This thesis describes two topological phases of matter, the Weyl semimetal and the line node semimetal, that are related to but distinct from topological insulator phases. These new topological phases are semimetallic, having electronic energy bands that touch at discrete points or along a continuous curve in momentum space. These states are achieved by breaking time-reversal symmetry near a transition between an ordinary insulator and a topological insulator, using a model based on alternating layers of topological and ordinary insulators, which can be tuned close to the transition by choosing the thicknesses of the layers. The semimetallic phases are topologically protected, with corresponding topological surface states, but the protection is due to separation of the band-touching points in momentum space and discrete symmetries, rather than being protected by an energy gap as in topological insulators. The chiral surface states of the Weyl semimetal give it a non-zero Hall conductivity, while the surface states of the line node semimetal have a flat energy dispersion in the region bounded by the line node. Some transport properties are derived, with a particular emphasis on the behaviour of the conductivity as a function of the impurity concentrations and the temperature.

This thesis describes two topological phases of matter, the Weyl semimetal and the line node semimetal, that are related to but distinct from topological insulator phases. These new topological phases are semimetallic, having electronic energy bands that touch at discrete points or along a continuous curve in momentum space. These states are achieved by breaking time-reversal symmetry near a transition between an ordinary insulator and a topological insulator, using a model based on alternating layers of topological and ordinary insulators, which can be tuned close to the transition by choosing the thicknesses of the layers. The semimetallic phases are topologically protected, with corresponding topological surface states, but the protection is due to separation of the band-touching points in momentum space and discrete symmetries, rather than being protected by an energy gap as in topological insulators. The chiral surface states of the Weyl semimetal give it a non-zero Hall conductivity, while the surface states of the line node semimetal have a flat energy dispersion in the region bounded by the line node. Some transport properties are derived, with a particular emphasis on the behaviour of the conductivity as a function of the impurity concentrations and the temperature.

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Optical spin injection in InAs/GaAs quantum dots (QDs) structures under cryogenic temperature has been investigated in this work using continuous-wave optical orientation spectroscopy. Circularly polarized luminescence from trions in the QDs was used as a measure for the degree of spin polarization of the carriers in the QD ground states. The efficiency of spin conservation of the carriers during the injection process into the QDs and also the influence of the nuclear spins in the QDs were studied both under zero and external magnetic field. It was shown in zero magnetic field that the spin states were less conserved during the injection process for correlated excitons and hot free carriers. While under the external magnetic field, measurements were done in Faraday configuration. Confined electron motion yielding the quantized Landau levels in the InGaAs wetting layer (WL) and lifting of the Landau level spin degeneracy was observed. Also possible spin thermalization in the InGaAs WL during spin injection process was found. Finally, the quench of hyperfine induced spin relaxation by dynamic nuclear polarization (DNP) in the QDs was discovered and believed to be a stronger effect under weak/zero magnetic field.

Multilayer epitaxial graphene has been shown to contain "massless Dirac fermions" and is believed to provide a possible route to industrial-scale graphene electronics. We used scanning tunneling microscopy (STM) and spectroscopy (STS) in high magnetic fields to obtain local information on these fermions. A new STS technique was developed to directly measure graphene's energy-momentum relationship and resulted in the highest precision measurement of graphene's Dirac cone. STS spectra similar to ideal graphene were observed, but additional anomalies were also found. Extra peaks and an asymmetry between electron and hole states were shown to be caused by the work function difference between the Iridium STM tip and graphene. This tip effect was extracted using modeled potentials and performing a least square fit using degenerate perturbation theory on graphene's eigenstates solved in the symmetric gauge. Defects on graphene were then investigated and magnetic field effects were shown to be due to a mixture of potential effect from defects and the tip potential. New defect states were observed to localize around specific defects, and are believed to interact with the STM tip by Stark shifting in energy. This Stark shift gives a direct measurement of the capacitive coupling between the tip and graphene and agrees with the modeled results found when extracting the tip potential.

