Topological electronic phases in graphene

Resumo

Graphene proved to be one of the most remarkable materials discovered in the last years, both for its potential in electronics, as well as its simplicity to be synthesized. In this thesis we have presented different mechanisms to drive graphene systems into topological states. In addition, we showed how the different topological states can break down, and their resilience towards perturbations. Regarding quantum spin Hall states, we discussed the two different mechanism by which they can arise in graphene, intrinsic spin orbit coupling and ferromagnetic quantum Hall effect. We showed that in the intrinsic quantum spin Hall effect, direction of the magnetization totally changed the transport properties, with a very small energy cost. For the ferromagnetic Hall state, we unveiled how the different electronic orders determined the topological state of the system, crucial to the proposal for Majorana bound states. Furthermore, we showed how inhomogeneous magnetism lead to backscattering channels, and how different spin waves emerge from such inhomogeneities. Therefore, magnetism opens different backscattering channels in both mechanisms, which suggests that transport measurements in those systems can act as detectors of local magnetic moments. Later we moved to mechanism driving graphene into a quantum anomalous Hall insulator. We showed how topological magnetic textures called skyrmions imprint their topological number into the graphene electronic structure. Remarkably, we show that this effect happened at arbitrary low coupling, in comparison with any other proposal. These phenomena suggested that graphene can be used as probe of non-trivial magnetic textures, by measuring anomalous transport signals. We also showed how the quantum anomalous Hall effect can arise in antiferromagnetic honeycomb lattices, for several multilayered states. This last proposal would be specially appealing to be realized in honeycomb oxides, where the interplay between correlations and spin orbit coupling could lead to anomalous Hall effect without net magnetization. After exploring the single electron topological states, we entered the land where magnetism encountered superconductivity. We showed that conventional magnetic impurities do not create bound states in graphene with proximized to superconductors, whereas single hydrogen deposition created a magnetic moments that binds very special superconducting Shiba in-gap states. We showed that such states break the conventional Shiba theory, and in particular allow to tune the in-gap energy by means of temperature. Furthermore, we showed that such in-gap states could be used as building blocks to create a one-dimensional topological superconductor. Finally, we moved to our proposal of Majorana bound states without any kind of spin orbit coupling, exploiting the topological nontrivial properties of the quantum Hall effect and symmetry broken Dirac equation. We showed how the unique quantum spin Hall effect in graphene driven by magnetic field created the chiral channel that upon superconducting pairing creates a p-wave superconductor. And more importantly, we showed that a similar mechanism could be used in the antiferromagnetic state, generating interface states with valley nature, that could also find a similar realization in antiferromagnetic oxides. Finally, we showed how the tight binding methods techniques used could also be applied to other 2D material, taking advantage of powerful density functional techniques, and the Wannierization procedure. We showed how MoS2 shows unconventional quantum Hall effect due to valley orbital fields, and how topological insulator and topological superconductors can be engineered in complex oxides. We have also presented a computational tool that allows non experts to reproduce many of the calculations presented in this thesis. The computational package Quantum Honeycomp is based fully on free software and is totally open, free and publicly available under the GPL public license. The program was intended to be as simple as possible, providing powerful numerical techniques and with a user friendly plug and play interface.