Autonomous navigation is the determination of satellites position and velocity vectors onboard the satellite, using the measurements available onboard. The orbital information of a satellite needs to be obtained to support different house keeping operations such as routine tracking for health monitoring, payload data processing and annotation, orbit manoeuver planning, and prediction of intrusion in various sensors' field of view by celestial bodies like Sun, Moon etc. Determination of the satellites orbital parameters is done in a number of ways using a variety of measurements. These measurements may originate from ground based systems as range and range rate measurements, or from another satellite as in the case of GPS (Global Positioning System) and TDUSS (Tracking Data Relay Satellite Systems), or from the same satellite by using sensors like horizon sensor^ sun sensor, star tracker, landmark tracker etc. Depending upon the measurement errors, sampling rates, and adequacy of the estimation scheme, the navigation accuracy can be anywhere in the range of 10m - 10 kms in absolute location. A wide variety of tracking sensors have been proposed in the literature for autonomous navigation. They are broadly classified as (1) Satellite-satellite tracking, (2) Ground- satellite tracking, (3) fully autonomous tracking. Of the various navigation sensors, it may be cost effective to use existing onboard sensors which are well proven in space. Hence, in the current thesis, the Horizon scanner is employed as the primary navigation sensor-. It has been shown in the literature that by using horizon sensors and gyros, a high accuracy pointing of the order of .01 - .03 deg can be achieved in the case of low earth orbits. Motivated by such a fact, the current thesis deals with autonomous orbit determination using measurements from the horizon sensors with the assumption that the attitude is known to the above quoted accuracies. The horizon scanners are mounted on either side of the yaw axis in the pitch yaw plane at an angle of 70 deg with respect to the yaw axis. The Field Of View (FOV) moves about the scanner axis on a cone of 45 deg half cone angle. During each scan, the FOV generates two horizon points, one at the space-Earth entry and the other at the Earth-space exit. The horizon points, therefore, lie• on the edge of the Earth disc seen by the satellite. For a spherical earth, a minimum of three such horizon points are needed to estimate the angular radius and the center of the circular horizon disc. Since a total of four horizon points are available from a pair of scanners, they can be used to extract the satellite-earth distance and direction.These horizon points are corrupted by noise due to uncertainties in the Earth's radiation pattern, detector mechanism, the truncation and roundoff errors due to digitisation of the measurements. Owing to the finite spin rate of the scanning mechanism, the measurements are available at discrete time intervals. Thus a filtering algorithm with appropriate state dynamics becomes essential to handle the •noise in the measurements, to obtain the best estimate and to propagate the state between the measurements. The orbit of a low earth satellite can be represented by either a state vector (position and velocity vectors in inertial frame) or Keplerian elements. The choice depends upon the available processors, functions and the end use of the estimated orbit information. It is shown in the thesis that position and velocity vectors in inertial frame or the position vector in local reference frame, do result in a simplified, state representation. By using the f and g series method for inertial position and velocity, the state propagation is achieved in linear form. i.e. Xk+1 = AXK where X is the state (position, velocity) and A the state transition matrix derived from 'f' and 'g' series. The configuration of a 3 axis stabilised spacecraft with two horizon scanners is used to simulate the measurements. As a step towards establishing the feasibility of extracting the orbital parameters, the governing equations are formulated to compute the satellite-earth vector from the four horizon points generated by a pair of Horizon Scanners in the presence of measurement noise. Using these derived satellite-earth vectors as measurements, Kalman filter equations are developed, where both the state and measurements equations are linear. Based on simulations, it is shown that a position accuracy of about 2 kms can be achieved. Additionally, the effect of sudden disturbances like substantial slewing of the solar panels prior and after the payload operations are also analysed. It is shown that a relatively simple Low Pass Filter (LPF) in the measurements loop with a cut-off frequency of 10 Wo (Wo = orbital frequency) effectively suppresses the high