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Numerical studies of magnetism and transport properties in graphene nanodevices

Abstract : 2D materials are attracting attention from a big research community in solid-state physics because of a large number of applications. Among these materials 'graphene' has been at the focus of attention ever since its experimental realization as a single layer of carbon atoms in 2004 as an alternative to silicon due to its many unusual properties. Honeycomb nanostructures such as quantum dots constitute fundamental building blocks for potential device applications. Essential ingredients of such nanostructures are provided by the edges since they give rise to low-energy excitations. Accordingly, such edge channels will dominate the transport of a nano-device. Furthermore, zigzag edges are unstable with respect to interactions such that one may get magnetism at these edges even if for example bulk graphene is non-magnetic. The combination of both factors bears promise for spintronic applications.The current work contributes to the theoretical understanding of the aforementioned phenomena. Concretely, we use a single-band Hubbard model with an on-site Coulomb interaction combined with the mean-field theory in order to compute the magnetic and transport properties of graphene nanoflakes. Previous investigations have shown that a mean-field decoupling of the interaction yields surprisingly accurate answers even for dynamical properties. At a technical level, once a static mean-field has been determined self-consistently, the problem is reduced to non-interacting electrons. A first part of this thesis revisits the Hartree-Fock mean-field approximation for bulk graphene to study the impact of electron-electron interaction with and without spin-orbit coupling and concurrently assess its accuracy by comparing with other numerical methods. The gapless semi-metal (for zero spin-orbit coupling) and the topological band insulator (for nonzero spin-orbit coupling) are stable for weak to intermediate electron-electron interaction, and undergo a transition to an antiferromagnetic phase at strong interaction. The antiferromagnetic order is of the Néel type without spin-orbit coupling, and of the easy-plane type with spin-orbit coupling. The systematic investigation of magnetism on graphenenanoflakes is the second part of the present work when ignoring the spin-orbit coupling. The onset of the edge magnetic moment strictly depends on the size of the graphene nanoflakes, the geometry and the edge termination. Herein, the origin of the magnetism on the edges of graphene nanoflakes is attributed to the localized edge states in zigzag edges which vanish in armchair edges. A final part of the dissertation investigates spin-resolved transport properties depending on the thermal bias, typically the transport of charge carriers via spin-up and spin-down channels, in a magnetic hexagonal graphene nanoflake connected with two metallic leads. As a temperature difference is applied, significant spin-up and spin-down currents, which are computed using the non-equilibrium Green’s Function technique combined with the mean-field theory, flow in opposite directions through the graphene nanoflakes. This is the consequence of the imbalance of charge carrier concentrations, which is determined by the Fermi-Dirac distribution at the two leads, and transmission spectra. Furthermore, our calculations show that a perfect spin-Seebeck effect, a purespin current without charge current, a high spin-filtering effect as well as the amplification of spin current can be obtained by tuning the temperature at the leads, the temperature gradient and the back-gate voltage. These results pave the way for new application potential of the graphene nanoflakes in the field of spin caloritronics.
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Thu Phung. Numerical studies of magnetism and transport properties in graphene nanodevices. Condensed Matter [cond-mat]. Université de Cergy Pontoise, 2019. English. ⟨NNT : 2019CERG1048⟩. ⟨tel-02930295v2⟩

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