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We present a fast and stable numerical technique to obtain the self-energyterms of electrodes for first-principles electron-transport calculations.Although first-principles calculations based on the real-spacefinite-difference method are advantageous for execution on massively parallelcomputers, large-scale transport calculations are hampered by the computationalcost and numerical instability of the computation of the self-energy terms.Using the orthogonal complement vectors of the space spanned by the generalizedBloch waves that actually contribute to transport phenomena, the computationalaccuracy of transport properties is significantly improved with a moderatecomputational cost. To demonstrate the efficiency of the present technique, theelectron-transport properties of a Stone-Wales (SW) defect in graphene andsilicene are examined. The resonance scattering of the SW defect is observed inthe conductance spectrum of silicene since the $\sigma^\ast$ state of silicenelies near the Fermi energy. In addition, we found that one conduction channelis sensitive to a defect near the Fermi energy, while the other channel ishardly affected. This characteristic behavior of the conduction channels isinterpreted in terms of the bonding network between the bilattices of thehoneycomb structure in the formation of the SW defect. The present techniqueenables us to distinguish the different behaviors of the two conductionchannels in graphene and silicene owing to its excellent accuracy.

Real-space method for first-principles electron-transport calculations: self-energy terms of electrodes for large systems