Origami-based spintronics in graphene

We show that periodically folded graphene sheets with enhanced spin-orbit interaction due to curvature effects can carry spin-polarized currents and have gaps in the electronic spectrum in the presence of weak magnetic fields. Our results indicate that such origami-like structures can be used efficiently in spintronic applications. Copyright c © EPLA, 2013 Often hailed as a wonder material due to its impressive physical properties [1], graphene has opened several venues of basic science exploration and it is a material that has a tremendous technological potential. Despite its potential applicability, the lack of a bandgap is a well-known limitation that currently prevents the use of graphene in digital electronic applications [2]. Different strategies have been attempted to remedy this shortcoming, namely, by quantum confinement in the form of nanoribbons and quantum dots [3,4], by stacking graphene sheets in bilayers in the presence of a perpendicular electric field [5–7], by strainengineering its electronic structure [8–11], or by simply chemically doping the graphene sheets [12,13]. Unfortunately, these attempts have so far failed to produce technologically relevant semiconducting graphene due to several difficulties that go from the small size of the gaps they produce to the disorder that they introduce. On a different front, the field of spintronics appears as one of the most promising areas for graphene since the extremely small spin-orbit interaction (SOI) of carbon makes the spin dissipation that otherwise exists in most materials practically negligible [14,15]. This suggests that information stored in the electronic spin of graphene can be retained for times considerably longer than in ordinary metals. Furthermore, this information can travel longer (a)E-mail: [email protected] (b)E-mail: [email protected] distances with very little loss [16–18]. Not surprisingly, there is a growing interest in graphene-based spintronics as demonstrated by the volume of recent literature on the topic [19]. Driven by the necessity of a bandgap and by the growing interest in graphene-based spintronics, in this letter we propose a simple mechanism that not only produces a gapped electronic structure in graphene but that also spin-polarizes its current. We show that this effect arises quite simply by the combined presence of two key ingredients: the SOI and an externally applied magnetic field. While magnetic fields are controllable, the SOI of a material is normally constant and small in the case of carbon. Therefore, it might seem too ambitious to amplify both ingredients enough for the appearence of a possible gap. Nevertheless, recent discoveries have demonstrated that the SOI is enhanced when graphene is mechanically bent away from its planar geometry [20–23] suggesting that folding might function as a viable mechanism to induce a bandgap. In fact, here we show that folded graphene sheets in the presence of externally applied magnetic fields may display both a bandgap and spin-polarized currents. Not possible with bulk 3-dimensional structures, folding may pave the way to a whole new approach of dealing with spin electronics in 2-dimensional systems, giving rise to the so-called origami spintronics. It is convenient to start by showing that the two aforementioned key ingredients indeed lead to a bandgap in