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Gated bilayer graphene exhibits spin-degenerate gapless states with a topological character localized at stacking domain walls. These states allow for one-dimensional currents along the domain walls. We herein demonstrate that these topologically protected currents are spin-polarized and locked in a single layer when bilayer graphene contains stacking domain walls decorated with magnetic defects. The magnetic defects, which we model as π-vacancies, perturb the topological states but also lift their spin degeneracy. One gapless state survives the perturbation of these defects, and its spin polarization is largely localized in one layer. The spin-polarized current in the topological state flows in a single layer, and this finding suggests the possibility of effectively exploiting these states in spintronic applications. ; This work was partially supported by project FIS2016-76617-P of the Spanish Ministry of Economy and Competitiveness MINECO, the Basque Government under the ELKARTEK project (SUPER), and the Gobierno Vasco-UPV/EHU (Grant No. IT1246- 19). AA and WJ acknowledge the hospitality of the Institute of Physics at Nicolaus Copernicus University and the Donostia International Physics Center, respectively.

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY). ; Zigzag graphene nanoribbons have spin-polarized edges, antiferromagnetically coupled in the ground state with total spin zero. Customarily, these ribbons are made ferromagnetic by producing an imbalance between the two sublattices. Here we show that zigzag ribbons can be ferromagnetic due to the presence of reconstructed divacancies near one edge. This effect takes place even though the divacancies are produced by removing two atoms from opposite sublattices, which were balanced before reconstruction to 5-8-5 defects. We demonstrate that there is a strong interaction between the defect-localized and edge bands which mix and split away from the Fermi level. This splitting is asymmetric, yielding a net edge spin polarization. Therefore, the formation of reconstructed divacancies close to the edges of the nanoribbons can be a practical way to make them partially ferromagnetic. ; This work was supported by the Polish National Science Center (Grant No. DEC-2011/03/B/ST3/00091), the Basque government through the NANOMATERIALS project (Grant No. IE05-151) under the ETORTEK Program iNanogune, the Spanish Ministry of Economy and Competitiveness MINECO (Grants No. FIS2013-48286-C2-1-P and No. FIS2012-33521), and the University of the Basque Country (Grant No. IT-366- 07). ; Peer Reviewed

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. ; Grain boundaries and defect lines in graphene are intensively studied for their novel electronic and magnetic properties. However, there is not a complete comprehension of the appearance of localized states along these defects. Graphene grain boundaries are herein seen as the outcome of matching two semi-infinite graphene sheets with different edges. We classify the energy spectra of grain boundaries into three different types, directly related to the combination of the four basic classes of spectra of graphene edges. From the specific geometry of the grains, we are able to obtain the band structure and the number of localized states close to the Fermi energy. This provides a new understanding of states localized at grain boundaries, showing that they are derived from the edge states of graphene. Such knowledge is crucial for the ultimate tailoring of electronic and optoelectronic applications. ; This work was supported by the Polish National Science Center (grant DEC-2011/03/B/ST3/00091), the Basque Government through the NANOMATERIALS project (grant IE05-151) under the ETORTEK Program (iNanogune), the Spanish Ministerio de Ciencia y Tecnología (grants FIS2010-21282-C02-02, FIS2012-33521 and MONACEM projects), and the University of the Basque Country (grant no. IT-366-07). ; Peer Reviewed

Trabajo presentado al 42th "Jaszowiec" International School and Conference on the Physics of Semiconductors (Wisla-Polonia 2013). ; We study graphene nanoribbons and carbon nanotubes with divacancies, i.e., local defects composed of one octagon and a pair of pentagons. We show that the presence of divacancies leads to the appearance of gap states, which may act as acceptor or donor states. We explain the origin of those defect-localized states and prove that they are directly related to the zero-energy states of carbon ring forming the octagonal topological defect. ; This work was supported by the Polish National Science Center (grant DEC-2011/03/B/ST3/00091), the Spanish Ministry of Economy and Competitiveness (grant No. FIS2012-33521), the Basque Departamento de Educación and the University of the Basque Country (grant No. IT-366-07), the Basque Departamento de Industria and the Diputación Foral de Guipuzcoa under the ETORTEK program (NANO-IKER grant No. IE11-304). ; Peer Reviewed

3 pages, 1 figure.-- PACS nrs.: 73.21.La, 73.22.-f, 73.20.At, 71.15.Ap.-- Presented as poster communication to TNT 2008: Trends in NanoTechnology (Oviedo, Spain, Sep 1-5, 2008). ; The interface states of all-metallic carbon nanotube quantum dots are studied based on a tight-binding approach and a Green's function matching technique. We have found that depending on the type of metallic tube, the energy of interface states may show an oscillatory behavior. We identify these as steamming from Friedel oscillations. We comment on the possible implications of this finding on other physical properties, such as stability during the growth of nanotube junctions and magnetic interaction through carbon nanotubes. ; We acknowledge financial support by the ETORTEK (NANOMAT) program of the Basque government, the Intramural Special Project (Ref. No. 2006601242), the Spanish Ministerio de Ciencia y Tecnología (Grants No. Fis 2007-66711-C02-C01 and MAT2006-06242) and the European Network of Excellence NANOQUANTA (NM4-CT-2004-500198). ; Peer reviewed

Proceedings of the XXXVII International School of Semiconducting Compounds, Jaszowiec 2008. ; Interface states of all-metallic carbon nanotube quantum dots and superlattices are studied within a tight-binding model. We focus on achiral systems made by connecting armchair (n; n) and zigzag (2n; 0) tubes with a full ring of n pentagon-heptagon topological defects. We show that the coupling between interface states, which arise from the topological defects, re°ects the existence of the Friedel oscillations in the (n; n) tube, with an unusually large decay exponent. We expect this interaction to be important for the understanding of other physical properties, such as selective dot growth, magnetic interaction through carbon tubes or optical spectroscopy of interface states. ; We acknowledge financial support by the ETORTEK (NANOMAT) program of the Basque government, the Intramural Special Project (Ref. 2006601242), the Spanish Ministerio de Ciencia y Tecnologia (Grants No. Fis 2007-66711-C02-C01 and MAT2006-06242), JCCM Grant No. PAI08-0067-2673 and the European Network of Excellence NANOQUANTA (NM4-CT-2004-500198). ; Peer reviewed

Experiments in gated bilayer graphene with stacking domain walls present topological gapless states protected by no-valley mixing. Here we research these states under gate voltages using atomistic models, which allow us to elucidate their origin. We find that the gate potential controls the layer localization of the two states, which switches non-trivially between layers depending on the applied gate voltage magnitude. We also show how these bilayer gapless states arise from bands of single-layer graphene by analyzing the formation of carbon bonds between layers. Based on this analysis we provide a model Hamiltonian with analytical solutions, which explains the layer localization as a function of the ratio between the applied potential and interlayer hopping. Our results open a route for the manipulation of gapless states in electronic devices, analogous to the proposed writing and reading memories in topological insulators. ; This work was partially supported by Projects FIS2015-64654-P and FIS2016-76617-P of the Spanish Ministry of Economy and Competitiveness MINECO, the Basque Government under the ELKARTEK project (SUPER), and the University of the Basque Country (Grant No. IT-756-13). ; Peer Reviewed