OFFPRINT Spatial distribution of local currents of massless Dirac fermions in quantum transport through graphene nanoribbons

We employ the formalism of bond currents, expressed in terms of the nonequilibrium Green functions, to image the charge flow between two sites of the honeycomb lattice of graphene ribbons of few nanometers width. In sharp contrast to nonrelativistic electrons, current density profiles of quantum transport at energies close to the Dirac point in clean zigzag graphene nanoribbons (ZGNR) differs markedly from the profiles of charge density peaked at the edges due to zero-energy localized edge states. For transport through the lowest propagating mode induced by these edge states, edge vacancies do not affect current density peaked in the center of ZGNR. Furthermore, the long-range potential of a single impurity placed in the center of ZGNR acts to reduce local current around it while concurrently increasing the current density along the zigzag edge, so that ZGNR conductance remains perfect G= 2e/h. Copyright c © EPLA, 2007 Introduction. – The recent experimental discovery of a two-dimensional (2D) allotrope of carbon, termed graphene, has ushered unforeseen avenues to explore transport and interactions of low-dimensional electron system, build quantum-coherent carbon-based nanoelectronic devices, and probe high-energy physics of “charged neutrinos” in table-top experiments [1,2]. Graphene represents one-atom–thick layer of carbon atoms tightly packed into a honeycomb crystal lattice whose symmetries impose linear energy-momentum dispersion of the low-energy quasiparticles [3]. Moreover, in the continuum limit sublattice degree of freedom can be regarded as an internal “pseudospin” degree of freedom which connects electrons and holes through “pseudochirality” (projection of pseudospin on the direction of motion) of opposite sign. Thus, the effective mass equation for graphene turns into the Weyl equation for massless Dirac fermions (familiar from neutrino physics) [3]. Relativistic energy spectrum, pseudospin, and zero gap with linearly vanishing density of states in the bulk graphene, have been probed in transport experiments unveiling the “chiral” quantum Hall effect, “minimal conductivity” at the charge-neutrality (Dirac) point EF = 0, and weak-localization–type of quantum interference effects [1]. The intriguing concept of pseudochirality, whose conservation would be responsible for the suppression [3] of backscattering from smooth (on the scale of the lattice constant) disorder and Klein tunneling [2] through high and wide electrostatic potential barriers, has also led to a number of theoretical predictions [4] for esoteric micrometer-size graphene-based devices. On the other hand, recent experiments on graphene wires of nanoscale width have demonstrated the existence of a gap in their energy spectrum [5], which would allow graphene nanoribbons (GNR) to replace semiconductor single-wall carbon nanotubes while making possible easy integration into nanoelectronic circuits via standard lithography end etching techniques. Direct STM imaging of the states localized at the edges of realistic GNR [6], as well as possible pseudochirality non-conserving scattering off the GNR edges, requires to examine the effects of the edge-topology–dependent transverse subband structure [7,8], the structure of edge states, impurities, and potential barriers in tailoring quantum transport properties of GNR-based devices. The effects of zero-energy quantum states localized at the edges of ZGNR shown in fig. 1 (which originate from the gauge field generated by lattice deformation [9] and reflect the topological order in the bulk of bipartite honeycomb lattice [10]), as well as the energy gaps in armchair graphene nanoribbons (AGNR) controllable by their width, have been studied theoretically for more than a decade, both in equilibrium [11–13] and in conduction properties [7,8,14–18] of GNRs. However, very little is known about local features of charge transport through GNR. Moreover, the application of recently advanced