Ab initio investigation of graphene nanoribbons in contact with topological insulators

Mean-field calculations indicate that zigzag-terminated graphene nanoribbons (GNRs) possess spin-polarized edge states. However, the stability of the edge magnetism is under debate, as its one-dimensional nature allows two types of intrinsic instabilities, namely thermal and quantum fluctuations. On the other hand, a generic stabilization mechanism is the anisotropy due to spin-orbit coupling (SOC), i.e. the dependence of the energy of electrons on the absolute orientation of their spins. Although the intrinsic SOC in GNRs is extremely weak, anisotropy effects can be greatly enhanced by depositing them on substrates with strong SOC, such as recently discovered class of band insulators, so-called three-dimensional topological insulators (TIs), which are insulating in the bulk but metallic on the surface. TI surface states have several remarkable properties, such as linear dispersion and spin-momentum locking, that stem from the strong SOC and time-reversal symmetry (TRS). In turn, they are protected against time-reversal-invariant perturbations. Breaking the TRS by proximity to a magnetic system, such as a ferromagnetic insulator, can lead to fascinating phenomena such as opening of a band gap and the so-called “anomalous quantum Hall effect”. The focus of this thesis is the ab initio investigation of the structural, electronic and magnetic properties of zigzag-terminated graphene nanoribbons (GNRs) deposited on the (111) surface of TI Sb2Te3 based on density functional theory (DFT). After an introduction to TIs and a review of the methodology, I start with the discussion of proximity effects of ferromagnetic Fe monolayers (MLs) deposited on the (111) surface of TI Sb2Te3. First, we show that the strength of the warping term in the clean Sb2Te3 (111) is quite large. Then, the structural, electronic and magnetic properties of Fe adatoms with coverages of one and three Fe MLs are studied. In the case of 1ML coverage, the computed magnetic anisotropy energies show that the easy-axis is in-plane. Despite the large warping term in the clean Sb2Te3 (111) surface, the in-plane magnetization induced by the Fe ML opens a tiny gap in the TI surface band structure. For thicker (3ML) coverage, no Dirac-like surface states can be anymore observed, except for one metastable structure, in which the Fe atoms form a layer over the topmost Te layer. In this structure, we find an out-of-plane easy-axis, which results in opening a gap in the Dirac surface spectrum of Sb2Te3. In the second part of the thesis, we study the perfect graphene sheet, H-terminated and H-free zigzag GNRs deposited on the (111) surface of Sb2Te3. In the first model, the enhanced SOC and broken inversion symmetry opens a gap in graphene Dirac cones. We also study the doping effect for different graphene-Sb2Te3 distances. Finally, our results for H-terminated and H-free GNRs deposited on the (111) surface of Sb2Te3 show that the edge magnetism is preserved in all models: The chemical interaction between surface states of Sb2Te3 and edge states of H-terminated GNRs is weak, whereas it is very strong for the H-free GNR. However, the strong SOC induced by the substrate and the broken inversion symmetry in H-free GNRs leads to a chiral Dzyaloshinskii-Moriya interaction (DMI), which twists the two antiferromagnetically-coupled edge states of the GNR. We estimate large Heisenberg spin-Hamiltonian couplings, both for the magnetic anisotropy energies and the DMI. The non-collinear magnetic structure results in a finite net magnetization that could be exploited as spin filters in spintronics devices. To the best of our knowledge, this is the first report of a chiral magnetic interaction between two edge states of a GNR