Tight binding calculations of band structure and conductance in graphene nano ribbons. We suggest a general approach based on the nearest-neighbor tight-binding approxima-tion (TB) to investigate the band structure and conductance ofa quasi-one dimensional calculations carried out for Graphene nanoribbons. | Communications in Physics, Vol. 19, No. 1 (2009), pp. 1-8 TIGHT-BINDING CALCULATIONS OF BAND STRUCTURE AND CONDUCTANCE IN GRAPHENE NANO-RIBBONS HOANG MANH TIEN, NGUYEN HAI CHAU Institute of Physics, VAST PHAN THI KIM LOAN Physics Department, School of Education, Can Tho University Abstract. We suggest a general approach based on the nearest-neighbor tight-binding approximation (TB) to investigate the band structure and conductance of a quasi-one dimensional system. Numerical calculations carried out for Graphene nanoribbons (GNRs) with different widths and edge conditions (zigzag and armchair) reveal the well-known results that the electronic properties of GNRs depend strongly on the size and geometry of the sample. Although various carbon-based structures have been studied for decades, graphene was only isolated experimentally in 2004 [1,2]. Graphene, the only truly two-dimensional (2D) nano crystal, is made out of carbon atoms arranged on the honeycomb structure. Recently, graphene has attracted much attention, both experimental and theoretical due to its unique and unusual electronic properties. One of the most interesting features is that, low energy excitations are massless, chiral, Dirac fermions which mimic the relativistic particles [1,2], though its Fermi velocity is 300 times smaller than the speed of light c (vF ≈ 106 ms−1 ). In addition, the density of material electrons may be huge, ne ≈ 4 × 1015 cm−2 [3] that makes the graphene look the most promising for nanoelectronic devices in the future. The fact that distinguishes graphene from ordinary semi-conductantor and metallic systems, the Dirac fermions do not obey the conventional Schr¨ odinger equation. In 1984, ~ based on the k.~ p approximation, Vincenzo and Mele found that the low energy excitations obey the two-dimensional Dirac-like equation [5]. Solving this equation, one can find out the wave functions of fermions and other dynamic properties of infinite graphene sheets [1,2,4]. However, in .
