Graphene armchair nanoribbon single-electron transistors: The peculiar influence of end states

We present a microscopic theory for interacting graphene armchair nanoribbon quantum dots. Long-range interaction processes are responsible for Coulomb blockade and spin-charge separation. Short-range ones, arising from the underlying honeycomb lattice of graphene smear the spin-charge separation and induce exchange correlations between bulk electrons —delocalized on the ribbon— and single electrons localized at the two ends. As a consequence, entangled end-bulk states where the bulk spin is no longer a conserved quantity occur. Entanglement’s signature is the occurrence of negative differential conductance effects in a fully symmetric set-up due to symmetry-forbidden transitions. Copyright c © EPLA, 2009 The first successful separation of graphene [1], a single atomic layer of graphite, has resulted in intense theoretical and experimental investigations on graphene-based structures [2], because of potential applications and fundamental physics issues arising from the linear dispersion relation in the electronic band structure of graphene. In graphene nanostructures, confinement effects typical of mesoscopic systems and electron-electron interactions are expected to play a crucial role on the transport properties. Indeed a tunable single-electron transistor has been demonstrated in a graphene island weakly coupled to leads [3]. Conductance quantization has been observed in 30 nm wide ribbons [4], while an energy gap near the charge neutrality point scaling with the inverse ribbon width was reported in [5]. Theoretical investigations [6,7] have attributed the existence of such a gap to Coulomb interaction effects. Confinement is also known to induce localized states at zig-zag boundaries [8], possessing a flat energy band and occuring in the mid of the gap. Those states have been analysed [9] under the assumption of a filled valence and an empty conduction band (half-filling), taking into account both Hubbard and long-ranged Coulomb interac(a)E-mail: [email protected] Fig. 1: (Colour on-line) A graphene armchair nanoribbon single-electron transistor. At the long sides, the lattice is terminated in armchair, at the small ends in zig-zag configuration. tion. There was a prediction of strong spin features in case of a low population of these midgap states. Above the half-filling regime, however, no detailed study on the interplay between longitudinal quantization effects and Coulomb interactions in the spectrum of narrow nanoribbons exists at present. The purpose of this letter is to derive a low-energy theory of armchair nanoribbons (ACN) single-electron transistors (SETs), see fig. 1, i.e., to investigate the consequences of confinement and interaction in narrow ACNs weakly coupled to leads. Short ACN have recently been synthesized [10]. We show that the long-range part of the