephson junction (pJJ) introduced in 2017 by F. Pientka et al. [Pie+17] and M. Hell et al. [HLF17] is a versatile platform for topological superconductivity. It harnesses the tunability of the superconducting phase difference across the Josephson junction as an external control parameter that switches the pJJ between the trivial and topological phases of matter. The junction between the (trivial) superconductors is quasi-one-dimensional and hosts one new Majorana zero mode at each of its ends following each topological phase transition. However, the creation of a second Majorana zero mode on one end triggers a return to the trivial regime as both zero modes hybridize into a regular non-topological fermion. It is then crucial to identify the model parameters that lead to topological phases with a single Majorana state per end. Our main result on the pJJ establishes the general constraint on its microscopic parameters—including the phase difference and a magnetic field—to cross the topo- logical phase transitions. The identification of sectors in parameter space leading to a single Majorana mode becomes then straightforward. In some limits the pJJ develops a topological sector at small magnetic field for a phase difference close to the value p while it remains trivial at the same field near zero phase difference. Since the phase is sufficient to turn on and off the topology, we call this feature “switchable topology”. Looking for switchable topology is experimentally relevant as it makes the topology easily tunable while keeping intact the proximitized su- perconductivity otherwise jeopardized by the applied field. Concretely, we found switchable topology in three configurations: in wide junctions with a transparent interface with the superconducting regions, in fine-tuned narrow junctions weakly coupled to the superconducting regions, and in junctions with a strong Zeeman energy when they are ultranarrow and transparent. Thanks to our exact analytical results, setups interpolating between these limits can adjust the desired properties at will. The other important finding about the pJJ concerns the stability of its topological phases, by which we mean the presence of a sizable spectral gap in the topological sector. We observed that the Rashba spin-orbit coupling is responsible for strongly decreasing the gap in the relevant topological sector at low Zeeman field, but sym- metry arguments justify that wide, transparent junctions are generically immune to this effect for large enough Rashba coupling. After 2017, other platforms started to use the Josephson superconducting phase difference as a knob to trigger topological superconductivity [Liu+19; JY21]. We introduce here the stacked Josephson junction (sJJ) as a new platform for topological superconductivity, which is made of two non-centrosymmetric superconductors sandwiching a two-dimensional magnet around which chiral Majorana edge modes propagate. Unlike the Majorana zero modes in the pJJ, chiral Majorana modes can add to each other if they propagate in the same direction, as indicated by the integer Chern number of their topological phase. The bulk-edge correspondence, however, only constrains the net number of topological edge states and allows room for other non-topological states to coexist with the chiral Majorana states without interacting with them. We found that the presence of trivial chiral edge modes in the sJJ restricts access to the Majorana states themselves. The symmetry protection of the trivial modes, fortunately, disappears with an in-plane magnetic field applied through the magnet or with superconducting leads different on the top and at the bottom of the stacked junction. The theoretical investigations of topological platforms have currently outnum- bered the experiments with convincing signatures of Majorana edge states. This imbalance calls for new ways to probe the agreement between topological models and laboratory setups. The critical current of a Josephson junction acts as a link between the microscopic description and macroscopic observables. Thermoelectric measurements, which distinguish between supercurrent and quasiparticle current, modify this model-dependent connection, and would provide an electrical probe to estimate the validity of a model like that of the pJJ. We computed the contribution to the thermoelectric coefficient of the bulk states of a uniform superconductor, that has a similar environment to that of the pJJ (i.e., Rashba coupling and in-plane Zeeman field). The results were not conclusive and motivated us to suggest new analytical and numerical approaches to obtain the thermoelectric response of the pJJ, in particular by including the contribution of the Andreev bound states and non-linear effects.:Foreword — how to read this thesis 1 Preamble A popular short story: pencils and lightbulbs 5 Basics and concepts 1 Introduction to Majorana physics 13 1.1 The electrons & their properties 13 1.1.1 Hamiltonian for the planar Josephson junction 17 1.2 The scattering matrix for bound states 19 1.3 Andreev bound states for topology 24 1.4 Topological superconductivity & Majorana edge states 28 1.5 Induced topological superconductivity 34 1.6 Summary 36 Appendices 37 1.A Microscopic dynamics 37 1.A.1 