frequency effects from sudden disturbances which otherwise camouflage the navigational information content of the signal. Then Kalman filter can continue to estimate the orbit with the same kind of accuracy as before without recourse to re-tuning of covariance matrices. Having established the feasibility of extracting the orbit information, the next step is to treat the measurements in its original form, namely, the non-linear form. The entry or exit timing pulses generated by the scanner when multiplied by the scan rate yield entry or exit azimuth angles in the scanner frame of reference, which in turn represents an effective measurement variable. These azimuth angles are obtained as inverse trigonometric functions of the satellite-earth vector. Thus the horizon scanner measurements are non-linear functions of the orbital state. The analytical equations for the horizon points as seen in the body frame are derived, first for a spherical earth case. To account for the oblate shape of the earth, a simple one step correction algorithm is developed to calculate the horizon points. The horizon points calculated from this simple algorithm matches well with the ones from accurate model within a bound of 5%. Since the horizon points (measurements) are non-linear functions of the state, an Extended Kalman Filter (EKF) is employed for state estimation. Through various simulation runs, it is observed that the along track state has got poor observability when the four horizon points are treated as measurements in their original form, as against the derived satellite-earth vector in the earlier strategy. This is also substantiated by means of condition number of the observability matrix. In order to examine this problem in detail, the observability of the three modes such as along-track, radial, and cross-track components (i.e. the local orbit frame of reference) are analysed. This difficulty in observability is obviated when an additional sensor is used in the roll-yaw plane. Subsequently the simulation studies are carried out with two scanners in pitch-yaw plane and one scanner in the roll-yaw plane (ie. a total of 6 horizon points at each time). Based on the simulations, it is shown that the achievable accuracy in absolute position is about 2 kms.- Since the scanner in the roll-yaw plane is susceptible to dazzling by Sun, the effect of data breaks due to sensor inhibition is also analysed. It is further established that such data breaks do not improve the accuracy of the estimates of the along-track component during the transient phase. However, filter does not diverge during this period. Following the analysis of the' filter performance, influence of Earth's oblateness on the measurement model studied. It is observed that the error in horizon points, due to spherical Earth approximation behave like a sinusoid of twice the orbital frequency alongwith a bias of about 0.21° in the case of a 900 kms sun synchronous orbit. The error in the 6 horizon points is shown to give rise to 6 sinusoids. Since the measurement model for a spherical earth is the simplest one, the feasibility of estimating these sinusoids along with the orbital state forms the next part of the thesis. Each sinusoid along with the bias is represented as a 3 state recursive equation in the following form where i refers to the ith sinusoid and T the sampling interval. The augmented or composite state variable X consists of bias, Sine and Cosine components of the sinusoids. The 6 sinusoids together with the three dimensional orbital position vector in local coordinate frame then lead to a 21 state augmented Kalman Filter. With the 21 state filter, observability problems are experienced. Hence the magnetic field strength, which is a function of radial distance as measured by an onboard magnetometer is proposed as additional measurement. Subsequently, on using 6 horizon point measurements and the radial distance measurements obtained from a magnetometer and taking advantage of relationships between sinusoids, it is shown that a ten state filter (ie. 3 local orbital states, one bias and 3 zero mean sinusoids) can effectively function as an onboard orbit filter. The filter performance is investigated for circular as well as low eccentricity orbits. The 10-state filter is shown to exhibit a lag while following the radial component in case of low eccentricity orbits. This deficiency is overcome by introducing two more states, namely the radial velocity and acceleration thus resulting in a 12-state filter. Simulation studies reveal that the 12-state filter performance is very good for low eccentricity orbits. The lag observed in 10-state filter is totally removed. Besides, the 12-state filter is able to follow the changes in orbit due to orbital manoeuvers which are part of orbit acquisition plans for any mission.