<p>We consider a system of few electrons trapped in a two-dimensional circularquantum dot with harmonic confinement and in the presence of ahomogeneous magnetic field, with focus on the role of e-e interaction. Byperforming the exact diagonalization of the Hamiltonian in second quantization,the low-lying energy levels for spin polarized system are obtained. The singlet-triplet oscillation in the ground state of the two-electron system showing up inthe result is explained due to the role of Coulomb interaction. The splitting ofthe lowest Landau level is another effect of the e-e interaction, which is alsoobserved in the results.</p>

We consider a system of few electrons trapped in a two-dimensional circularquantum dot with harmonic confinement and in the presence of ahomogeneous magnetic field, with focus on the role of e-e interaction. Byperforming the exact diagonalization of the Hamiltonian in second quantization,the low-lying energy levels for spin polarized system are obtained. The singlet-triplet oscillation in the ground state of the two-electron system showing up inthe result is explained due to the role of Coulomb interaction. The splitting ofthe lowest Landau level is another effect of the e-e interaction, which is alsoobserved in the results.

Cette thèse présente des mesures de transport électronique dans des systèmes bi-dimensionels et uni-dimensionels à base de graphène sous champ magnétique pulsé (60T). L'objectif de ces travaux consiste à sonder la dynamique des porteurs de charge en modifiant la densité d'états du système par l'application d'un champ magnétique. Une première partie est consacrée à l'étude de l'influence des îlots électrons-trous sur les propriétés de transport du graphène au voisinage du point de neutralité de charge. Nous avons constaté l'apparition de fluctuations de la magnéto-résistance liée à la transition progressive des îlots de taille finie dans le régime quantique lorsque le champ magnétique augmente. Nous avons aussi montré que la variation de l'énergie de Fermi, liée à l'augmentation de la dégénérescence orbitale des niveaux de Landau, est directement responsable d'une modification du ratio entre électrons et trous. Dans une deuxième partie consacrée à l'étude des nanorubans de graphène, nous avons exploré deux gammes de largeur différentes. Dans les rubans larges (W>60nm), la quantification de la résistance a été observée révélant ainsi une signature évidente de la quantification du spectre énergétique en niveaux de Landau. Le confinement magnétique des porteurs de charge sur les bords des nanorubans a permis de mettre en évidence, pour la première fois, la levée de dégénérescence de vallée liée à la configuration armchair du ruban. Pour des rubans plus étroits (W<30nm), en présence de défauts de bord et d'impuretés chargées, la formation progressive des états de bords chiraux donne lieu à une magnéto-conductance positive quelque soit la densité de porteurs. Enfin, la dernière partie traite du magnéto-transport dans le graphene multi-feuillet. En particulier, nous avons observé l'effet Hall quantique dans les systèmes tri-couche de graphène. Une étude comparative des résultats expérimentaux avec des simulations numériques a permis de déterminer l'empilement rhombohedral des trois couches de graphene constituant l'échantillon / This thesis presents transport measurements on two-dimensional and one-dimensional graphene-based systems under pulsed magnetic field (60T). The objective of this work is to probe the dynamics of charge carriers by changing the density of states of the system by applying a strong magnetic field. The first part is devoted to the study of the influence of electron-hole pockets on the transport properties of graphene near the charge neutrality point. We found the appearance of fluctuations in the magneto-resistance due to the progressive transition of the electron/hole puddles of finite size in the quantum regime as the magnetic field increases. We have also shown that the variation of the Fermi energy, due to the increase of orbital Landau level degeneracy, is directly responsible of a change in the electron and hole ratio. The second part is devoted to the study of graphene nano-ribbons, we explored two different ranges of width. In the broad nano-ribbons of width W larger than 60 nm, the quantification of the resistance is observed, revealing a clear signature of the quantization of the energy spectrum into Landau levels. We show for the first time the effect of valley degeneracy lifting induced by the magnetic confinement of charge carriers at the edges of the armchair nano-ribbons. For narrower nano-ribbons (W <30 nm) in presence of edge defects and charged impurities, the progressive formation of chiral edge states leads to a positive magneto-conductance whatever the carrier density. Finally, the last part of this thesis deals with magneto-transport fingerprints in multi-layer graphene as we observed the quantum Hall effect in tri-layer graphene. A comparative study of the experimental results with numerical simulations was used to determine the rhombohedral stacking of three layers of graphene in the sample