Spin Currents in Rough Graphene Nanoribbons: Universal Fluctuations and Spin Injection

Abstract

We investigate spin conductance in zigzag graphene nanoribbons and propose a spin injection mechanism based only on graphitic nanostructures. We find that nanoribbons with atomically straight, symmetric edges show zero spin conductance but nonzero spin Hall conductance. Only nanoribbons with asymmetrically shaped edges give rise to a finite spin conductance and can be used for spin injection into graphene. Furthermore, nanoribbons with rough edges exhibit mesoscopic spin conductance fluctuations with a universal value of rmsG s 0:4e=4 . DOI: 10.1103/PhysRevLett.100.177207 PACS numbers: 85.75.ÿd, 72.25.ÿb, 73.22.ÿf, 73.63.ÿb After their experimental discovery in 2004 [1], monolayers of graphite have attracted much experimental and theoretical attention owing to their unusual band structure [2]. Graphene has also been suggested as a good candidate for spin-based quantum computing and spintronics [3], as it is expected to have long spin decoherence or relaxation times [4]. This prospect led to the recent interest in generating and manipulating net spin distributions in graphene. Recently, spin injection from ferromagnetic metal contacts into graphene has been achieved [5][6][7][8].Transport properties of graphene nanoribbons (GNRs) are expected to depend strongly on whether they have an armchair or zigzag edge [9]. In GNRs with zigzag edges, transport is dominated by edge states which have been observed in scanning tunneling microscopy [10]. Moreover, owing to their high degeneracy, these states are expected to be spin-polarized [11], making zigzag GNRs attractive for spintronics [12]. In addition, edge states are expected to occur also in nanoribbons with other edge orientations [13]. Recently, the first transport experiments have been performed in narrow ribbons of graphene [14], albeit with not well defined edges. Recent theoretical work focused on charge transport through rough GNRs [15], but spin transport properties have not been explored yet.In the present work, we focus on spin transport in GNRs with rough zigzag edges. Ideal zigzag GNRs are not efficient spin injectors due to the symmetry between the edges with opposite magnetization. In order to obtain net spin injection, this symmetry must be broken. Existing proposals to achieve this require very large transverse electric fields [12]. We sidestep this difficulty by showing that edge imperfections (such as vacancies), which usually cannot be avoided experimentally, break the symmetry between the edges and lead to a finite spin conductance of the GNR. Thus, rough zigzag GNRs can be used as spin injectors or detectors in graphene spintronics.We start with a description of the electronic ground state properties of the zigzag GNR, which captures the essential physics relevant to spin transport, given by the single band tight- Here t ij t if i and j are nearest neighbors, t ij t 0 if i and j are next nearest neighbors [16], and are the Pauli matrices corresponding to the spin degree of freedom. The local magnetization m i can be obtained from the self-con...

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