Energy Gaps in Etched Graphene Nanoribbons

Abstract

Transport measurements on an etched graphene nanoribbon are presented. It is shown that two distinct voltage scales can be experimentally extracted that characterize the parameter region of suppressed conductance at low charge density in the ribbon. One of them is related to the charging energy of localized states, the other to the strength of the disorder potential. The lever arms of gates vary by up to 30% for different localized states which must therefore be spread in position along the ribbon. A single-electron transistor is used to prove the addition of individual electrons to the localized states. In our sample the characteristic charging energy is of the order of 10 meV, the characteristic strength of the disorder potential of the order of 100 meV.PACS numbers: 71.15. Mb, 78.30Na, 81.05.Uw, 63.20.Kr Graphene nanoribbons [1,2,3,4,5] and narrow graphene constrictions [6,7,8] display unique electronic properties based on truly two-dimensional (2D) graphene [9] with potential applications in nanoelectronics [10] and spintronics [11]. Quasi-1D graphene nanoribbons and constrictions are of interest due to the presence of an effective energy gap, overcoming the gap-less band structure of graphene and leading to overall semiconducting behavior, most promising for the fabrication of nanoscale graphene transistors [5], tunnel barriers, and quantum dots [6,7,8]. On the other hand, ideal graphene nanoribbons [12,13] promise interesting quasi-1D physics with strong relations to carbon nanotubes [14]. Zonefolding approximations [13], π-orbital tight-binding models [15,16], and first principle calculations [17,18] predict an energy gap E g scaling as E g = α/W with the nanoribbon width W , where α ranges between 0.2-1.5 eV×nm, depending on the model and the crystallographic orientation of the nanoribbon [4]. However, these theoretical estimates can neither explain the experimentally observed energy gaps of etched nanoribbons of widths beyond 20 nm, which turn out to be larger than predicted, nor do they explain the large number of resonances found inside the gap [1,2,8]. This has led to the suggestion that localized states (and interactions effects) due to edge roughness, bond contractions at the edges [20] and disorder may dominate the transport gap. Several mechanisms have been proposed to describe the observed gap, including re-normalized lateral confinement [2], quasi-1D Anderson localization [21], percolation models [22] and many-body effects (incl. quantum dots) [19], where substantial edge disorder is required. Recently, it has been shown that also moderate amounts of edge roughness can substantially suppress the linear conductance near the charge neutrality point [23], giving rise to localized states relevant for both single particle and many-body descriptions.In this paper we show experimental evidence that the transport gap in an etched graphene nanoribbon (see schematic in Fig. 1a) is primarily formed by local resonances and quantum dots along the ribbon. We employ lateral graphene gates to show that size...

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