Origin of spin–orbit coupling 37 1.A.2 Bogoliubov-deGennes symmetrization 37 1.A.3 Andreev reflection below the coherence length 38 1.A.4 Proximity-induced superconductivity 40 1.A.5 From s- to p-wave superconductivity 41 1.B Scattering theory for bound states 44 1.B.1 Bound states as trapped waves 44 1.B.2 Scattering theory for an open region 45 1.B.3 Scattering theory for two open regions 46 1.B.4 Bound states recovered from an open region 47 1.B.5 Numerical scattering theory for bound states 48 2 Perspectives on electronic transport 53 2.1 Electric current in a metal 53 2.2 Quantum-mechanical current 54 2.2.1 Expression for the microscopic current 55 2.3 Thermoelectric current 57 2.3.1 The Boltzmann transport equation 61 2.4 Supercurrents and the superconducting coherence phase 64 2.4.1 Josephson currents 67 Appendices 71 2.A Electric current from a potential difference 71 2.B Scattering and current 71 2.C Hole-based current in metals 73 Introduction Introduction to the Research Projects 77 i Topological properties of Josephson junctions 3 Switchable topology in the planar Josephson junction 85 Motivation & Overview of the Study 85 3.1 The planar Josephson junction and the nanowire setup 87 3.1.1 Comparison with the nanowire setup. 89 3.2 Model 92 3.3 General formula for the phase transitions 94 3.3.1 Spin decoupling for the phase transitions 96 3.3.2 Exact reflection coefficients 97 3.3.3 Exact scattering formula and Andreev reflectivity 98 3.3.4 Andreev approximation 100 3.3.5 Dimensionless formulation 101 3.3.6 Numerical and analytical checks 103 3.4 Three regimes for switchable topology 105 3.4.1 Diamond-shape regime 108 3.4.2 V-shape regime 110 3.4.3 Nanowire regime 111 3.4.4 Summary: extent of the topological transitions 114 3.5 Avoiding regimes with a small topological gap 117 3.5.1 Gapless lines as BDI phase transitions 119 3.5.2 Opening the gap in f = p 120 3.5.3 Role of the Rashba coupling 121 3.6 Conclusion 125 Appendices 129 3.A Limiting cases of the pJJ 129 3.A.1 Andreev approximation 129 3.A.2 Small field limit 131 3.A.3 Delta-barrier junction 131 3.A.4 Semiconductor nanowire 132 3.B Normal reflection via surface impurity and surface refraction 134 3.C Symmetry-constrained gap closings 136 3.D Linear deviation of the gapless line near f = p 138 3.E Calculations for the scattering formula 141 3.E.1 Boundary conditions 141 3.E.2 Combinations of scattering coefficients 142 3.E.3 Andreev coefficients for the phase transitions 143 3.E.4 Formula for B > μ 145 4 Topological and trivial chiral states in the stacked Josephson junction 147 Motivation & Overview of the Study 147 4.1 The basics of the stacked Josephson junction 149 4.2 Continuous and lattice models 151 4.3 Topological index 155 4.3.1 Methodology for the Chern number 155 4.3.2 Interpretation of the results 156 4.4 Topological and trivial edge states 162 4.5 BDI phase transitions 167 4.5.1 Dimensional reduction 168 4.5.2 Link between topological invariants 170 4.5.3 Explaining the low-energy sector 171 4.6 Conclusion 174 Appendices 177 4.A Symmetries of the Hamiltonian 177 4.A.1 Class D 177 4.A.2 Class BDI 177 4.A.3 Gapless line in f = p 178 4.A.4 Symmetry around f = p 179 4.B The parity index in 2D TSC 180 ii Transport properties of the planar Josephson junction 5 An approach to thermoelectric effects in the planar Josephson junction 183 Motivation & Overview of the Study 183 5.1 From the Josephson junction to a homogeneous superconductor 185 5.2 Model and Phenomenology 187 5.2.1 Homogeneous superconductor 187 5.2.2 Analytical spectrum and two-surface approximation 188 5.2.3 Magnetoelectric supercurrent: phenomenology 191 5.3 Electric current in a spin–orbit coupled superconductor 194 5.3.1 Formula for the current 196 5.3.2 Zero-temperature current 198 5.3.3 Small perturbations at finite temperature 200 5.4 Thermoelectric current in a spin–orbit coupled superconductor 206 5.4.1 Distribution imbalance under temperature bias 208 5.4.2 Explicit formula for the thermoelectric current 209 5.5 Discussion and Outlook 213 Appendices 219 5.A The Boltzmann equation in temperature-biased superconductors 219 5.A.1 The linear approximation 220 5.A.2 The low-temperature approximation 220 5.A.3 Integral solution of the Boltzmann equation 223 5.B Diagonalisation of the planar superconductor 225 5.B.1 Eigenstates of spin–orbit coupled superconductor 225 5.B.2 Eigenstates with a small Zeeman field 227 Conclusion Majorana quasiparticles in Josephson junctions 233 Extra Material 6 Mathematical details of Scattering theory 241 6.1 Asymmetric quantum well 241 6.2 Scattering theory for an open region 243 6.2.1 Change in potential over a small region 243 6.2.2 Change in spin-orbit coupling over a small region 245 6.2.3 Change in mass over a small region 245 7 Numerical codes for chapter 4 247 7.1 BDI index 247 7.2 Chern number 255 7.3 Spectral gap 257 7.4 Localized edge states 258 8 Short courses 261 8.1 Two formulations of superconductivity 261 8.1.1 The BCS Hamiltonian 261 8.1.2 The Bogoliubov transformation 263 8.1.3 Bogoliubov-de Gennes symmetrization 264 8.1.4 Building the semiconductor representation 266 8.2 Topological band theory 270 8.3 Majorana physics in 1D 274 8.3.1 The SSH chain 275 8.3.2 The Kitaev chain 277 Bibliography 283