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Band gap engineering in graphene may open the routes towards transistordevices in which electric current can be switched off and on at will. One may,however, ask if a semiconducting band gap alone is sufficient to quench thecurrent in graphene. In this paper we demonstrate that despite a bulk band gapgraphene can still have metallic conductance along the sample edges (providedthat they are shorter than the localization length). We find this forsingle-layer graphene with a zigzag-type boundary which hosts gaplesspropagating edge states even in the presence of a bulk band gap. By generatinginter-valley scattering, sample disorder reduces the edge conductance. However,for weak scattering a metallic regime emerges with the diffusive conductance G= (e^2/h)(l_KK' / L) per spin, where l_KK' is the transport mean-free path dueto the inter-valley scattering and L >> l_KK' is the edge length. We also takeintra-valley scattering by smooth disorder (e.g. by remote ionized impuritiesin the substrate) into account. Albeit contributing to the elasticquasiparticle life-time, the intra-valley scattering has no effect on G.

Diffusion on edges of insulating graphene with intravalley and intervalley scattering