Afin de réduire la consommation de puissance des futures générations de systèmesélectroniques, une solution est d’intégrer de la non-volatilité au sein même des cellulesmémoires. Dans cette optique, l’utilisation du retournement de l’aimantation d’un matériauferromagnétique comme support de l’information a été utilisée initialement dans un conceptde mémoire, la MRAM. La dernière évolution de cette technologie, la SOT-RAM, utilise desphénomènes nouveaux appelés SOTs afin de contrôler la direction de l’aimantation. Parrapport aux générations précédentes (STT-MRAM notamment), elle devrait permettred’améliorer la vitesse d’écriture en conservant une endurance adaptée pour des utilisations enmémoires cache où en mémoire centrale. Le terme SOTs est une dénomination généraledésignant l’ensemble des effets, encore mal connus, liés au couplage spin-orbite et permettantle retournement de l’aimantation d’une cellule mémoire.Ce travail de thèse a eu pour objectif d’étudier les SOTs via un système expérimental demesure quasi-statique basé sur les effets Hall extraordinaires et planaires. Sonimplémentation et la méthode d’analyse associée, ainsi que les considérations théoriquesnécessaires à l’interprétation des résultats sont détaillées dans ce manuscrit. Il a été montréque le retournement de l’aimantation dans des systèmes à aimantation perpendiculaire à basede cobalt-platine ne peut être expliqué par les modèles simples considérés jusqu’à présentdans la littérature. En effet, il a été mis en évidence qu’au moins deux effets simultanés doiventêtre pris en compte pour expliquer les phénomènes observés. Par ailleurs, ceux-ci présententune sensibilité différente à la fois à une altération de la structure cristalline et à une variationde température. / In order to reduce power consumption in next generations’ electronic devices, one potentialsolution is to implement non-volatility in memory cells. In this goal, the magnetizationswitching of a ferromagnetic material has been used in a memory concept: the MRAM. Thelatest development of this technology, called SOT-RAM, is based on new phenomena calledSOTs (Spin-Orbit Torques) in order to control magnetization direction. Contrary to precedentgenerations (STT-MRAM), it should achieve a higher operating speed and an enduranceadapted for cache and main memories applications. SOTs is a generic term referring to all theeffects, linked to the spin-orbit interaction, and that enable magnetization reversal. They areyet not perfectly understood.The main objective of this Ph.D. was then to study these SOTs through a quasi-staticexperimental measurement setup based on anomalous and planar Hall effects. Itsimplementation and the associated analysis method, as well as the required theoreticalconsiderations for data interpretation are detailed in this manuscript. It has been highlightedthat magnetization switching in perpendicularly magnetization cobalt-platinum systemscannot be explained by the simple models considered thus far in the literature. As a matter offact it has been evidenced that at least two effects have to be considered in order to explainobserved phenomena. In addition, they present different susceptibility both to a modificationof the crystal structure and to a temperature change.

The successful completion of the Hiten mission in 1991 provided real-world validation of a class of trajectories defined as ballistic lunar capture transfers. This class of transfers is often considered for missions to the Moon and for tours of the moons of other planets. In this study, the dynamics of the three and four body problems are examined to better explain the mechanisms of low energy transfers in the Earth-Moon system, and to determine their optimality. Families of periodic orbits in the restricted Earth-Sun-spacecraft three body problem are shown to be generating families for low energy transfers between orbits of the Earth. The low energy orbit-to-orbit transfers are shown to require less fuel than optimal direct transfers between the same orbits in the Earth-Sun-spacecraft circular restricted three body problem. The low energy transfers are categorized based on their generating family and the number of flybys in the reference three body trajectory. The practical application of these generating families to spacecraft mission design is demonstrated through a robust nonlinear targeting algorithm for finding Sun-Earth- Moon-spacecraft four body transfers based on startup transfers indentified in the Earth- Sun three body problem. The local optimality of the transfers is examined through use of Lawden’s primer vector theory, and new conditions of optimality for single-impulse-to-capture lunar transfers are established. / text

Orbital debris poses a serious threat to ongoing operations in space.  Recognising this threat, the European Commission has funded the three-year Technology for Self Removal (TeSeR) project with the goal of developing a standard scalable Post Mission Disposal (PMD) module to remove satellites from orbit following the completion of their mission.  As the project coordinator and key member of the TeSeR Project, Airbus Defence and Space Germany will invest significant resources in achieving this goal over the course of the project. This thesis details the initial analysis of potential PMD module designs conducted by the author during an internship within the AOCS/GNC department of Airbus Defence and Space Friedrichshafen between 1 April 2016 and 31 August 2016.  Three main concepts, drag sails, drag balloons and Electrodynamic Tethers (EDTs), were evaluated during this time with an emphasis on determining the ability of each design to permit passive attitude stabilisation of the satellite during PMD.  Following the required modification of a pre-existing MATLAB/Simulink model, several key findings were made for each device concept.  It was found that no drag sail designs investigated permitted passive aerodynamic attitude stabilisation at orbit heights above 550 km.  When deorbiting from 800 km, however, the lack of the desired and stable attitude was not found to have a significant increase on the deorbit time or the area‑time product. Drag balloon designs were predicted to be comparatively unstable and less mass efficient for deorbiting purposes, with area‑time products up to approximately 50 per cent higher than the equivalent mass drag sail designs.  In spite of this, unstable drag balloons were found to provide shorter deorbit times than stable balloons due to the contribution of the satellite body and solar array to the total frontal area of the satellite.  This indicated that attitude stabilisation is not required for satellites equipped with drag balloon devices. Modelling of bare EDTs suggested that tethers with lengths of 1000 metres or more would not permit passive attitude stabilisation at an orbit height of 800 km.  Simulation of a 500 metre EDT, however, indicated that passive attitude stabilisation can be achieved with EDT devices and proved that EDTs can generate significantly higher drag forces than aerodynamic devices while possessing a significantly lower device mass.  Following the analysis of these results, a recommendation was made for future work to be aimed at improving the EDT model used in this investigation.

