... gets2.1
We consider only the valence $ \pi $ and the conduction $ \pi ^*$ energy band of graphene and CNTs.

... energy2.2
Experimentally the value $ \vert t\vert=2.7~\mathrm{eV}$ has been reported [19].

... systems2.3
A mesoscopic system is a solid small enough in size, so that the interference of electron wave-functions can be observed. A typical size of a mesoscopic system is around $ 1-100~\mathrm{nm}$ which is larger than the microscopic size of around $ 1-10$ Å and smaller than the macroscopic size which is more than $ 1~\mu\mathrm{m}$ [60].

... CNTs2.4
The work function is defined as the sum of the CNT electron affinity and half of the band-gap in the bulk.

... shift2.5
Note that this is unique for the contact between a metal and a CNT. In a conventional, planar semiconductor device the position of the FERMI energy is pinned by metal-induced gap states [72].

... state3.1
Here the PAULI exclusion principle which leads to a nonlinear master equation is neglected

... commutationA.1
The commutation relation for Bosons is defined by $ [A,B]_{-}=[A,B]=AB-BA$.

... anti-commutationA.2
The anti-commutation relation for FERMIons is defined by $ [A,B]_{+}=\{A,B\}=AB+BA$.

... functionB.1
The step function is defined as $ \theta(t) \ = \ \left\{\begin{array}{ll} 1 & \mbox{$t>0$} \\
\frac{1}{2} & \mbox{$t = 0$} \\ 0 & \mbox{$t<0$}

... functionF.1
Screening is defined by the inverse dielectric function. An external potential induces a charge density in the system. This induced charge density gives rise to a change in the potential via the COULOMB interaction, which in turn yields an induced charge density and so forth. The result of this infinite series of charge redistribution process is the screening of the external potential.