In last two years, the proposal to create artificial graphene in standard semiconducting 2D systems via surface patterning has emerged. This way, an alternative system would be created, allowing us to study phenomena related to Dirac-type particles in a fully carbon free system. The main idea of the concept assumes the creation of an additional potential in a quantum well by nanopatterning of the specimen surface or by using local electrodes. The additionally introduced modulation can transform the conventional (i.e. parabolic) energy dispersion into separated minibands with possible appearance of Dirac cones. In the theoretical part, we introduce four basic criteria that estimate appropriate technological parameters and the required experimental conditions. Experimentally, we study the cyclotron resonance of prepared heterostructures AlGaAs/GaAs with induced hexagonal potential via the etching lateral holes. The observed multi-mode resonance response is discussed with respect to the expected appearance of Dirac cones.

Inspired by graphene, I investigate the properties of several different real and artificial Dirac materials. Firstly, I consider a two-dimensional honeycomb lattice of metallic nanoparticles, each supporting localised surface plasmons, and study the quantum properties of the collective plasmons resulting from the near field dipolar interaction between the nanoparticles. I analytically investigate the dispersion, the effective Hamiltonian and the eigenstates of the collective plasmons for an arbitrary orientation of the individual dipole moments. When the polarisation points close to normal to the plane the spectrum presents Dirac cones, similar to those present in the electronic band structure of graphene. I derive the effective Dirac Hamiltonian for the collective plasmons and show that the corresponding spinor eigenstates represent chiral Dirac-like massless bosonic excitations that present similar effects to those of electrons in graphene, such as a non-trivial Berry phase and the absence of backscattering from smooth inhomogeneities. I further discuss how one can manipulate the Dirac points in the Brillouin zone and open a gap in the collective plasmon dispersion by modifying the polarisation of the localized surface plasmons, paving the way for a fully tunable plasmonic analogue of graphene. I present a phase diagram of gapless and gapped phases in the collective plasmon dispersion depending on the dipole orientation. When the inversion symmetry of the honeycomb structure is broken, the collective plasmons become gapped chiral Dirac modes with an energy-dependent Berry phase. I show that this concept can be generalised to describe many real and artificial graphene-like systems, labeling them Dirac materials with a linear gapped spectrum. I also show that biased bilayer graphene is another Dirac material with an energy dependent Berry phase, but with a parabolic gapped spectrum. I analyse the relativistic phenomenon of Klein Tunneling in both types of system. The Klein paradox is one of the most counter-intuitive results from quantum electrodynamics but it has been seen experimentally to occur in both monolayer and bilayer graphene, due to the chiral nature of the Dirac quasiparticles in these materials. The non-trivial Berry phase of pi in monolayer graphene leads to remarkable effects in transmission through potential barriers, whereas there is always zero transmission at normal incidence in unbiased bilayer graphene in the npn regime. These, and many other 2D materials have attracted attention due to their possible usefulness for the next generation of nano-electronic devices, but some of their Klein tunneling results may be a hindrance to this application. I will highlight how breaking the inversion symmetry of the system allows for results that are not possible in these system's inversion symmetrical counterparts.

Le transport des ondes joue un rôle majeur dans les systèmes de communication comme le Wifi ou les fibres optiques. Les principaux problèmes rencontrés dans ces systèmes concernent la protection contre les intrusions, la consommation d’énergie et le filtrage modal. Nous proposons différentes expériences micro-ondes mettant toutes en œuvre une mise en forme des ondes, pour traiter ces problèmes. Dans une cavité micro-ondes, des états de diffusion particuliers sont générés en s’appuyant uniquement sur des mesures de transmission et sur le formalisme du temps de retard de Wigner-Smith. Ces états sont capables d’éviter une région déterminée de la cavité, de se concentrer sur un point particulier, ou de suivre une trajectoire d’une particule classique. Le filtrage de mode est mis en œuvre dans un guide d’ondes aux frontières ondulées et en présence de pertes dépendant de la position. Le profil du guide est choisi de façon à ce que les deux modes de Bloch qui se propagent encerclent un point exceptionnel. Cette trajectoire s’accompagne d’une transition non-adiabatique entre les deux modes et d'un filtrage asymétrique de ces modes. La thèse présente également des travaux liés à la problématique des algorithmes de « recherche quantique », notamment l’algorithme de Grover. Cette recherche est mise en œuvre dans un réseau en nid d’abeilles de résonateurs micro-ondes couplés, bien décrits par un modèle de liaisons fortes (le système constitue un analogue micro-ondes du graphène). Une expérience de preuve de principe propose la recherche de deux résonateurs distincts reliés au réseau. La loi d’échelle attendue pour cet algorithme est expérimentalement obtenue dans une chaîne linéaire / Transport of waves plays an important role in modern communication systems like Wi-Fi or optical fibres. Typical problems in such systems concern security against possible intruders, energy consumption, time efficiency and the possibility of mode filtering. Microwave experiments are suited to study this kind of problems, because they offer a good control of the experimental parameters. Thus we can implement the method of wave shaping to investigate atypical transport phenomena, which address the mentioned problems. Wave front shaping solely based on the transmission together with the Wigner-Smith time delay formalism allows me to establish special scattering states in situ. These scattering states avoid a pre-selected region, focus on a specific spot or follow trajectories of classical particles, so called particle-like scattering states. Mode filtering is induced inside a waveguide with wavy boundaries and position dependent loss. The boundary profiles are chosen in such a way that the two propagating modes describe an encircling of an exceptional point in the Bloch picture. The asymmetric mode filtering is found due to the appearing non-adiabatic transitions. Another part of my work deals with Grover’s quantum search. I put such a search into practice in a two-dimensional graphene-lattice using coupled resonators, which form a tight-binding analogue. In this proof of principle experiment we search for different resonators attached to the graphene-lattice. Furthermore, the scaling behaviour of the quantum search is quantified for a linear chain of resonators