This thesis investigates the use of the Swedish Allsky Meteor Network (SAMN) for observing, identifying, and determining the orbits of satellites. The overall goal of this project is to determine the feasibility of using such a network for Space Situational Awareness (SSA) purposes, which requires identification and monitoring of objects in orbit. This thesis is a collaboration with the Swedish Defense Research Agency (FOI) to support their efforts in SSA. Within the frame of this project, the author developed software that can take data of observations of an object collected from the all-sky cameras of SAMN and do an Initial Orbit Determination (IOD) of the object. An algorithm that improves the results of the IOD was developed and integrated into the software. The software can also identify the object if it is in a database that the program has access to or, if it could not be identified, make an approximate prediction of when and where the object will be visible again the next time it flies over. A program that analyses the stability of the results of the IOD was also developed. This measures the spread in results of the IOD when a small amount of artificial noise is added to one or more of the observed coordinates in the sky. It was found that using multiple cameras at different locations greatly improves the stability of the solutions. Gauss' method was used for doing the IODs. The advantages and disadvantages of using this method are discussed, and ultimately other methods, such as the Gooding method or Double R iteration, are recommended for future works. This is mostly because Gauss' method has a singularity when all three lines of sight from observer to object lie in the same plane, which makes the results unreliable. The software was tested on a number of observations, both synthetic and real, and the results were compared against known data from public databases. It was found that these techniques can, with some changes, be used for doing IOD and satellite identification, but that doing very accurate position determination required for full orbit determination is not feasible. / Detta examensarbete undersöker möjligheterna att använda ett svenskt nätverk av allskykameror kallat SAMN (Swedish Allsky Meteor Network) för att observera, identifiera och banbestämma satelliter. Det övergripande målet med detta projekt är att bestämma hur användbart ett sådant nätverk skulle vara för att skapa en rymdlägesbild, vilken i sin tur kräver bevakning och identifikation av objekt som ligger i omloppsbana. Detta examensarbete är ett samarbete mellan Uppsala Universitet och FOI (Totalförsvarets Forskningsinstitut). Inom ramen för detta projekt har författaren utvecklat mjukvara som kan ta data från observationer av objekt utförda av SAMN och göra initiala banbestämningar av objekten. En algoritm som förbättrar resultaten av den initiala banbestämningen utvecklades och integrerades i programmen. Programmen kan också identifiera satelliter om de finns med i en databas som programmet har tillgång till eller förutsäga objektets nästa passage över observatören om det inte kunde identifieras. Ett annat program som analyserar känsligheten av resultaten av den initiala banbestämningen utvecklades också. Detta program mäter spridningen i resultat som orsakas av små störningar i de observerade koordinaterna på himlen. Det framkom att stabiliteten av resultaten kan förbättras avsevärt genom att använda flera observatörer på olika orter. I detta projekt användes Gauss metod för att göra banbestämningarna. Metodens för- och nackdelar diskuteras och i slutänden rekommenderas istället andra metoder, som Goodings metod eller Dubbel R-iteration, för framtida arbeten. Detta beror mest på att Gauss metod innehåller en singularitet när alla siktlinjer från observatören till objektet ligger i samma plan som varandra vilket gör resultaten opålitliga i de fallen. Programmen testkördes på ett antal olika observationer, både artificiella och verkliga, och resultaten jämfördes med kända positioner. Slutsatsen av arbetet är att de undersökta teknikerna kan, med vissa modifikationer, användas för att göra initiala banbestämningar och satellitidentifikationer, men att göra de väldigt precisa positionsbestämningarna som krävs för fullständig banbestämning är inte genomförbart.

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.

