 junction. ](xueFig0.eps){height="0.0in" width="0.0in"}  ![\[xueFig0\] Electrostatics of the Au-SWNT-Ti junction for SWNT channels of different lengths. (a) Upper figure shows transferred charge per atom as a function of position along the SWNT axis for SWNT channel lengths of $0.0, 0.0 00.0, 00.0$ and $00.0$ nm. Lower figure shows the magnified view of the transferred charge in the middle of the channel for the longest (00.0 nm) SWNT studied. (b) Upper figure shows the electrostatic potential change at the cylindrical surface of the 00 (0.0 nm) and 00- unitcell (00.0 nm) SWNTs studied. The dotted line denote the linear voltage ramp $V_{ext}$ (contact potential) due to the work function difference of gold and titanium. The dashed line show the charge-transfer induced electrostatic potential change $\delta V(\delta \rho)$. The solid line shows the net electrostatic potential change $V_{ext}+\delta V$. Lower figure shows the magnified view of the electrostatic potential change in the middle of the 00-unitcell SWNT junction. ](xueFig0-0.eps "fig:"){height="0.0in" width="0.0in"} ![\[xueFig0\] Electrostatics of the Au-SWNT-Ti junction for SWNT channels of different lengths. (a) Upper figure shows transferred charge per atom as a function of position along the SWNT axis for SWNT channel lengths of $0.0, 0.0 00.0, 00.0$ and $00.0$ nm. Lower figure shows the magnified view of the transferred charge in the middle of the channel for the longest (00.0 nm) SWNT studied. (b) Upper figure shows the electrostatic potential change at the cylindrical surface of the 00 (0.0 nm) and 00- unitcell (00.0 nm) SWNTs studied. The dotted line denote the linear voltage ramp $V_{ext}$ (contact potential) due to the work function difference of gold and titanium. The dashed line show the charge-transfer induced electrostatic potential change $\delta V(\delta \rho)$. The solid line shows the net electrostatic potential change $V_{ext}+\delta V$. Lower figure shows the magnified view of the electrostatic potential change in the middle of the 00-unitcell SWNT junction. ](xueFig0-0.eps "fig:"){height="0.0in" width="0.0in"}  ![\[xueFig0\] (Color online) Local density of states (LDOS) as a function of position along the SWNT axis for SWNT channel length of $00.0 nm$. We show the result when self-consistent SWNT screening of the build-in electric field is included in (a). For comparison we have also shown the result for non self-consistent calculation in (b). The plotted LDOS is obtained by summing over the $00$ atoms of each carbon ring of the $(00,0)$ SWNT. Note that each cut along the energy axis at a given axial position gives the LDOS of the corresponding carbon ring and each cut along the position axis at a given energy gives the corresponding band shift. ](xueFig0-0.eps "fig:"){height="0.0in" width="0.0in"} ![\[xueFig0\] (Color online) Local density of states (LDOS) as a function of position along the SWNT axis for SWNT channel length of $00.0 nm$. We show the result when self-consistent SWNT screening of the build-in electric field is included in (a). For comparison we have also shown the result for non self-consistent calculation in (b). The plotted LDOS is obtained by summing over the $00$ atoms of each carbon ring of the $(00,0)$ SWNT. Note that each cut along the energy axis at a given axial position gives the LDOS of the corresponding carbon ring and each cut along the position axis at a given energy gives the corresponding band shift. ](xueFig0-0.eps "fig:"){height="0.0in" width="0.0in"}  ![\[xueFig0\] 