Impurity and boundary modes in the honeycomb lattice

Abstract : Two fields of research define the framework in which the present thesis can be apprehended. The first one deals with impurity and boundary modes in the hexagonal lattice. The second one concerns a spin accumulation in an out-Of-Equilibrium superconductor.Two fields of research define the framework in which the present thesis can be apprehended. The first one deals with impurity and boundary modes in the hexagonal lattice. The second one concerns a spin accumulation in an out-Of-Equilibrium superconductor.Graphene is the main motivation of the first part. From a crystallographic perspective, the carbon atoms in graphene, a graphite layer, design a triangular Bravais lattice with a diatomic pattern. This gives rise to an extra degree of freedom in the electronic band structure that crucially reveals chiral massless Dirac electrons at low-Energy. First of all, it is possible to make these chiral fermions annihilate when a uniaxial strain stretches the graphene layer. For a critical value of the strain, all the fermions become massive and nonrelativistic, which defines a Lifshitz transition. We study the impurity scattering as a function of the strain magnitude. A localised impurity yields quantum interferences in the local density of states that are known as Friedel oscillations. Because they are affected by the chiral nature of the electrons, we show that the decaying laws of these oscillations are specific to the phase the system belongs to. Thus, the impurity scattering offers the possibility to fully characterise the transition.Second, the diatomic pattern of the graphene lattice can also be considered as an invitation to the world of topological insulators and superconductors. The existence of edge states in such systems relies on the topological characterization of the band structure. Here we especially introduce a model of topological superconductor based on the honeycomb lattice with induces spin-Singlet superconductivity. When a Zeeman field breaks the time-Reversal invariance, and in the presence of Rashba spin-Orbit interactions, we give a prescription to describe the topological phases of the system and predict the emergence of Majorana modes (edge states) in strained and doped nanoribbons.The second part discusses the study of a spin accumulation in an out-Of-Equilibrium s-Wave superconductor. At the equilibrium, the superconductor is made of particles coupled by a s-Wave pairing, as well as unpaired quasiparticles. Injecting spin-Polarised electrons into the superconductor induces charge and spin imbalances. When the injection stops, it may happen that charge and spin do not relax over the same time-Scale. The first experiment that points out such a spin-Charge decoupling has recently been realised. In order to confirm this chargeless spin-Relaxation time, a new experiment has been developed [96], based on measurements in the frequency domain. Here, we address a model that fits the experimental data and thus enables the extraction of this characteristic time that is of the order of a few nanoseconds.
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Clément Dutreix. Impurity and boundary modes in the honeycomb lattice. Quantum Physics [quant-ph]. Université Paris Sud - Paris XI, 2014. English. ⟨NNT : 2014PA112217⟩. ⟨tel-01126856⟩

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