An integral part of NASA's vision for the coming years is a sustained infrastructure in cislunar space. The current baseline trajectory for this facility is a Near Rectilinear Halo Orbit (NRHO), a periodic orbit in the Circular Restricted Three-Body Problem. One of the goals of the facility is to serve as a proving ground for human spaceflight operations in deep space. Thus, this investigation focuses on transfers between the baseline NRHO and a family of periodic orbits that originate from a period-doubling bifurcation along the halo family. This new family of orbits has been termed the ``butterfly" family. This investigation also provides an overview of the evolution for a large subset of the butterfly family. Transfers to multiple subsets of the family are found by leveraging different design strategies and techniques from dynamical systems theory. The different design strategies are discussed in detail, and the transfers to each of these regions are compared in terms of propellant costs and times of flight.

Thesis (MEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Throughout its lifetime in space, a spacecraft is exposed to risk of collision with orbital debris or operational satellites. This risk is especially high within the Low Earth Orbit (LEO) region where the highest density of space debris is accumulated. This study investigates orbital decay of some LEO micro-satellites and accelerating orbit decay by using a deorbitsail. The Semi-Analytical Liu Theory (SALT) and the Satellite Toolkit was employed to determine the mean elements and expressions for the time rates of change. Test cases of observed decayed satellites (Iridium-85 and Starshine-1) are used to evaluate the predicted theory. Results for the test cases indicated that the theory tted observational data well within acceptable limits. Orbit decay progress of the SUNSAT micro-satellite was analysed using relevant orbital parameters derived from historic Two Line Element (TLE) sets and comparing with decay and lifetime prediction models. The study also explored the deorbit date and time for a 1U CubeSat (ZACUBE-01). A proposed orbital debris solution or technology known as deorbitsail was also investigated to gain insight in sail technology to reduce the orbit life of spacecraft with regards to de- orbiting using aerodynamic drag. The deorbitsail technique signi cantly increases the e ective cross-sectional area of a satellite, subsequently increasing atmospheric drag and accelerating orbit decay. The concept proposed in this work introduces a very useful technique of orbit decay as well as deorbiting of spacecraft. / AFRIKAANSE OPSOMMING: Gedurende sy leeftyd in die ruimte word 'n ruimtetuig blootgestel aan die risiko van 'n botsing met ruimterommel of met funksionele satelliete. Hierdie risiko is veral hoog in die lae-aardbaan gebied waar die hoogste digtheid ruimterommel voorkom. Hierdie studie ondersoek die wentelbaanverval van sommige Lae-aardbaan mikrosatelliete asook die versnelde baanverval wanneer van 'n deorbitaal meganisme gebruik gemaak word. Die Semi-Analitiese Liu Teorie en die Satellite Toolkit sagtewarepakket is gebruik om die gemiddelde baan-elemente en uitdrukkings vir hul tyd-afhanlike tempo van verandering te bepaal. Toetsgevalle van waargenome vervalde satelliete (Iridium-85 en Starshine-1) is gebruik om die verloop van die voorspelde teoretiese verval te evalueer. Resultate vir die toetsgevalle toon dat die teorie binne aanvaarbare perke met die waarnemings ooreenstem. Die verloop van die SUNSAT mikrosatelliet se wentelbaanverval is ook ontleed deur gebruik te maak van historiese Tweelyn Elemente datastelle en dit te vergelyk met voorspelde baan- elemente. Die studie het ook ondersoek ingestel na die voorspelde baan-verbyval van 'n 1-eenheid cubesat (ZACUBE-01). Die impak op wentelbaanverval deur 'n voorgestelde oplossing vir die beperking van ruimterommel, 'n deorbitaalseil, is ook ondersoek. So seil verkort 'n satelliet se ruimte- leeftyd deur sy e ektiewe deursnee-area te vergroot en dan van verhoogde atmosferiese sleur en sonstralingsdruk gebruik te maak om die vervalproses te versnel. Hierdie voorgestelde konsep is 'n moontlike nuttige tegniek vir versnelde baanverval en beheerde deorbitalering van ruimtetuie om ruimterommel te verminder.

Quantum spin liquids represent a novel phase of magnetic matter where quantum fluctuations are large enough to suppress the formation of local order parameters, even down to zero temperature. Quantum spin liquid states can emerge from frustrated quantum magnets. These states show several peculiar properties, such as topological order, fractional excitations, and long-range entanglement. The Kitaev spin model on the honeycomb lattice is one of the few models proposed which can exactly show the existence of a $\mathbb{Z}_2$ quantum spin liquid. The model describes spins featuring frustrated compass interactions, and it exhibits a quantum spin liquid ground state. The model's ground state can be found exactly by representing spins in terms of Majorana fermions. It turns out that spin excitations fractionalize into two degrees of freedom: spinless matter fermions and flux excitations of the emergent $\mathbb{Z}_2$ gauge theory. Recently, possible solid-state realizations of Kitaev quantum spin liquids have been proposed in a class of frustrated Mott insulators. Unfortunately, experiments can not unambiguously identify quantum spin liquids, due to their elusive nature. Nevertheless, indirect observations on a spin liquid state can be done by looking at its excitations. Along this line, thermal transport investigations provide for an option to study heat-carrying excitations, and thus the properties of the related spin liquid state. In this doctoral thesis work, I performed a study of longitudinal thermal transport properties in the two-dimensional Kitaev spin model. This study aims to advance the understanding of transport in prototypical frustrated quantum magnets that might harbor Kitaev physics, and in particular quantum spin liquid states. For this purpose, I explored the model for varying exchange coupling regimes $-$ to underline the impact of anisotropy on transport $-$ and I studied transport over a wide range of temperatures. Transport properties have been explored within the formalism of the linear response theory. Based on the latter, thermal transport coefficients can be evaluated by calculating dynamical energy-current auto-correlation functions. First, I performed an analytical study of the uniform gauge sector of the model $-$ where excitations of gauge degrees of freedom are neglected. Analytical findings for the energy-current correlations, and their related transport coefficients, imply a finite-temperature ballistic heat conductor in terms of free matter fermion excitations $-$ independent of exchange couplings. Second, thermal transport has been studied at finite temperatures, considering thermal gauge excitations off the uniform gauge sector. For this purpose, I made use of two complementary numerical methods able to treat finite-temperature systems. On the one hand, I resorted on the exact diagonalization of the Kitaev Hamiltonian given in terms of fermions and a real-space dependent $\mathbb{Z}_2$ gauge potential, to study relatively small systems. On the other hand, I used an approximate method based on a mean-field treatment of thermal gauge fluctuations. The method allowed to extend the study of thermal transport to systems with up to $\sim\mathcal{O}(10^4)$ spinful sites. It made possible the computation of correlation functions by reducing the exact trace over all gauge states to an average over dominant gauge states suited to a given temperature range. The reliability of the method has been checked by comparing to numerically exact thermodynamics of systems. Based on the thermodynamic analysis, the method has been restricted to a temperature range where the mean-field treatment of gauge fluctuations is acceptable. Within such temperature range, the method succeeded in well reproducing exact results. The prime advantage of this method is its capability to reveal important features in the energy-current correlation spectra, not captured by the exact diagonalization approach because of finite-size effects. I found that the energy-current correlation spectra, in the presence of thermal gauge excitations, show clear signatures of spin fractionalization. In particular, the low-energy part of spectra displays features arising from a temperature-dependent matter-fermion density relaxation off an emergent thermal gauge disorder. This static gauge disorder also leads to the appearance of a pseudogap in the zero-frequency limit, which closes in the thermodynamic limit. The extracted dc heat conductivity is consequently influenced by this interplay between matter fermions and gauge degrees of freedom. The anisotropy in the exchange couplings moves Kitaev systems through gapless and gapped phases of the matter fermion sector. Effects of anisotropy are visible in the dc conductivities which display a low-temperature dependence crossing over from power-law to exponentially activated behavior upon entering the gapped phase. Therefore, I found that in the thermodynamic limit, two-dimensional Kitaev systems feature dissipative transport, regardless of exchange couplings. This finding is in contrast to the ballistic transport found discarding gauge excitations in the uniform gauge sector, which underlines the relevance of gauge degrees of freedom in thermal transport properties of Kitaev systems.

Spin resonance of a two-dimensional electron system confined in a GaN/AlGaN heterostructure grown by molecular beam epitaxy was resistively detected over a wide range of magnetic field and microwave frequency. Although the spin-orbit interaction is strong in this type of heterostructure at zero magnetic field, surprisingly the width of the detected spin resonance line was very narrow—down to 6.5 mT at 13.3 T. The spin depolarization time extracted from the resonance linewidth was estimated to be 2 ns. The electron g-factor was measured with high accuracy, resembling a value close to the free-electron value and its dependence on the magnetic field was studied.